CivilFEM
is a program intended for solving practical engineering problems. Many
theoretical problems are not realistic in that the assumptions necessary to
obtain a closed-form analytical solution make the mathematical model depart
from a practical application problem.
Theoretical
solutions are generally based on a continuous or differential approach. In some
cases, an exact comparison with a finite-element solution would require an
infinite number of elements and/or an infinite number of iterations separated
by an infinitely small step size. Such a comparison is neither practical nor
desirable.
The
CivilFEM solutions in this manual are compared with solutions from textbooks or
technical publications. In some cases noted below, the target (theoretical) answers
reported in this manual may differ from those shown in the reference. Any
problems having significantly different recalculated values are noted as such.
Differences between CivilFEM results and target values are reported as ratios
except in cases where the target solution is zero or non-numerical in nature.
The
examples in this manual have been modeled to give reasonably accurate
comparisons ("engineering accuracy") with a low number of elements
and iterations. In some cases, even fewer elements and/or iterations will still
yield an acceptable engineering accuracy. There are also cases where larger
differences may exist with regard to references, for example when comparing
against experimental solutions. These differences have been examined and are considered
acceptable. A survey of the results comparisons in this manual shows an average
accuracy within 1-5% of the target solution.
Some
references have incorrect answers printed and some have incorrect equations.
Reference's answers presented without regard to sign are reported with the
appropriate sign. Theoretical derivations not having a specific numerical
example in the text are solved for a representative numerical example and both
the theoretical and CivilFEM results are given.
Considerable
time, effort and expense have gone into the development and documentation of
CivilFEM. The program has been thoroughly tested and used. In using the
program, however, the user accepts and understands that no warranty is
expressed or implied by the developers or the distributors on the accuracy or
the reliability of the program.
The
user must explicitly understand the assumptions of the program and must
independently verify the results.
Test
cases use the following format:
ˇ
A
description of the test case, including the dimensions, loading, material
properties, and other relevant data.
ˇ
Theoretical
reference(s).
ˇ
Figures
describing the problem.
ˇ
Analysis
assumptions, modeling notes, and comments.
ˇ
Target
results, CivilFEM results, and normalized ratio.
ˇ
Graphics
displays of the results (optional).
All
analysis test cases use the following code nomenclature:
VCF_A_B_CC_DD_EE_FF_GGG
|
APPLICATION
TYPE (A)
|
ID
|
|
STRUCTURAL
|
1
|
|
THERMAL
|
2
|
|
THERMAL-
STRUCTURAL(COUPLED)
|
3
|
|
SEEPAGE
|
4
|
|
ANALYSIS
TYPE (B)
|
ID
|
|
STATIC
|
0
|
|
MODAL
|
1
|
|
HARMONIC
|
2
|
|
TRANSIENT
|
3
|
|
BUCKLING
|
4
|
|
SPECTRAL
|
5
|
|
LINEAR/NONLINEAR
(CC)
|
ID
|
|
LINEAR
|
00
|
|
MATERIAL
NONLINEARITY
|
01
|
|
CONTACT
|
02
|
|
GEOMETRIC
NONLINEARITY
|
03
|
|
ACTIVATION/DEACTIVATION
|
04
|
|
MATERIAL
(EE)
|
ID
|
|
REINFORCED
CONCRETE
|
00
|
|
PRESTRESSED
CONCRETE
|
01
|
|
STRUCTURAL
STEEL
|
02
|
|
GEOTECHNICAL
|
03
|
|
GENERIC
|
04
|
|
ENTITIES
(DD)
|
ID
|
|
BEAM
|
00
|
|
TRUSS
|
01
|
|
SHELL
|
02
|
|
2D
SOLID
|
03
|
|
3D
SOLID
|
04
|
|
TEST
CASE NUMBER (GGG)
|
ID
|
|
ID
REFERENCE
|
From 1 to 999
|
All
code checking test cases use the following code nomenclature:
|
CODE (DD)
|
ID
|
|
EC3
|
00
|
|
LRFD
|
01
|
|
ASD
|
02
|
|
N690
|
03
|
|
IS800
|
04
|
|
BS5950
|
05
|
|
GB50017
|
06
|
|
IS800
|
07
|
|
AASHTO LRFD
|
08
|
|
ASME
|
09
|
|
CTE
|
10
|
|
EC2
|
50
|
|
ACI318
|
51
|
|
EHE
|
52
|
|
EHE
|
52
|
|
BS8110
|
54
|
|
GB50010
|
55
|
|
NBR6118
|
56
|
|
AASHTO HB
|
57
|
|
IS456
|
58
|
|
CΠ52-101
|
59
|
|
AS3600
|
60
|
|
ACI349
|
61
|
|
ACI359
|
62
|
|
ITER
|
63
|
|
ASD14
|
64
|
|
LRFD14
|
65
|
|
ACI318-14
|
66
|
|
ACI349-06
|
67
|
|
ACI349-13
|
68
|
|
AISC15
|
69
|
|
STRCODSP-C
|
70
|
|
STRCODSP-ST
|
71
|
CVCF_A_B_CC_DD_EEE
|
APPLICATION
TYPE (A)
|
ID
|
|
CHECK
|
1
|
|
DESIGN
|
2
|
|
SECTION
(B)
|
ID
|
|
LIBRARY
|
1
|
|
DIMENSIONS
|
2
|
|
PLATES
|
3
|
|
CAPTURE
|
4
|
|
GENERIC
|
5
|
|
SHELL
|
6
|
|
LOAD TYPE (CC)
|
ID
|
|
TENSION
|
00
|
|
COMPRESSION
|
01
|
|
BUCKLING
|
02
|
|
3D BENDING
|
03
|
|
2D BENDING
|
04
|
|
SHEAR
|
05
|
|
TORSION
|
06
|
|
SHEAR+TORSION
|
07
|
|
CEB
|
08
|
|
ORTHOGONAL DIRECTIONS
|
09
|
|
MOST UNFAVORABLE DIRECTION
|
10
|
|
WOOD-ARMER
|
11
|
|
IN PLANE SHEAR
|
12
|
|
BEAM CRACKING
|
13
|
|
SHELL CRACKING
|
14
|
|
BENDING+AXIAL BUCKLING
|
15
|
|
TEST
CASE NUMBER (EEE)
|
ID
|
|
ID
REFERENCE
|
From 1 to 999
|
CVCF_1_1_00_08_001
Description:
(TRACTIONS CHECKING ACCORDING
TO AASHTO LRFD 2012)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AASHTO LRFD 2012, bridges ,traction checking beams
|
|
File:
|
CVCF_1_1_00_08_001.xcf
|
Test Case CVCF_1_1_00_08_001
Checking a beam model submitted to
traction forces, according to AASHTO LRFD 2012.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Length: in
Time: s
Force: Kip
|
ASTM A36
Fy=36 Ksi
Fu=58 Ksi
E=29000 Ksi
G=11154 Ksi
|
d= 4 in
bf= 4 in
tw=tf=0.5 in
A= 3.75 in2
|
P=135 kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
CVCF_1_1_02_08_001
Description:
(COMPRESSION FLEXURAL BUCKLING
CHECKING ACCORDING TO AASHTO LRFD 2012)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AASHTO LRFD 2012, bridges , compression flexural buckling checking
|
|
File:
|
CVCF_1_1_02_08_001.xcf
|
Checking a beam model submitted to
buckling forces, according to AASHTO LRFD 2012.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Kip
|
A572 Gr50
Fy=50 Ksi
E=29000 Ksi
G=11154 Ksi
|
T. height
(d): 14.7 in
Height (h):
10 in
Width (bf):
14.7 in
Web
thickness (tw): 0.645 in
Flange
thickness (tf): 1.03 in
L= 21 in
K=2
A=38.8 in2
rmin=
3.76 in
|
P=500 kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
Flanges:
Web:
Without slender elementsŕQ=1
CVCF_1_1_03_08_001
Description:
(BENDGIN CHECKING ACCORDING TO
AASHTO LRFD 2012)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AASHTO LRFD 2012, bridges , bending checking
|
|
File:
|
CVCF_1_1_03_08_001.xcf
|
Checking a beam model submitted to
bending moments, according to AASHTO LRFD 2012.
|
Units
|
Material
|
Geometry
|
Section
properties
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Kip
|
A572 Gr50
E=29000 Ksi
G=11154 Ksi
|
T. height
(d): 9.73 in
Height (h):
7.5 in
Width (bf):
14.7 in
Web
thickness (tw): 0.29 in
Flange
thickness (tf): 0.435 in
L= 168 in
|
W 10x33
A= 9.71 in2
Wezz=35
in3
Weyy=9.2
in3
Wpz=38
in3
Wpy=14
in3
rs=1.94
in
rGS=2.2
in
j=0.583 in4
|
P=30 kips
My=144Kipˇin
Mz=1080 Kipˇin
|
Node O: u=v=w=0
θx=θy=θz=0
|
Flanges:
Web:
Local buckling resistance
Lateral torsional buckling resistance.
Y axis.
CVCF_1_1_05_08_001
Description:
(SHEAR CHECKING ACCORDING TO
AASHTO LRFD 2012)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AASHTO LRFD 2012, bridges , shear checking
|
|
File:
|
CVCF_1_1_05_08_001.xcf
|
Checking a beam model submitted to
shear forces, according to AASHTO LRFD 2012.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Kip
|
A572 Gr50
E=29000 Ksi
G=11154 Ksi
|
OD=5.563 in
Thickness
(t)= 0.258
L= 100 in
Ag= 4.3 in2
|
q= 1 Kip/in
|
Node 1: u=v=0
Node 2: v=0
|
Nominal shear resistance
CVCF_2_2_04_51_007
Description:
(BEAM REINFORCEMENT DESIGN
ACCORDING TO ACI 318)
|
Reference:
|
ACI Committee. (2005). Building code requirements for
structural concrete (ACI 318-05) and commentary (ACI 318R-05). American
Concrete Institute, example 7.4, pg. 7-33.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key
words:
|
Beam,
concrete T section, reinforcement steel, ACI 318, axial-bending design
beams, bending reinforcement
|
|
File:
|
CVCF_2_2_04_51_007.xcf
|
Design the necessary steel amount
according to ACI 318 for a reinforced concrete T-section beam shown. The beam
is braced against sidesway and has an unsupported height of 102 in. Use fc =
4000 psi and fy = 60000psi. Required load strengths: Mu=227 ft-kips.
|
Material
|
Geometry
|
Reinforcement
|
Loading
|
Boundary
Condition
|
|
fc = 4000
psi
fy = 60000psi
|
Height (h) =
21 in.
Web
thickness (tw)= 10 in.
Top flange
length (b) = 30 in.
Top flange
thickness (tf) = 2.5 in.
Mechanical
cover (mc) = 2 in.
|
Initial
longitudinal reinforcement = 1 in2.
|
Mu = 227
ft-kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
The unit system selected is Imperial system (inches). A
concrete T-Section beam with 10 elements is modeled.
;
CVCF_1_2_04_66_002
Description:
(BENDING CHECKING ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, ACI 318 2014, bending checking beams
|
|
File:
|
CVCF_1_2_04_66_002.xcf
|
Checking a beam model submitted to
bending solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Mp
|
fc = 4000
psi
fy = 60000psi
|
Height (h) =
21.56 in.
Width (b) =
30 in.
Flange
thickness (ft)= 2.5 in
Web
thickness (wt)= 30 in
λ= 0.8
|
Q= 250
ft-kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
Calculation
process has been carried out by means of sPColumn program. This one has been
useful so as to obtain the interaction concrete diagram, which will be plotted
ahead:
CVCF_1_2_04_66_006
Description:
(BENDING CHECKING ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, ACI 318 2014, bending checking beams
|
|
File:
|
CVCF_1_2_04_66_006.xcf
|
Checking a beam model submitted to
bending solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Mp
|
fc = 5000
psi
fy = 60000psi
|
Diameter
(OD): 20 in
Thickness
(t): 4 in
λ= 0.8
|
M= 276
ft-kips
F=214 kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
Calculation
process has been carried out by means of sPColumn program. This one has been
useful so as to obtain the interaction concrete diagram, which will be plotted
ahead:
CVCF_1_2_05_66_001
Description:
(SHEAR CHECKING ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, ACI 318 2014, shear checking beams,
|
|
File:
|
CVCF_1_2_05_66_001.xcf
|
Checking a beam model submitted to
shear solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
fc = 4500
psi
fy = 60000psi
|
Length (L) =
10 m.
Height (h) =
0.3 m.
Width (b) =
0.5 m.
Av/s=1.28ˇ10-3
m2/m
rc= 0.04 m
(reinforcement cover)
λ= 0.8
|
Q= 6.75 Mp/m
|
Node A: u=v=0
Node B: v=0
|
;
being 
CONDITION:
ŕ 
ŕ 
CVCF_1_2_06_66_001
Description:
(TORSION CHECKING ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, ACI 318 2014, torsion checking beams,
|
|
File:
|
CVCF_1_2_06_66_001.xcf
|
Checking a beam model submitted to
torsion solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
fc = 3500
psi
fy = 60000psi
|
Length (L) =
1 m.
Height (h) =
0.3 m.
Width (b) =
0.4 m.
|
Q= 7.52 Mp
T= 1.52 Mpˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
CONDITION: 
; being 
ˇ
ˇ
ˇ
ˇ
: shall not be taken less than 30 degrees
nor greater than 60 degrees.
CVCF_1_2_13_66_001
Description:
(CRACKING CHECKING ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, ACI 318 2014, cracking check in beams,
|
|
File:
|
CVCF_1_2_13_66_001.xcf
|
Checking a beam model submitted to
cracking effects, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: N
|
fc = 3500 psi
Ec=26.339ˇ109
Pa
fy = 70000psi
Es=2ˇ1011 Pa
|
Length (L) =
5 m.
Height (a) =
1 m.
Width (b) =
0.6 m.
d = 0.0525
m.
d´= a-d=
0.9478 m.
AST=0.003927
m2.
ASC=0 m2
|
Nx=750000 N
Mz=
Nxˇr=3/4ˇaˇNx= 562500Nˇm
|
Node O:
u=v=w=0
|
FORCES AND MOMENTS
Concrete
Steel
REPLACING IN (1)
AND (2):
RESULTS
CRITERION BY ACI 318 2014
CVCF_2_2_04_66_002
Description:
(BENDING DESIGN ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, ACI 318 2014, bending design beams
|
|
File:
|
CVCF_2_2_04_66_002.xcf
|
Designing a beam model submitted
to bending solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Mp
|
fc = 4000
psi
fy = 60000psi
|
Height (h) =
21.56 in.
Width (b) =
30 in.
Flange
thickness (ft)= 2.5 in
Web
thickness (wt)= 30 in
λ= 0.8
|
Q= 250
ft-kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
Calculation
process has been carried out by means of sPColumn program. This one has been
useful so as to obtain the interaction concrete diagram, which will be plotted
ahead:
CVCF_2_2_04_66_004
Description:
(BENDING DESIGNING ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, ACI 318 2014, bending designing beams
|
|
File:
|
CVCF_2_2_04_66_004.xcf
|
Designing a beam model submitted
to bending solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: in
Time: s
Force: Mp
|
fc = 4000
psi
fy = 60000psi
|
Height (h):
30 in
Width (b):
21.6
Thickness (t):
5 in
λ= 0.8
|
M= 250
ft-kips
|
Node O: u=v=w=0
θx=θy=θz=0
|
Calculation
process has been carried out by means of sPColumn program. This one has been
useful so as to obtain the interaction concrete diagram, which will be plotted
ahead:
CVCF_2_2_05_66_001
Description:
(SHEAR DESIGN ACCORDING TO ACI
318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, ACI 318 2014, shear design beams,
|
|
File:
|
CVCF_2_2_05_66_001.xcf
|
Design of a beam model submitted
to shear solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
fc = 4500
psi
fy = 60000psi
|
Length (L) =
10 m.
Height (h) =
0.3 m.
Width (b) =
0.5 m.
Av/s=1.28ˇ10-3
m2/m
rc= 0.04 m
(reinforcement cover)
λ= 0.8
|
Q= 6.75 Mp/m
|
Node A: u=v=0
Node B: v=0
|
;
being
CONDITION: 
ŕ 
ŕ
ŕ 
CVCF_2_2_06_66_001
Description:
(TORSION DESIGN ACCORDING TO
ACI 318 2014)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, ACI 318 2014, torsion design beams,
|
|
File:
|
CVCF_2_2_06_66_001.xcf
|
Designing a beam model submitted
to torsion solicitation, according to ACI 318 2014.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
fc = 3500
psi
fy = 60000psi
|
Length (L) =
1 m.
Height (h) =
0.3 m.
Width (b) =
0.4 m.
|
Q= 7.52 Mp
T= 1.52 Mpˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
TRANSVERSAL
REINFORCEMENT
CONDITION: 
;
being 
- : shall
not be taken less than 30 degrees nor greater than 60 degrees.
LONGITUDINAL
REINFORCEMENT
CVCF_1_1_04_02_001
Description:
(W-SHAPE FLEXURAL MEMBER DESIGN
IN STRONG-AXIS BENDING ACCORDING TO AISC ASD 13 th)
|
Reference:
|
CONSTRUCTION, S. (2005). DESIGN EXAMPLES Version 13.0,
example F.1-1b
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key
words:
|
Beam,
steel W section, AISC ASD 13th, check beams, bending
|
|
File:
|
CVCF_1_1_04_02_001.xcf
|
Check a W 18x50 beam with a simple
span of 35 feet. The nominal load is a uniform load of 1.2 kip/ft. Assume the
beam is continuously braced. Select an ASTM A529 grade 50 steel.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
fy = 50000psi
|
l = 35 ft.
Height = 18
in.
Width = 7.5
in.
Web
thickness =0.355 in.
Flange
thickness = 0.57 in.
|
q = 1.20
kip/ft
|
Node 1: u=v= 0
Node 2: v=0
|
The unit system selected is Imperial system (inches). A
steel W18x50 section beam with 20 elements is modeled.
The required flexural strength:
Since the beam is continuously braced and compact, only the
yielding limit state applies. From Manual, table 3-2:
CVCF_1_1_02_64_001 and CVCF_1_1_02_65_001
Description:
(COMPRESSION AND FLEX-BUCKLING
CHECKING ACCORDING TO AISC LRFD/ASD 14th)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AISC LRFD/ASD 14th, compression and flex-buckling checking beams
|
|
File:
|
CVCF_1_1_02_64_001 and CVCF_1_1_02_65_001.xcf
|
Test Case CVCF_1_1_02_64_001 and CVCF_1_1_02_65_001
Checking a beam model in relation
with the compression and the flex-buckling forces, according to AISC LRFD/ASD
14th.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Length: ft
Time: s
Force: Kp
|
ASTM A572 Gr50 Steel
E= 29000 Ksi
G= 11154 Ksi
Fy=50 Ksi
Fu= 65 Ksi
|
T. Height
(d): 14.66 in
Height (h):
20.75
Width (bf):
14.725 in
Web
thickness (tw): 0.645 in
Flange
thickness (tf): 1.03 in
Section: W14
x 132
Ag: 38.8 in2
rmin=
3.76 in
|
V= 500 Kp
|
Node 1: u=v=0
Node 2: v=0
|
Effective length
Classification
of elements which are submitted to a compression force.
Flanges:
Web:
Section E3, E4
Limit Stats ŕ FB, TB
FB: Flexural buckling
TB Torsional
and flexural torsional buckling
Torsional
unbraced length= lateral unbraced length
CVCF_1_1_03_64_001 and CVCF_1_1_03_65_001
Description:
(BENDING + AXIAL FORCE CHECKING
ACCORDING TO AISC LRFD/ASD 14th)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AISC LRFD/ASD 14th, bending + axial force checking beams
|
|
File:
|
CVCF_1_1_03_64_001 and
CVCF_1_1_03_65_001.xcf
|
Test Case CVCF_1_1_03_64_001 and CVCF_1_1_03_65_001
Checking a beam model in relation
with the bending moments and axial forces applied in this one, according to
AISC LRFD/ASD 14th.
|
Units
|
Material
|
Geometry
|
Section props
|
Loading
|
Boundary Condition
|
|
Length: in
Time: s
Force: Kip
|
ASTM A572 Gr50 Steel
E= 29000 Ksi
G= 11154 Ksi
Fy=50 Ksi
Fu= 65 Ksi
|
T. height
(d): 9.73 in
Height (h):
7.5 in
Width (bf):
7.96 in
Web
thickness (tw): 0.29 in
Flange
thickness (tf): 0.435 in
L=14 ft =
168 in
|
Section: W
10 x 33
Ag: 9.71 in2
Zz=38.8
in3
rmin=1.94
in
sz=35
in3
Zy=14
in3
Sy=9.2
in3
J= 0.583 in4
Cw=
791 in6
Iz=
171 in4
Iy=
36.6 in4
|
F= 20 Kip
Mz=720
Kipˇin
My=
96 Kipˇin
|
Node O: u=v=w=0
θx=θy=θz=0
|
FB: Flexural Buckling
![F_cr=[〖0.658〗^(F_y/F_e ) ]ˇF_y](index_archivos/image201.png)
TB: Torsional and Flexural- Torsional buckling
Moment in Z axis (Mcz).
Y: yielding
LTB: lateral-torsional buckling
Bending moment in Y axis (Mcy).
In relation with Y axis ŕLimit States: y, FLB
y: Yielding
FLB: compact flanges-Local buckling does
not apply.
Total criterion calculation
CVCF_1_1_04_64_001 and CVCF_1_1_04_65_001
Description:
(BENDING CHECKING ACCORDING TO
AISC LRFD/ASD 14th)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AISC LRFD/ASD 14th, bending checking
|
|
File:
|
CVCF_1_1_04_64_001 and
CVCF_1_1_04_65_001.xcf
|
Test Case CVCF_1_1_04_64_001 and CVCF_1_1_04_65_001
Checking a beam model in relation
with the bending moments, according to AISC LRFD/ASD 14th.
|
Units
|
Material
|
Geometry
|
Section
props
|
Loading
|
Boundary
Condition
|
|
Length: ft
Time: s
Force: Kip
|
ASTM A529 Gr50 Steel
E= 29000 Ksi
G= 11154 Ksi
Fy=50 Ksi
Fu= 70 Ksi
Cb= 1
|
T. height
(d): 17.99 in
Height (T):
15.5 in
Width (bf):
7.495 in
Web
thickness (tw): 0.355 in
Flange
thickness (tf): 0.57 in
L= 35 ft
|
Section: W18
x 50
Ag: 14.7 in2
Zz=101
in3
ry=1.65
in
sz=88.9
in3
ho=17.4
in
Jc=1.24
in4
Cw=3040
in6
|
q= 12 Kip/ft
|
Node 1: u=v=0
Node 2: v=0
|
First step:
Ratios calculation.
Flanges:
Web:
F2:
LIMIT STATESŕ y, LTB.
Y: Yielding; 
LBT: habitual
torsional buckling.
CVCF_1_1_02_64_001 and CVCF_1_1_02_65_001
Description:
(SHEAR CHECKING ACCORDING TO
AISC LRFD/ASD 14th)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, AISC LRFD/ASD 14th, shear checking beams,
|
|
File:
|
CVCF_1_1_05_64_001 and
CVCF_1_1_05_65_001.xcf
|
Test Case CVCF_1_1_02_64_001 and CVCF_1_1_02_65_001
Checking a beam model in relation
with the shear forces, according to AISC LRFD/ASD 14th.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: ft
Time: s
Force: Kip
|
ASTM A572 Gr50 Steel
E= 29000 Ksi
G= 11154 Ksi
Fy=50 Ksi
Fu= 65 Ksi
|
T. height
(d): 23.74 in
Height (h):
20.75 in
Width (bf):
7.04 in
Web
thickness (tw): 0.43 in
Flange
thickness (tf): 0.59 in
Section: W24
x 62
Ag: 18.2 in2
L=100 ft
|
F= 193 Kip
|
Node O: u=v=w=0
θx=θy=θz=0
|
CVCF_1_2_06_50_001
Description:
(TORSION CHECK ACCORDING TO
EUROCODE 2)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EC 02 (2008), Torsion check beams
|
|
File:
|
CVCF_1_2_06_50_001.xcf
|
Checking a beam model submitted to
torsion solicitation, according to EC2.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
C25/30
Reinforcement
steel:S400
|
Height (h) =
0.3 m.
Width (b) =
0.4 m.
|
Ted
= 1.52 Mp m= 14911.2 Nˇm
|
Node 0: u=v=w=0
θx=θy=θz=0
|
Needed ASL:
CVCF_1_2_07_50_001
Description:
(SHEAR CHECK ACCORDING TO
EUROCODE 2)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EC 02 (2008), Shear check beams
|
|
File:
|
CVCF_1_2_07_50_001.xcf
|
Checking a beam model submitted to
shear solicitation, according to EC2. Based on 1244 example.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete: C25/30
Reinforcement
steel:S400
|
Height (h) =
0.3 m.
Width (b) =
0.4 m.
rc= 0.04 m
|
Ted
= 1.52 Mp m= 14911.2 Nˇm
|
Node 0: u=v=w=0
θx=θy=θz=0
|
N=0 ŕ 
From
1244 (torsion checking):
;
; 
;
CVCF_2_2_06_50_001
Description:
(TORSION CHECK ACCORDING TO
EUROCODE 2)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EC 02 (2008), Torsion check beams
|
|
File:
|
CVCF_2_2_06_50_001.xcf
|
Checking a beam model submitted to
torsion solicitation, according to EC2. Based on CFVR 1244
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
C25/30
Reinforcement
steel:S400
|
Height (h) =
0.3 m.
Width (b) =
0.4 m.
|
Ted
= 1.52 Mp m= 14911.2 Nˇm
|
Node 0: u=v=w=0
θx=θy=θz=0
|
CVCF_2_2_07_50_001
Description:
(SHEAR AND TORSION DESIGN
ACCORDING TO EUROCODE 2)
|
Reference:
|
Ingeciber, S.A.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key
words:
|
Beam,
concrete rectangular section, reinforcement steel, EC 02 (2008), Shear and
Torsion design beams, shear reinforcement, torsion reinforcement
|
|
File:
|
CVCF_2_2_07_50_001.xcf
|
A fixed beam with a rectangular
reinforced concrete section subjected to a uniform distributed load of 7.52 Mp.
and a torsional moment of 1.52 Mpm. Obtain the reinforcement according to
Eurocode 2 (2008).
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Concrete:
C25/30
Reinforcement
steel:S400
|
Height (h) =
0.3 m.
Width (b)=
0.4 m.
Mechanical
Cover (mc) = 0.04 m
|
V = 7.52 Mp
Mt = 1.52
Mp m
|
Node 1: u=v=w=0
θx=θy=θz=0
|
The force unit selected is Mp. A concrete beam with 10
elements is modeled.
2; 
CVCF_2_6_09_50_002
Description:
(SHELL REINFORCEMENT DESIGN
ACCORDING TO EUROCODE 2)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key
words:
|
Shell,
concrete, Eurocode 2, design, bending reinforcement, orthogonal directions
|
|
File:
|
CVCF_2_6_09_50_002.xcf
|
A rectangular reinforced concrete
slab (C35/45, S500) has a length of 12.0m and a width of 7.0m and is subjected
to a vertical pressure, a vertical acceleration and horizontal pressures
(compression). The edges of the plate are fixed except in the x displacement
direction. Calculate the maximum top and bottom reinforcement in the x
direction.
|
Material
|
Geometry
|
Reinforcement
|
Loading
|
Boundary
Condition
|
|
C35/45
S500
ρc =2,5t/m3
|
b=7 m
a=12 m
t=0.30 m
mc
(mechanical cover) = 0.07m
|
Area per
unit length at the top X face=0.0001m2/m
Area per
unit length at the top Y face=0.0001m2/m
Area per
unit length at the bot.X face=0.0001m2/m
Area per
unit length at the bot.X face=0.0001m2/m
|
Vertical
press. P=20kPa
Horizontal
press. F=150kN/m
Vertical
Accel. a=10m/s2
|
Perimeter: uy=uz=0
θx=θy=θz=0
|
A shell element is modeled with a quadrangle mesh type with
elements of size 0.5m. A surface load normal to the surface and a linear
load in the longer edges can be selected. Gravity must be added to the load
case by changing the acceleration in the Z axis at 10 m/s2. You have
to select the Unfavorable Direction design method of shells taking into
account Torsional moments and membrane shear force (compression).
Forces and moments at the center of the plate: NRd = 150kN;
Mb=51.1kNm/m
Forces and moments at the extreme of the plate: NRd =
150kN; Mb=-81.2kNm/m
At the centre of the plate: x=17.64 ŽAs=307mm2/m=0.307e-3m2/m
At the extreme of the plate: x=27.39 ŽAs=667mm2/m=0.667e-3m2/m
CVCF_1_1_01_00_001
Description:
(COMPRESSION AND TRACTION
CHECKING ACCORDING TO EC3-05)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, EC3-05, compression and traction checking
|
|
File:
|
CVCF_1_1_01_00_001.xcf
|
Checking a beam model submitted to
compression and traction forces, according to EC3-05.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: KN
|
Fe-430
fy= 275 E06 Pa
fu=430 E06
|
d= 0.12 m
bf= 0.12 m
tw=tf=1.2E-02
|
F=300 KN
|
Node 1: u=v=w=0
θx=θy=θz=0
Node 2: u=v=w=0
θx=θy=θz=0
|
Traction
checking
Compression
checking
a) Class
b) Design solicitation
c) Section
Class 3
CVCF_1_1_02_00_001
Description:
(BENDING BUCKLING CHECKING
ACCORDING TO EC3-05)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, EC3-05, bending and buckling checking beams
|
|
File:
|
CVCF_1_1_02_00_001.xcf
|
Checking a beam model submitted to
bending and buckling moments, according to EC3-05.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: KN
|
Fe-360
Fy=235E06
|
T. height
(d): 0.45 m
Width (bf):
0.19 m
Web
thickness (tw): 9.4E-03 m
Flange
thickness (tf): 1.46E-02 m
L= 6 m
|
q=120 KN/m
|
Node 1: u=v=0
Node 2: v=0
|
a)
Type
Flange
Web:
b) Lateral buckling
CVCF_1_1_03_00_001
Description:
(BENDING+BIAXIAL CHECKING
ACCORDING TO EC3-05)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, EC3-05, bending + axial bending checking
|
|
File:
|
CVCF_1_1_03_00_001.xcf
|
Checking a beam model submitted to
bending + axial solicitations, according to EC3-05.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Length: m
Time: s
Force: KN
|
Fe-430
|
T. height
(d): 0.2 m
Width (bf):
0.2 m
Web
thickness (tw): 9E-03 m
Flange
thickness (tf): 1.5E-02 m
L= 1 m
|
N= 500 KN
My=30 KNˇm
Mz=80 KNˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
a) Class
Flange:
Web:
b) 
CVCF_1_1_04_00_001
Description:
(BENDING CHECKING ACCORDING TO
EC3-05)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, EC3-05, bending checking beams
|
|
File:
|
CVCF_1_1_04_00_001.xcf
|
Test Case CVCF_1_1_04_00_001
Checking a beam model submitted to
bending moments, according to EC3-05.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: KN
|
Fe-430
|
T. height
(d): 0.2 m
Width (bf):
0.1 m
Web
thickness (tw): 5.6e-03 m
Flange
thickness (tf): 8.5e-03 m
L= 12 m
|
q= 2.75 KN/m
|
Node 1: u=v=0
Node 2: v=0
|
a)
Type
Flange
ŕ Type 1
Web:
b)
Proving if a
bending resistance decreasing happens in relation with the shear forces.
Besides, proving
if dent is able to be developed in the web, is necessary.
Dent in web
will not be carried out.
CVCF_1_1_04_00_003
Description:
(BENDING AND SHEAR CHECKING
ACCORDING TO EC3-05)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, EC3-05, bending and shear checking beams
|
|
File:
|
CVCF_1_1_04_00_003.xcf
|
Checking a beam model submitted to
bending moments and shear forces, according to EC3-05.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: KN
|
Fe-430
Fy=275E06
Fu=30E06
|
T. height
(d): 0.4 m
Width (bf):
0.18 m
Web
thickness (tw): 8.6e-03 m
Flange
thickness (tf): 1.35E-02 m
L= 12 m
|
P=1000 KN/m
|
Node 1: u=v=0
Node 2: v=0
|
a) Type
Flange:
Web:
b) One of the most important steps is proving if
dent is coming about as a result of the shear forces.
Shear
resistance checking is specified ahead:
c) Bending resistance
ŕ A
reduction will be needed. Resistance to bending moments (6.2.8)
IPE 400 (6.3):
CVCF_1_1_05_00_001
Description:
(SHEAR CHECKING ACCORDING TO
EC3-05)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, EC3-05, shear checking beams
|
|
File:
|
CVCF_1_1_05_00_001.xcf
|
Checking a beam model submitted to
shear forces, according to EC3-05.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: KN
|
Fe-430
|
T. height
(d): 0.2 m
Width (bf):
0.1 m
Web
thickness (tw): 5.6e-03 m
Flange
thickness (tf): 8.5E-03 m
L= 12 m
|
P=2.75 KN/m
|
Node 1: u=v=0
Node 2: v=0
|
a)
Type
Flange
Web:
b)
It will be
necessary to check if a decreasing of bending resistance is coming about as a
result of the shear forces:
CVCF_1_2_05_52_001
Description:
(SHEAR CHECK ACCORDING TO
EHE08)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EHE08, shear check beams
|
|
File:
|
CVCF_1_2_05_52_001.xcf
|
Checking a beam model submitted to
shear solicitation, according to EHE08.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
HA-35
Reinforcement
steel:B400S
|
Length (L) =
10 m
Height (h) =
0.5 m.
Width (b) =
0.3 m.
|
Q=4.5ˇ1.5
Mp/m (distributed load)
|
Node 1: u=v=0
Node 2: u=0
|
Material properties:
ŕ 
Section properties:
Obtain 
(44.2.3.1):
(Neither
prestressed elements nor compression axil)
Obtain 
and 
(There aren´t neither axil loads nor compressed reinforcement)
Total
criterion.
CVCF_1_2_06_52_001
Description:
(TORSION CHECK ACCORDING TO
EHE08)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EHE08,torsion check beams
|
|
File:
|
CVCF_1_2_06_52_001.xcf
|
Checking a beam model submitted to
torsion solicitation, according to EHE08.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
HA-25
Reinforcement
steel:B400S
|
Length (L) =
1 m
Height (h) =
0.4 m.
Width (b) =
0.3 m.
|
Q=4.7ˇ1.6 Mp
T=0.95ˇ1.6
Mpˇm
|
Node 0: u=v=w=0
θx=θy=θz=0
|
Material properties:
ŕ
Section properties:
Obtain 
(45.2.2.1.):
Obtain 
(45.2.2.2.)
Obtain 
(45.2.2.3.)
Total criterion
CVCF_1_2_07_52_001
Description:
(SHEAR AND TORSION CHECK
ACCORDING TO EHE08)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EHE08,torsion check beams, shear check beam
|
|
File:
|
CVCF_1_2_07_52_001.xcf
|
Checking a beam model submitted to
torsion solicitation, according to EHE08.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
HA-25
Reinforcement
steel:B400S
|
Length (L) =
1 m
Height (h) =
0.4 m.
Width (b) =
0.3 m.
|
Q=4.7ˇ1.6 Mp
T=0.95ˇ1.6
Mpˇm
|
Node 0: u=v=w=0
θx=θy=θz=0
|
Material properties:
ŕ
Section properties:
Obtain (44.2.3.1):
(Neither prestressed elements nor
compression axil)
Obtain and
(There aren´t neither axil loads nor
compressed reinforcement)
Obtain (45.2.2.1.):
Obtain (45.2.2.2.)
Obtain (45.2.2.3.)
Shear total criterion.
Torsion total criterion
Total criterion
CVCF_2_2_05_52_001
Description:
(SHEAR DESIGN ACCORDING TO
EHE08)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EHE08, shear design beams
|
|
File:
|
CVCF_2_2_05_52_001.xcf
|
Designing a beam model submitted
to shear solicitation, according to EHE08.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
HA-35
Reinforcement
steel:B400S
|
Length (L) =
10 m
Height (h) =
0.5 m.
Width (b) =
0.3 m.
|
Q=4.5ˇ1.5
Mp/m (distributed load)
|
Node 1: u=v=0
Node 2: u=0
|
Material properties:
ŕ
Section properties:
Obtain (44.2.3.1):
(Neither prestressed elements nor
compression axil)
Due to 
, sizing is possible to be carried out.
It is necessary to be proved if a shear
reinforcement will be needed (44.2.3.2.1.2).
(There aren´t neither axil loads nor
compressed reinforcement)
ŕ 
As a result of 
, 
.
Obtain the shear reinforcement per unit length
(44.2.3.2.2).
; 
= 25.47 Mp
CVCF_2_2_06_52_001
Description:
(TORSION DESIGN ACCORDING TO
EHE08)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, EHE08,torsion check beams
|
|
File:
|
CVCF_2_2_06_52_001.xcf
|
Designing a beam model submitted
to torsion solicitation, according to EHE08.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: m
Time: s
Force: Mp
|
Concrete:
HA-25
Reinforcement
steel:B400S
|
Length (L) =
1 m
Height (h) =
0.4 m.
Width (b) =
0.3 m.
|
Q=4.7ˇ1.6 Mp
T=0.95ˇ1.6
Mpˇm
|
Node 0: u=v=w=0
θx=θy=θz=0
|
Material properties:
ŕ
Section properties:
Obtain (45.2.2.1.):
Calculation torsional moment
Sizing is available to be done due to 
.
Proving if a transversal torsion reinforcement is
required.
.
Proving if a longitudinal´s torsion reinforcement
is required.
CVCF_1_2_04_55_001
Description:
(BENDING CHECKING ACCORDING TO
GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, GB50010N, bending checking, Chinese code
|
|
File:
|
CVCF_1_2_04_55_001.xcf
|
Checking a beam model submitted to
a bending solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C20
Reinforcement
steel: HPB300
|
Height (h):
0.85
Width (b):
1.2
Flange
thickness (ft): 0.2
Web
thickness (wt): 0.3
|
M= 1400 KNˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
According to the Chinese
code formulation, in relation with bending moment, the obtained interaction
diagram is showed ahead:
CVCF_1_2_04_55_006
Description:
(BENDING CHECKING ACCORDING TO GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, GB50010N, bending checking, Chinese code
|
|
File:
|
CVCF_1_2_04_55_006.xcf
|
Checking a beam model submitted to
a bending solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel: HPB300
|
Height (h):
0.5
Width (b):
0.3
|
V=800 KN
M= 250 KNˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
According to the
Chinese code formulation, in relation with bending moment, the obtained
interaction diagram is showed ahead:
CVCF_1_2_05_55_001
Description:
(SHEAR CHECK ACCORDING TO
GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, GB50010N, shear chec, Chinese code
|
|
File:
|
CVCF_1_2_05_55_001.xcf
|
Checking a beam model submitted to
shear solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel:HPB300
|
L1=1500
L2=L1+1000
L3=L2+L1
Height (h) =
600 mm
Width (b) =
250 mm
Thickness
(t)= 40 mm
|
qL=10
Fp=120
|
Node 1: u=v=0
Node 2: u=0
|
Section reinforcement: Shear
reinforcement= 
@341
Section requirements.
Maximum shear force
resisted without shear reinforcement
Maximum load resisted by the
reinforcement
CVCF_1_2_05_55_002
Description:
(SHEAR CHECK ACCORDING TO
GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, GB50010N, shear check, seismic action, Chinese code
|
|
File:
|
CVCF_1_2_05_55_002.xcf
|
Test Case CVCF_1_2_05_55_002
Checking a beam
model submitted to shear solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: N
|
Concrete:
C30
Reinforcement
steel:HPB300
|
Height (h) =
500 mm
Width (b) =
500 mm
Total height
(Hn)=4.4 m
|
V=380 KN
N=1300 KN
|
Node O: u=v=w=0
θx=θy=θz=0
|
CVCF_2_2_04_55_002
Description:
(BENDING REINFORCEMENT DESIGN
ACCORDING TO GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
circular section, GB50010N, bending design, Chinese code
|
|
File:
|
CVCF_2_2_04_55_002.xcf
|
Test Case CVCF_2_2_04_55_002
Checking a beam model submitted to
a bending solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel: HPB300
|
Φ=0.6 m
|
V=1030.3 Mp
M= 91 Mpˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
According to the
Chinese code formulation, in relation with bending moment, the obtained
interaction diagram is showed ahead:
Firstly, the diagram
has been designed in an initial reinforcement quantity condition, obtaining the
scaled reinforcement factor.
- Reinforcement
quantity: 0.000994 m2. Divided into 19 heights.
Once the scaled
reinforcement factor has been obtained, this one is necessary to be applied
over the total reinforcement quantity so as to fix the section´s conditions.
- Scaled
reinforcement factor= 5.2. Thus, the new reinforcement quantity is
5.19688E-03 m2.
CVCF_2_2_04_55_003
Description:
(BENDING REINFORCEMENT DESIGN
ACCORDING TO GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
circular section, GB50010N, bending design, Chinese code
|
|
File:
|
CVCF_2_2_04_55_003.xcf
|
Checking a beam model submitted to
a bending solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel: HPB300
|
Tky=0.85
Tkz=1.2
Twy=0.2
Twz=0.15
|
V=-100 Mp
M= 1490 Mpˇm
|
Node O: u=v=w=0
θx=θy=θz=0
|
According to the Chinese code formulation, in relation with bending
moment, the obtained interaction diagram is showed ahead:
Firstly, the diagram
has been designed in an initial reinforcement quantity condition, obtaining the
scaled reinforcement factor.
- Reinforcement
quantity: 0.001 m2.
Once the scaled
reinforcement factor has been obtained, this one is necessary to be applied
over the total reinforcement quantity so as to fix the section´s conditions.
- Scaled
reinforcement factor= 7.4. Thus, the new reinforcement quantity is 7.4E-03
m2.
CVCF_2_2_05_55_001
Description:
(SHEAR REINFORCEMENT DESIGN
ACCORDING TO GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete rectangular
section, GB50010N, shear design, Chinese code
|
|
File:
|
CVCF_2_2_05_55_001.xcf
|
Designing a beam model submitted
to shear solicitation, according to GB50010N (Chinese code). Based on 4051.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel:HPB300
|
L1=1500
L2=L1+1000
L3=L2+L1
Height (h) =
600 mm
Width (b) =
250 mm
Thickness
(t)= 40 mm
|
qL=10
Fp=140
|
Node 1: u=v=0
Node 2: u=0
|
Section
requirements.
Maximum shear
force resisted without shear reinforcement
Requirement
transverse reinforcement ratio
According to GB50010N-2010: 
CVCF_2_2_05_55_002
Description:
(SHEAR REINFORCEMENT DESIGN ACCORDING
TO GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
rectangular section, GB50010N, shear design, seismic action, Chinese code
|
|
File:
|
CVCF_2_2_05_55_002.xcf
|
Designing a beam model submitted
to shear solicitation, according to GB50010N (Chinese code). Based on 4051.
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel:HPB335
|
L1=1950 mm
L2=2400 mm
Height (h) =
900 mm
Width (b) =
400 mm
Thickness
(t)= 80 mm
|
q= 163.17
Fp=325.164
|
Node 1: u=v=0
Node 2: u=0
|
Section
requirements.
Maximum shear force resisted without shear
reinforcement
Requirement
transverse reinforcement ratio
According to GB50010N-2010:
CVCF_2_2_07_55_001
Description:
(SHEAR AND TORSION DESIGN
ACCORDING TO GB50010N)
|
Reference:
|
Ingeciber,
S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
Key words:
|
Beam, concrete
section, GB50010N, shear and torsion design, Chinese code
|
|
File:
|
CVCF_2_2_07_55_001.xcf
|
Checking a beam model submitted to
shear and torsion solicitation, according to GB50010N (Chinese code).
|
Units
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Length: mm
Time: s
Force: KN
|
Concrete:
C30
Reinforcement
steel (Shear):HPB300
Reinforcement
steel (Torsion):HPB335
|
L=2000
Section dimensions:
in picture
|
F= 100
Mt=
24000
|
Node O: u=v=w=0
θx=θy=θz=0
|
Section reinforcement: Shear reinforcement= 
@341
Section
requirements.
Torsion design
According to GB50010-2010:
Input data
Longitudinal
torsion reinforcement (WEB):
Shear design
According to GB50010-2010:
VCF_1_0_00_00_00_01_001
Description: (2D
Concrete beam on elastic foundation)
|
Reference:
|
S. Parvanova, University of Civil
Engineering, Geodesy and Architecture- Sofia. 2011.
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_00_00_01_001.xcf
|
Consider a beam on elastic foundation with free ends.
The geometrical dimensions, mechanical properties and loadings are shown in
table and Fig. 1.
The Winklers constant or constant of the foundation
is:
k= k0ˇb=50000x1.1=55000.
Calculate maximum vertical deflection, maximum
rotation in z axis, maximum bending and shear in top and bottom of the
foundation beam.
|
Material
|
Geometry
|
Loading
|
Boundary Conditions
|
|
E1
= 3*107 kN/m2
k0=50000
kN/m2/m.
|
h
(height) = 0.50 m
b
(width) = 1.10 m.
Beam
total length = 10 m
|
F
= 250 kN.
M
= 100 kNm.
q
= 200 kN/m.
|
Free in
horizontal direction
|
F
M
q
0.50
m
k
1,1 m
1m 3m 1
m 5 m
10 m
Analysis Assumption and Modeling Notes
The
beam length is considered as medium according to its stiffness L⋅α, so the method of initial conditions is applicable. Beams of medium
length: 0.5 ≥ αˇL ≤ 5. For these beams
the method of initial conditions is very suitable and the obtained results are
accurate.
100
elements are used to model beam and to ground as spring type.
; 
; 
; 
;
; 
VCF_1_0_00_00_00_01_002
Description:
(Timoshenko Beam on an Elastic
Foundation)
|
Reference:
|
S.
Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd Edition,
McGraw-Hill Book Co. Inc., New York, NY, 1970
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_00_01_002.xcf
|
Elastic analysis of a rectangular
section beam subjected to a concentrated load at the center of the beam.
The beam rests on an elastic
foundation.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2 x 105 psi
υ = 0.3
k = 10 lb/in
|
L= 200 in
H = 5.885 in
W = 1 in
|
P/2= 1000 lbf
|
x = y =0; u = θ= 0
|
Only half of the beam is modeled
due to symmetry. The beam is divided into 110 elements.
For structural element properties, Shear
effects option is selected to apply analysis on Timoshenko curved beam.
The results are taken at the point of loading.
VCF_1_0_00_00_00_01_005
Description:
(BEAM TORSION TWIST ROTATION
STRESSES)
|
Reference:
|
Ingeciber, S.A.
|
|
Analysis Type(s):
|
Static Linear
Analysis
|
|
File:
|
VCF_1_0_00_00_00_01_005.xcf
|
The cantilever quadrangle section
beam is subjected to a load of 100 KN at its end, besides an imposed
displacement of 1 cm in beam´s axis. Calculate the displacements in the A end.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
C25/30
E28=30471.6
MPa
|
L=10m.
Width (b) =
0.6 m.
Height (H) =
0.4 m.
A= 0.24 m2
I=0.0032 m4
|
P=100 KN
|
Node 1: u=v=w=0
θx=θy=θz=0
|
One beam is modeled with 20 elements. It can be recalled
that the torsion area corresponds to the midsection (At).
Displacements in the A end
Z axis, which correspond to the beam axis, is shaped by the
vector (1, 1, 1), taken as reference the Global Cartesian system.
Vector decomposition:
Displacements in the new coordinate system of the beam.
Converting these displacements into Global Cartesian
system:
VCF_1_0_00_00_02_00_001
Description:
(Portal Frame Subjected to
Symmetric Loading)
|
Reference:
|
N.
J. Hoff, The Analysis of Structures, John Wiley and Sons, Inc., New
York, NY, 1956, pp. 115-119.
|
|
Analysis
Type(s):
|
Static
Linear Structural
|
|
File:
|
VCF_1_0_00_00_02_00_001.xcf
|
A rigid rectangular frame is subjected to uniformly
distributed load ω across the
span. Determine the maximum rotation, and maximum bending moment. The moment of
inertia for the span, Ispan is five times the moment of inertia fort
the columns, is Icol.
|
Material
|
Geometry
|
Beam Section Data
|
Loading
|
Boundary Condition
|
|
E = 30 x 106
psi
υ = 0.0
|
a = 400 in
L = 800 in
Ispan =5
Icol
Ďcol
=20300 in4
|
W1 = W2 = 16.655 in
W3 = 36.74 in
t1 = t2 = 1.68 in
t3 =0.945 in
|
ω = 500
lb/in
|
Node A: u=v=w=0
Node D: u =v=w=0
|
All the members of the frame are modeled using an I-beam
cross section. The cross section for the columns is chosen to be a W36 x 300.
The dimensions used in the horizontal span are scaled by a factor of 1.49535 to
produce a moment of inertia that is five times the moment of inertia in the
columns. The theoretical maximum rotation is 
and
the theoretical maximum bend moment is 
.
VCF_1_0_00_00_02_01_001
Description:
(Beam maximum bending stress
and deflection)
|
Reference:
|
S.
Timoshenko, Strength of Material, Part I, Elementary Theory and Problems,
3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 98, problem
4.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_02_01_001.xcf
|
An I-section beam, with dimension
and geometric properties as shown below, subjected to uniformly distributed
load q on the overhangs. Determine the maximum bending stress and the
deflection at the middle of the beam.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 30x106
psi
|
Height (H) = 30 in
Width (W) = 15 in
Web
thickness (Wt) = 0.6 in
Flange
thickness (Ft) = 1 in
a= 120in
b= 240in
|
q = 10000
lb/ft
|
Node 2: u=v=w=0
Node 4: v=w=0
|
The unit system selected is Imperial system (inches).
I-section steel beam is modeled. Due to its symmetrical cross section, the
model can be solved using half beam.
VCF_1_0_00_00_02_01_002
Description:
(T shape Beam maximum bending
stress)
|
Reference:
|
S.
H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids,
McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 294, ex. 7.2.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_02_01_002.xcf
|
A T-section beam, with dimension
and geometric properties as shown below, is subjected to a uniform bending.
Determine the maximum tensile and compressive bending stresses.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 30x106
psi
|
Height: 20 in
Width: 9 in
Web
thickness: 1.5 in
Flange
thickness: 4 in
yG
= 14in
L=100 in
|
Mz = 100000
lbf žin
|
Node 1: u=v=w=θ0
Node 4:
v=w=0
|
The unit system selected is Imperial system (inches). A
steel cantilever T section beam is modeled.
; 
VCF_1_0_00_00_02_01_003
Description: (BEAM
TORSION TWIST ROTATION STRESSES)
|
Reference:
|
Ingeciber, S.A. Adaptation of Problem
9.15 from the book "Resistencia de Materiales". Second
Edition, 1991. Author: Mr. Manuel Vázquez.
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_00_02_01_003.xcf
|
The cantilever steel box section beam is subjected to a torsional
moment of 4 tnf∙m at its end. Calculate the maximum torsional stress and
angle of rotation of the twisted beam.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
G = 0,8236x106 Kg/cm2.
|
l =3,0 m.
Width (W) = 10 cm.
Height (H) = 20 cm.
t flanges (tf) =1 cm.
t web (tw)= 1 cm.
|
Mt = 4,0 tn fxm.
|
Node 1: u=v=w=0
θx=θy=θz=0
|
Analysis Assumption and Modeling Notes
One beam is
modeled with 20 elements. It can be recalled that the torsion area corresponds
to the midsection (At).
; 
; 
; 
; 
VCF_1_0_00_00_02_01_004
Description: (Thin-walled
Beam on an Elastic Foundation)
|
Reference:
|
S. Timoshenko, J. N. Goodier, Theory
of Elasticity, 3rd Edition, McGraw-Hill
Book Co. Inc., New York, NY, 1970
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_00_02_01_004.xcf
|
Elastic analysis of a pipe section beam subjected to a concentrated
load at the center of the beam.
The beam rests on an elastic foundation.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2 x 105 psi
υ = 0.3
k = 10 lb/in
|
L= 200 in
r = 3 in
t = 0.2 in
|
P/2= 1000 lbf
|
x = y =0; u = θ= 0
|
Analysis Assumption and Modeling Notes
Only half of the beam is modeled due to symmetry. The beam is
divided in 80 elements.
VCF_1_0_00_00_04_01_001
Description:
(Bending of a Beam on an
Elastic Foundation)
|
Reference:
|
S.
Timoshenko, Strength of Material, Part II, Elementary Theory and Problems,
3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 12, article
2.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_04_01_001.xcf
|
A long (semi-infinite) beam on an elastic foundation
is bent by a force F and a moment M at the end as shown. Determine the lateral
end deflection of the beam 
. The elastic
foundation stiffness k is based on 0.3 inches deflection under 10.000lb loads spaced
22 inches apart.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 30 x 106
psi
k = 1515.15
lb/in3
|
A = 23 in2
I = 44 in4
|
F = 1000 lb
M = 10.000
in-lb
|
Node 1: u=v=w=0
|
A nodal spacing
of 26 inches is selected to match the discrete foundation locations upon which
the stiffness is based. The beam length is arbitrary selected to be 286 in. The
cross sectional height of the beam h is arbitrary taken as 5 inches (this should
not affect the end displacement).
VCF_1_0_00_00_04_01_002
Description:
(ARTICULATED PLANE TRUSS)
|
Reference:
|
Societe
Francaise des Mecaniciens. Guide de validation des progiciels de calcul de
structures. Paris,
Afnor Technique, 1990. Test No. SSLL14/89.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
File:
|
VCF_1_0_00_00_04_01_002.xcf
|
This test is a
linear statics analysis of a straight cantilever beam with plane bending and
tension- compression.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=2.1x1011 Pa
|
I1=5x10-4 m4
I2=2.5x10-4
m4
|
P=-3000 N/m
F1=-20000 N
F2=-10000 N
M=-100000 Nm
|
Left
support: Simple support.
Right
support: Simple support
|
A 3D case needs to be defined in order to allow
the inclusion of M (moment in the perpendicular axis). We have to include BCs
in the Z direction to restrict movement. Structural elements used are beams.
VCF_1_0_00_00_04_01_003
Description:
(BEAM TORSION TWIST ROTATION
STRESSES)
|
Reference:
|
Ingeciber, S.A.
|
|
Analysis Type(s):
|
Static Linear
Analysis
|
|
File:
|
VCF_1_0_00_00_04_01_003.xcf
|
A quadrangle beam, embedded in
both ends, is subjected to a Kd of 10000 kpˇm/rad in point 2, besides an
imposed displacement of 1 cm in Y axis. Calculate Z moment in both ends.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Generic material:
E=2.1ˇ109
kp/m2
ν=0.2
ρ=2500 kg/cm3
G=8.75ˇ108
kp/m2
|
L=10m.
Width (b) =
0.1 m.
Height (H) =
0.4 m.
|
δ=0.01 m (2)
Kd=
10000 kpˇm/rad
|
Node 1: u=v=w=0
θx=θy=θz=0
Node 2: u=v=w=0
θx=θy=θz=0
|
One beam is modeled with 20 elements. It can be recalled
that the torsion area corresponds to the midsection (At).
VCF_1_0_00_00_04_04_001
Description:
(Beam maximum bending stress
and deflection)
|
Reference:
|
Arthur
P. Boresi, Omar M. Sidebottom, Advanced Mechanics of Materials , 4rd
Edition, John Wiley & Sons, Inc., New York, 1985, pg. 421, problem set
9-4 nş4.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_04_04_001.xcf
|
A long brass beam rests on a hard
rubber foundation (spring constant = k). If the beam is subjected to a
concentrated load P as shown below, determine the maximum deflection of the
beam.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Ebrass
= 82.7 GPa
|
Area (A) =
600 mm2
Inertia y axis (Iyy) = 5625 mm4
Inertia z axis (Izz) = 10000 mm4
B=200mm
|
P = 700N
|
Element B :
Elastic foundation linear k=3ž106
N/m2
Node 1: u=v=0
θx
= θz = 0
|
The unit system selected is Imperial system (inches). A
generic material and with generic section is modeled. The elastic foundation is
modeled by a linear spring along the beam.
VCF_1_0_00_00_04_04_002
Description:
(SPRINGS SUPPORTED BEAM 2D)
|
Reference:
|
Arthur
P. Boresi, Omar M. Sidebottom, Advanced Mechanics of Materials , 4rd
Ed., John Wiley & Sons, Inc., New York, 1985, pg. 213, example 4-5.4
|
|
Analysis
Type(s):
|
Static
Linear Analysis.
|
|
File:
|
VCF_1_0_00_00_04_04_002.xcf
|
A beam made of aluminum is
supported by seven springs (k = 110.000 N/m) spaced a distance of 1.10 m each
along the beam. The springs simulate the behavior of the ground. A load P is
applied at the center of the beam over the central spring. Calculate the load
carried by each spring, the deflection (δ) of the beam under the load, the
maximum bending moment and the maximum bending stress in the beam.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 72.000
MPa.
|
L=6.80 m.
l (distance
between springs)=1.10 m
H (height) =
100 mm.
Iy
= 2.45x106 mm4
|
P = 12.0 kN.
|
Node M4 =
u=0
k springs=
110.000 N/m
|
Turn effects of shear for cutting in the beam
element. It is assumed that the springs can develop tensile as well as
compressive forces. The problem can be solved using the equations of the strain
energy U, and making the balance of the reactions A, B, C, D, with
symmetry.
U= Strain Energy
;
;
; 
VCF_1_0_00_00_04_04_003
Description:
(Statically Reaction Force
Analysis)
|
Reference:
|
S.
Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd
Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 26, problem 10.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_04_04_003.xcf
|
A prismatic
bar with built-in ends is loaded axially at two intermediate cross-sections by
forces F1 and F2. Determine the reaction forces R1 and R2.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 3∙107
psi
|
h (height)=
1.00 in
b (base) =
1.00 in
L = 10 in
a = 7 in
b = 4 in
|
F1 = 1000
lbf.
F2= 500 lbf.
|
In supports,
all displacements and rotations are constrained.
|
Nodes are defined where loads are to be applied. Since
stress results are not to be determined, a unit cross-sectional area is
arbitrarily chosen.
VCF_1_0_00_00_04_04_004
Description:
(Double-Hinged Arc)
|
Reference:
|
P. Dellus, Résistance des
matériaux, Paris, Technique et Vulgarisation, 1958
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_00_04_04_004.xcf
|
Static analysis of a double-hinged arc.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2.0 E+11Pa
v = 0.3
|
Area
of Section
A
= 1.131 E-4 mm2
Moment
of Inertia,
I
= 4.637 E -9 m4
|
P
= 100 N at node 16
|
Node
1 =
Constrain
Dx and Dy
Node
31 =
Constrain
Dy
|
A
generic material and generic section are used. Arc is modeled by one beam
structural element and it is meshed into 30 elements.
VCF_1_0_00_00_16_01_001
Description:
(Spring connected to beams)
|
Reference:
|
Ingeciber
S.A.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
File:
|
VCF_1_0_00_00_16_01_001.xcf
|
The model consists of two
cantilever beams, connected by a punctual spring of a known elastic constant K2.
The upper beam (1) is made of concrete, while the bottom (3) is a cable steel
beam with a circular section loaded on the end (F). Determine the maximum
spring deflection and the vertical reactions in each of the beams.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E1 = 3.0*105
kg/cm2
E3 = 2.1*106
kg/cm2
K2
= 40000 kg/m
|
Concrete(1):
h = 0.3 m
B = 0.2 m
Steel (2):
D = 0.20 m
L1
(span beam 1) = 5m
L2
(span beam 2) = 7 m
|
F = 3500 kg
|
Node A: u=v=0; θx
= θz = 0
Node B: u=v=0; θx
= θz = 0
|
A mesh with 50 elements has been used to model each beam
with a 2D static analysis. Superposition effects are supported. The structure
is subjected to loading without being previously deformed.
The theoretical solution was
obtained by equivalent springs in series and parallel:
;
;
;
;
;
VCF_1_0_00_08_04_01_001
Description:
(Static analysis comparing beam
and truss elements under thermal stress )
|
Reference:
|
A. S. Hall, An Introduction to the Mechanics of Solid, Wiley, 1984.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_08_04_01_001.xcf
|
The same model is analyzed using truss and beam elements.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E
= Modulus of Elasticity
 =Thermal expansión coefficient
Refer to chart below
|
A1
= A3 = 300mm2
A2 = 200mm2
|
A temperature
change
ΔT = -50 °C
|
points 1, 4: Constrain all DOFs.
points 2, 3: Constrain Dz. (Only for Truss elements)
|
Analysis Assumption and Modeling Notes
All entities are modeled with circular
section and using generic materials
VCF_1_0_01_00_02_00_001
Description:
(Clamped Beam Plasticity).
|
Reference:
|
Ingeciber S.A.
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_01_00_02_00_001.xcf
|
Calculate the yield load which
collapses the clamped beam (q). Obtain plastic moment and vertical reactions.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Steel type S-275.
γ1=γ2=1.0.
fymax = 275 MPa
|
Steel section HEB-180.
L = 4 m.
|
Yield load = q
|
Node 1: u=v=0
θz = 0
Node 2: u=v=0
θz = 0
|
Analysis Assumption and Modeling Notes
The beam is modelled with 25 elements. Step fractions
(initial, minimum and maximum) in global solution controls = 0.01.
In this case load q matches the plastic
moment.
;
; 
; Wpl = Plastic modulus of the section.
VCF_1_0_01_00_02_00_003
Description:
(Truss Structure Yielding).
|
Reference:
|
Ingeciber S.A.
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_01_00_02_00_003.xcf
|
Calculate the force F causing
the plastic collapse of the truss structure shown below (dimensions in mm).
Obtain reactions in supports.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Steel type
S-355.
γ1=γ2=1.0.
fymax =
355 MPa
|
A = 2000 mm2.
|
F yield
force
|
Node 2 (left
node): u=v=0
Node 4 (central node):
u=v=0
Node 6
(right node): u=v=0
|
The beam is modelled with a
single element. Step fractions (initial, minimum and maximum) in global
solution controls are set to 0.002. Activate incremental results.
; 
; 
VCF_1_0_01_00_04_01_001
Description:
(Plastic Limit Load Frame).
|
Reference:
|
Ingeciber S.A.
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_01_00_04_01_001.xcf
|
The simple
frame structure is loaded by a horizontal load of 32 kN with cross-section
properties and generic material data. The material is elastic-plastic with a
small isotropic work hardening slope in the plastic range. The maximum load of
32 kN is close to the plastic limit load of the structure. The generic material
data relevant in this analysis are: Young's modulus, Poisson's ratio, yield
strength, and the plastic work hardening slope.
Calculate the
maximum horizontal displacement of the loaded point (3).
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 200000 MPa.
fy = 200
MPa.
ν = 0.3.
dσ/
dεp = 20 Mpa
|
View figure
The depth of
the beam is 0.01 and width of 0.1 m.
|
P = 32 kN.
|
Node 1: u=v=0
θz
= 0
Node 2: u=v=0
θz
= 0
|
The beam is modeled with 50 elements. Step fractions
(initial, minimum and maximum) in global solution controls are set to 0.01.
Tolerance in u, F, M and θ convergence equal to 0.005.
VCF_1_0_01_01_02_01_003
Description:
(Cables verification when
cracking is applied)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_01_02_01_003.xcf
|
Tensional analysis of a cable
section that is supporting a beam structure submitted to a 1 t/m linear load.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=210000MPa
υ = 0.3
|
Lb= 10 m
Lc = 11.547 m
|
q= 9.80665 KN/m
|
Node 0: x = y = z = 0; θx= θy= θz =0
|
The beam is modelled with 100
element numbers while cable structural element is only shaped by 1 element.
Column sectionŕ
Cable sectionŕ 
VCF_1_0_01_08_16_01_001
Description:
(Loaded Support Structure).
|
Reference:
|
Any basic
calculus book
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_01_08_16_01_001.xcf
|
Calculate the force P that
causes plastic collapse of the truss structure and obtain reactions at
supports.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
σPL1=σPL2 =200 MPa
σPL3=σPL4 =400 MPa
ε1
elastic máx = ε2 elastic máx = 0.0010750
ε3
elastic máx = ε4 elastic máx = 0.0015952
|
Acables
= 300 mm2.
hbeam
(height) = 0.5 m.
bbeam
(weight) = 0.5 m.
|
P, applied
in the middle of the beam.
|
Node 2: u=v=0
Node 19: u=v=0
Node 21:
u=v=0
Node 4: u=v=0
|
Truss 1 and 2 start to yield, then truss 3 and
at the end, truss 4 and the structure collapses.
The beam is modelled with twelve elements, and
truss with just one. Step fractions (initial, minimum and maximum) in global
solution controls are set to 0.01. Incremental results are activated.
A beam with infinite stiffness is needed to
apply an even force on all cables.
; 
; 
and obtain P =
280 kN ; 
and obtain R4
= 40 kN.
VCF_1_0_03_00_00_01_002
Description: (shrinking
and creeping deformation)
|
Reference:
|
Ingeciber, S.A.
|
|
Analysis Type(s):
|
Static Analisys
|
|
File:
|
VCF_1_0_03_00_00_01_002.xcf
|
Calculate the shrinking, initial deformation and both creep &
instant deformation.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
HA- 35
70% wet
Ho= 100 mm
P in load state from the
28th day.
|
L=0.4m.
a= 0.2m
b= 0.2 m
|
P = 50 KN
|
u=v=w=0
θx=θy=θz=0
|
Analysis Assumption and Modeling Notes
This beam is modeled with 40 elements.
Applying:
|
Time t(days)
|
50
|
100
|
730
|
|
|
0.19
|
0.24
|
0.32
|
|
|
0.047
|
0.054
|
0.062
|
|
|
0.24
|
0.30
|
0.38
|
VCF_1_0_03_00_04_01_001
Description:
(Straight Cantilever with Axial
End Point Load)
|
Reference:
|
National Agency for
Finite Element Methods and Standards, NAFEMS Non-Linear Benchmarks.
Glasgow: NAFEMS, Oct., 1989, Rev. 1. Test No. NL6.
|
|
Analysis Type(s):
|
Static Nonlinear
Analysis
|
|
File:
|
VCF_1_0_03_00_04_01_001.xcf
|
A slender
square cross-sectional beam of length L, and area A, fixed at one end and free
at the other end, is loaded at the free end with an axial load P and a
transverse load Q=P/100. Determine the displacement (ux, uy)
when PL2/(2pEI)=3.190 and 22.493.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 210 GPa
|
h(height) =
0.02 m
b(width) =
0.03 m
A= 0.0006m2
L = 1.2 m
|
PL2/(2pEI)= 3.190
PL2/(2pEI)=22.493
Q=P/100
|
Node B: u=v=0
θ =
0
|
Analysis Assumption and Modeling Notes
This is a nonlinear analysis, so that Large
deflections option must be activated. If the option Create incremental
results is activated the results for intermediate nonlinear analysis are
stored for all the load increments.
VCF_1_0_03_00_04_01_002
Description:
(Clamped beam, non-linear
deformation).
|
Reference:
|
NAFEMS,
Non-Linear Benchmarks (Report No.NNB.), Glasgow, UK, 1989
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_03_00_04_01_002.xcf
|
Calculate the UX and UY
displacements and check the non-linear geometric behavior of a clamped beam.
The applied load is a moment in the Z direction.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E= 2.1x1011
N/m2
ν=0.0
|
Rectangular
section:
b=0.1 m
h=0.1 m
L = 3.2 m
|
M= 3436116.25 Nxm
|
Node 1: u=v=0
θz
= 0
|
Analysis Assumption and Modeling Notes
The beam is modelled with 20 elements. Step
fractions (initial, minimum and maximum) in global solution controls are 0.1,
1e-06 and 0.1 respectively. Check F convergence must be unchecked.
VCF_1_0_03_00_04_01_003
Description:
(Lees Frame Buckling problem).
|
Reference:
|
Test NL7 from NAFEMS Publication NNB, Rev. 1,
NAFEMS Non-Linear Benchmarks, October 1989.
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_03_00_04_01_003.xcf
|
Calculate the UY displacement and
check the non-linear geometric behavior of a frame. The applied load is a
punctual load applied at 0.24 m from the left side of the top beam.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E= 71.74 GPa
ν=0.0
|
Rectangular
section:
width=0.03 m
height=0.02
m
Length of
pillar and beam = 1.2 m
|
P= 18485
Nxm applied at node 22 with a 0.24 m distance from the leftmost side of the
top beam
|
Node 1: u=v=0
Node 33: u=v=0
|
The beams are modelled using 10 elements. Check
F convergence and Check u convergence must be checked.
VCF_1_0_03_00_04_04_003
Description:
(Arch with punctual load,
non-linear deformation).
|
Reference:
|
O.C.
Zienkiewicz, The Finite Element Method, McGraw Hill Book Company, 1977.
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_03_00_04_04_003.xcf
|
Calculate the UY displacement of
the top node and check the non-linear geometric behavior of an arch with a
punctual load.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E= 6x106
N/m2
ν=0.3
|
Generic
section:
A=1 m2
I=0.1667 m4
Radius=100 m
Arc
angle=215o
|
P= 0.897*1000N
|
Node 1: u=v=0
Node 41: u=v=0
θz = 0
|
The arch is modelled using 40 elements. The
applied load is the maximum load used in the reference file, that is 0.897*1000
N = 897 N. See page 3 of reference file. The maximum load factor is 0.897.
VCF_1_0_03_00_04_04_004
Description:
(Non Linear Analysis Beams)
|
Reference:
|
Haengsoo Lee,
Dong-Woo Jung, Jin-Ho Joeng and Seyoung Im. (1993). Finite element analysis
of lateral buckling for beam structures. Computers and Structures, 53(6),
1357-1371.
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_03_00_04_04_004.xcf
|
A right-angle
frame of Length L, and dimensions bxh, is fixed at the top and
free at the base. Determine the reaction force Z in node 1.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 7.124*104
MPa
|
h(height) =
30 mm
b(width) =
0.6 mm
L = 240 mm
|
P0
= 1.1 N
|
Node 1: u=v=w=0
θx
= θy = θz = 0
|
The frame was modeled with 20 elements. The
model is deformed by the mode_19 of the buckling model. Results are from the 24
iteration.
The load factor, λ = 1.0 is used for calculation of the critical load P.
Pcrit = tP0
+ λ (tP - t-ΔtP) Being t = 1 and Δt = 0.01
VCF_1_5_00_00_02_00_001
Description:
(Seismic Analysis on a 1 DOF
beam according to Eurocode 8).
|
Reference:
|
Ingeciber S.A.
|
|
Analysis
Type(s):
|
Spectral
Analysis
|
|
File:
|
VCF_1_5_00_00_02_00_001.xcf
|
The model is a single beam element
with only one degree of freedom: horizontal displacement at one of its ends.
The beam has no mass. A punctual mass is applied at the free end of the beam.
Check the response acceleration is
equal to spectrum acceleration.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Steel type:
S-275
E=2.1ž105 MPa
Soil type: C
Damping: 7%
|
L = 10 cm.
Beam
Section: IPE80
Izz= 801400 mm4
|
Eurocode 8 EN
1998-1:2004 Response Spectrum
Base
acceleration: 1.2753 cm/s2
m = 3.96144ž107 kg
|
Node 1:
Fixed
Node 2: ux,
uy=0
qx, qy, qz =0
|
The beam is modelled with a
single element. Three vibration modes are obtained and
the square root SRSS method of the sum of
the squares is used
; 
; 
;
;
=0. 243mm
VCF_1_0_01_03_00_01_002
Description:
(Evaluation of traction tension
under a Buyukozturk analysis)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_03_00_01_002.xcf
|
Analyse tensions to which the concrete beam, modelled
as a solid, would start plasticizing in tractions.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
C25/30. 28
days
|
A= 0.5 m
L= 6 m
|
P= 10KN/m
|
Point (0,0)
constrain X and Y movements.
Point (6,0)
constrain Y movment.
|
Evaluate a
Buyukozturk non-linear analysis. Mesh controls: edge length, edge sizes 0.1 m.
f´c is the
concrete tension from this one starts plasticizing in compressions.
Checking in the
mid span:
A 10 KN/m linear
load is applied with a 0.5 KN/m step, being 20 the number of steps. In the 11th
step, the beam does not plasticize but in the 12th. Tensions in the 11th step
will be approximately 1.19 MPa.
VCF_1_0_01_03_00_01_003
Description:
(Compression forces in a Buyukozturk
analysis)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_03_00_01_003.xcf
|
Determine when this 2D concrete structure starts
plasticizing when a compression linear load is applied.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = It is
obtained over the first step of  diagram of Buyukorturk curve analysis.
C25/30. 28
days
|
a=b =1m
|
Loads in the
scheme
|
0.001 m of
displacement in (1,0) direction. $Curve(4)
$Curve (2):
constrains mov x.
$Curve (1):
constrains mov y.
|
Evaluate a
Buyukozturk non-linear analysis. Solid 2D plane strain. Mesh controls: Edge
length, quadrangle and edge sizes 1 m.
Structure
starts plasticizing by compression forces:
In regard to
Buyukozturk, structure starts plasticizing when a 10.51 MPa tension is reached.
Buyukozturk: 
Step 0.5 MPa ŕ 10.5 MPa
(step 21)
Plasticization
is not happening at step 21 but step 22.
VCF_1_0_01_04_00_01_001
Description:
(Stresses and strains
evaluation under a Buyukozturk analysis)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_04_00_01_001.xcf
|
Concrete structure is affected by a cracking
statement. Besides a Buyukozturk non-linear analysis is assigned. Calculate the
strain and stress in the second 0.0025.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = It is
obtained over the first step of diagram of Buyukorturk curve analysis.
C25/30. 28
days
Cracking:
Critical
 ; softening modulus= 150 MPa
|
a=b=c= 1m
|
|
Displacement
in (1,0,0) direction.
$Surface(4):
constrain mov x.
$Surface(2):
constrain mov z.
$Surface(3):
constrain mov y.
|
Evaluate a
Buyukozturk non-linear analysis. Mesh controls: extrude surface, extrude and
edge sizes 1 m.
Calculation time
in 0.0025ŕ Load Case 64.
VCF_1_0_01_04_00_01_002
Description:
(Stresses and strains
evaluation under a Buyukozturk analysis)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_04_00_01_002.xcf
|
Concrete structure is affected by a cracking
statement. Besides a Buyukozturk non-linear analysis is assigned. Calculate the
strain and stress in the second 0.0025.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = It is
obtained over the first step of diagram of Buyukorturk curve analysis.
C25/30. 1000
days
Cracking:
Critical ; softening modulus= 150 MPa
|
a=b=c= 1m
|
|
Displacement
in (1,0,0) direction.
$Surface(4):
constrain mov x.
$Surface(2):
constrain mov z.
$Surface(3):
constrain mov y.
|
Evaluate a
Buyukozturk non-linear analysis. Mesh controls: extrude surface, extrude and
edge sizes 1 m.
Calculation time
in 0.0025
VCF_1_0_01_04_00_01_003
Description:
(Stresses and strains
evaluation under a Buyukozturk analysis)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_04_00_01_003.xcf
|
Concrete structure is affected by a cracking
statement. Besides a Buyukozturk non-linear analysis is assigned. Calculate the
strain and stress in the second 0.0025.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = It is
obtained over the first step of diagram of short-term curve analysis.
C25/30. 1000
days
Multilinear
elastic analysis: critical 
|
a=b=c= 1m
|
|
Displacement
in (1,0,0) direction.
$Surface(4):
constrain mov x.
$Surface(2):
constrain mov z.
$Surface(3):
constrain mov y.
|
Evaluate a
Multilinear elastic non-linear analysis. Mesh controls: extrude surface,
extrude and edge sizes 1 m.
It is tested
that if 
ŕ
both in LC 30 and
100.
VCF_1_0_00_02_00_01_002
Description:
(RECTANGULAR PLATE SIMPLY
SUPPORTED)
|
Reference:
|
Warren
C. Young, Richard G. Budynas, Roarks Formulas for Stress and
Strain, 7th Edition, McGraw-Hill, Table 11.4, case 2a, pg. 505.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_02_00_01_002.xcf
|
A rectangular
concrete slab (C35/45, S500) has a length of 12.0 m and a width of 6.0 m and is
subjected to a vertical pressure, q. Three edges of the plate are simply
supported and one edge (b) is free. Calculate the maximum stress and the
maximum deflection of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
C35/45;
E=31600MPa
|
b=6 m
a=12 m
t=0.35 m
|
Vertical
press. q=80kPa
|
Edges 1, 2, 3: uz=0
Nodo O: ux,y=0;qz=0
|
A shell element is modeled with a quadrangle mesh type with
elements of size 0.5m. A surface load normal to the surface and linear
boundary conditions can be selected.
VCF_1_0_00_02_00_01_005
Description:
(RECTANGULAR PLATE SIMPLY
SUPPORTED)
|
Reference:
|
INGECIBER S.A
|
|
Analysis Type(s):
|
Static Linear
Analysis
|
|
File:
|
VCF_1_0_00_02_00_01_005.xcf
|
A rectangular
concrete slab (C25/30, S500) has a length of 100 cm, a width of 100 cm and a
thickness of 10 cm. The shell is subjected to a vertical pressure, q. The
element has one edge completely fixed and another edge simply supported.
Besides, shell is submitted to an imposed displacement of -2 mm in Z axis.
Calculate the maximum stresses.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=30000MPa
ν=0.2
|
b=100 cm
a=100 cm
t=10 cm
|
Vertical
press.
q=0.1 MPa
|
Edge 1: ux,y=0;qz=0
Edge 2: uz=0
|
A shell element is modeled with a quadrangle mesh type with
elements of size 0.5m. A surface load normal to the surface and linear
boundary conditions can be selected.
Element: 1; node: 2; end: 0; P.I: 0
VCF_1_0_00_02_02_01_001
Description:
(RECTANGULAR PLATE WITH FIXED
EDGES)
|
Reference:
|
Aplication
of formulas obtained from H. M. Westergaard, Moments and Stresses in Slabs
Proceedings of American Concrete Institute, Vol 17, 1921
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
File:
|
VCF_1_0_00_02_02_01_001.xcf
|
A rectangular steel plate
(E=200000MPa, ν=0.29) has a length of 2m and a width of 1.5m and is
subjected to a uniform load of 5 kPa. The edges of the plate are fixed.
Calculate the maximum bending moment per unit width and the maximum deflection
at the center of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E =
210000MPa
ν=0.3
|
b=1.5m
a=2m
α
=b/a=0.75
t=0.01m
|
q=50kPa
|
Perimeter: u=v=w=0
θx=θy=θz=0
|
A shell element is modeled with a quadrangle mesh type. A
surface load normal to the surface can be selected.
Moment in span b at
center of the plate
Maximum deflection:
=
0.0266m = 26.66mm
VCF_1_0_00_02_02_01_002
Description: (CIRCULAR
PLATE WITH FIXED EDGES)
|
Reference:
|
Ingeciber S.A.
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_00_02_02_01_002.xcf
|
A circular steel plate has a radius of 5m and is
subjected to a uniform load of 1500 kp/m2. The edges of the plate
are fixed. Calculate the maximum bending moment (X axis) per unit width in
perimeter, the maximum bending moment (X axis) per unit width in the center
and the maximum deflection at the center of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 210000MPa
ν=0.3
|
a (radius) =5.0 m
|
P0=1500 kp/m2
|
Perimeter: u=v=w=0
θx=θy=θz=0
|
Analysis Assumption and Modeling Notes
A shell element is modeled with a
triangular mesh type, with 0.5 m elements size. A surface load normal to the
surface can be selected.
Moment at center of the plate: 
Moment at perimeter of plate: 
Maximum deflection: 
VCF_1_0_00_02_02_01_003
Description: (Circular
Clamped Plate Under Normal Pressure)
|
Reference:
|
S.P. Timoshenko and a. Woinowsky-Krieger,
Theory of Plates and Shells(2nd edition) McGraw-Hill,
N.Y. 1970
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_02_02_01_003.xcf
|
Static analysis of a circular clamped plate
under normal surface pressure.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Modulus of
Elasticity,
E =
2.1 E+11Pa
v =
0.3
|
Circular plate
Radius = 1m
Thickness t =
0.01 m
|
Surface load
on 10ş slice P = 10 000 Pa
|
Center: Dx,
Dy, Rx, Ry, Rz
Perimeter of
the circle: all DOFs constrained
Symmetric condition: Dy,
Rx
|
Analysis
Assumption and Modeling Notes
Due to symmetry only 10 ş of the total
plate is modeled.
VCF_1_0_00_02_02_01_004
Description:
(Spherical Shell under Internal
Pressure)
|
Reference:
|
Any elementary elasticity book
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_02_02_01_004.xcf
|
A thin spherical shell is analyzed to uniform internal
pressure.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Modulus of Elasticity,
E = 2.1 E+11Pa
v = 0.3
|
ź
spherical shell
Radius,
R = 1.0 in
Thickness
t = 0.01 in
|
Internal
pressure:
P
= 1.0 psi
|
Symmetric
condition L1:Dx,qx=0
L2:Dy,qy=0
L3:Dz,qz=0
|
Problem Sketch
Due
to symmetry only 1/4 of the entire sphere is modeled.
For
a thin spherical shell, the solution is that the circumferential stress is equal
to: PR/2t
VCF_1_0_00_02_02_01_005
Description:
(SIMPLY SUPPORTED RECTANGULAR
PLATES UNDER HYDROSTATIC PRESSURE)
|
Reference:
|
Theory
of Plates and Shells Timoshenko
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
File:
|
VCF_1_0_00_02_02_01_005.xcf
|
This test is a
linear static analysis of a rectangular plate under a hydrostatic load.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=2.1x1011 Pa
|
Side 1.2 m.
|
P=15000 Pa
maximum value with a slope of 12500 Pa/m.
|
Simple
supports at all borders.
|
The shell is modelled using 144 quadrangular
elements.
VCF_1_0_00_02_02_01_006
Description:
(CIRCULAR PLATE LOADED AT THE
CENTER)
|
Reference:
|
Theory
of Plates and Shells Timoshenko
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
File:
|
VCF_1_0_00_02_02_01_006.xcf
|
This test is a
linear static analysis of a circular plate loaded at its center, supported at
its border.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=2.1x1011 Pa
|
Radius 1.5
m.
|
P=1250 N
|
Simple
supports at border. Simmetry BCs.
|
Only a quarter of the shell is modelled, using a
shell with quadrangular elements. The BCs are defined to comply with the
symmetry of the plate.
VCF_1_0_00_02_04_01_001
Description:
(Pinched cylinder with end
diaphragms)
|
Reference:
|
|
R. D. Cook, Concepts and Applications of Finite
Element Analysis, 2nd Edition, John Wiley and Sons, Inc., New
York, NY, 1981, pp. 284-287.
|
|
H. Takemoto, R. D. Cook, "Some Modifications of an
Isoparametric Shell Element", International Journal for Numerical
Methods in Engineering, Vol. 7 No. 3, 1973.
|
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_02_04_01_001.xcf
|
A cylindrical shell is closed at
both ends by rigid diaphragms and is pinched by two opposite forces P applied
at the middle section. This test involves in extensional bending and complex membrane
states of stress. Determine the radial displacement d at the point where F is
applied.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 10.5e6
psi
ν=
0.3125
|
L=10.35 in
R = 4.953 in
t = 0.094 in
|
P = 100 lbf
|
Both ends
are free edges
|
One-eighth symmetry model is used.
One-fourth of the load is applied due to symmetry.
VCF_1_0_00_02_04_01_002
Description: (Bending of a Long Uniformly Loaded Rectangular Plate)
|
Reference:
|
S.
Timoshenko, Strength of Material, Part II, Elementary Theory and Problems,
3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 80, article
14.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_02_04_01_002.xcf
|
A rectangular plate is
subjected to uniform pressure p as shown. The shorter edges are
simply-supported. Determine the direct stress σx (MID) at the middle of the plate and the
maximum combined stress (direct plus bending) σx (BOT) at the
bottom of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 30 x 106
psi
υ = 0.3
|
ℓ = 45
in
w = 9 in
t = 0.375 in
|
P = 10lb/in2
|
Cuve(2): u=v=w=0
Curve (4): u =v=w=0
|
Edges size is set as 5 in to improve results.
VCF_1_0_00_02_04_01_004
Description:
(PLANE STRESS ANALYSIS OF
MEMBRANE WITH HOT-SPOT)
|
Reference:
|
Test T1 from NAFEMS Publication TNSB,
Rev. 3, The Standard NAFEMS Benchmarks, October 1990
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
File:
|
VCF_1_0_00_02_04_01_004.xcf
|
A plane stress
analysis is performed with a temperature difference between the center of the
plate (the hot-spot) and the rest of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=100 GPa
ν=0.3
|
Square plate
side 20 mm.
Thickness=1
mm
|
Thermal
strain in hot-spot is αT=0.001 and 0 outside the spot
|
A quarter of
the plate is modeled where symmetry conditions are applied.
|
The shell is modelled using 49 quadrangular
elements for the shell and 16 for the hot spot.
VCF_1_0_00_10_00_01_001
Description: (Combined
load cases on a table)
|
Reference:
|
Any
basic mechanics text
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_00_10_00_01_001.xcf
|
Analysis applied on a simple desk model with various
load groups. Deformation, Axial Force, Stress and Maximum Bending moment of are
compared to the results when multiples and combinations of these loads are
applied.
|
Material
|
Geometry [m]
|
Loading [kg/m/s2]
|
Boundary Condition
|
|
Eurocode
2
C12/15
|
L =
1.58/2
W =
0.79/2
H = 0.74
|
LG1(top)
= 600
LG2(side)
= 100
LG3(vertical)
= 300
|
For
(-L,-W,-H)
u(x),
v(y), w(z) = 0 Mx, My, Mz = 0
u(x),
w(z) = 0
for
(-L, W, -H), (L, W, -H), (L,-W, -H)
|
Full scale model analyzed. For the following node and elements.
Displacement Z: node 12 node 28
Bending moment per unit width
about y-axis: all nodes of element 280 and element 536
X component of stress: all nodes
of element 280 and element 536
User combination has been used as
well as pre-processing load cases.
Node Results Displacement in
z [m]
Single load displacement [m ]
End Result Bending Moment per
unit width alonf Y- axis [Nm]
Single
load Beding moment [Nm/m ] 
Results
Element Results X Component
of stress [Pa]
Single Load results [Pa]
VCF_1_0_00_10_02_01_001
Description:
(UPN-300 shape submitted to
forces)
|
Reference:
|
INGECIBER S.A
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_00_10_02_01_001.xcf
|
Calculate the axil forces in both
the nail 2 and 3 (corresponding to those which are submitted to a bigger
force).
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
Nails
10.9.Φ20 mm.
|
Specified in
model
|
Fz=
160 KN
Fx=
80 KN
Fy=
100 KN
|
Perimeter: u=v=w=0
θx=θy=θz=0
|
A shell element is modeled with a quadrangle mesh type. A
surface load normal to the surface can be selected.
Nails 10.9.Φ20 mm.
EAE-_>Nails 10-9.
;
;
Reactions in the CG will be
calculated:
Traction forces are quantified:
VCF_1_0_02_02_04_01_001
Description:
(WRAPPED THICK CYLINDER UNDER
PRESSURE)
|
Reference:
|
National Agency for Finite Element
Methods and Standards (U.K.): Test R0031/2
from
NAFEMS publication R0031, Composites Benchmarks, February 1995.
|
|
Analysis
Type(s):
|
Static
Linear Analysis
|
|
File:
|
VCF_1_0_02_02_04_01_001.xcf
|
A wrapped
thick cylinder of 200mm in length consists of two layers, and subjected to a
pressure, q. The inner cylinder is isotropic and the outside is orthotropic.
The properties of the geometry and materials are shown in the following table.
Calculate the hoop stress in the inner and outer layer.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Inner Cylinder:
E=2.1x105MPa
n=0.3
Outer Cylinder:
E1=130
GPa; E2=5 GPa; E3=5 GPa
n12=0.25; n13=0.25; n23=0
G12=10
GPa; G13=10 GPa; G23=5GPa
|
L = 200mm
r1=23 mm
r2=25 mm
r2=27 mm
|
Vertical press.
q=200 MPa
|
Axial displacement of the cylinder is
zero at z=0
|
One-quarter of the cylinder cross-section and half of the
length is modeled. Each lamina is modeled as one shell element with a
quadrangle mesh type of eight elements along the hoop direction and four
VCF_1_0_03_02_04_01_001
Description:
(Bending of a Long Uniformly
Loaded Rectangular Plate)
|
Reference:
|
S.
Timoshenko, Strength of Material, Part II, Elementary Theory and Problems,
3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 80, article
14.
|
|
Analysis
Type(s):
|
Static
Nonlinear Analysis
|
|
File:
|
VCF_1_0_03_02_04_01_001.xcf
|
A rectangular plate is subjected to uniform pressure P
as shown. The shorter edges are simply-supported. Determine the direct stress σx (MID) at the middle of the
plate and the maximum combined stress (direct plus bending) σx
(BOT) at the bottom of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 30 x 106
psi
υ = 0.3
|
ℓ = 45
in
w = 9 in
t = 0.375 in
|
P = 10lb/in2
υ = 0.3
|
Node 11: u=v=w=0
Node 1: u =v=w=0
Node 15: u=v=w=0
Node 5: u =v=w=0
|
Large deflection
activated. Edges size is set as 5 inches to improve results.
VCF_1_0_08_02_04_00_001
Description:
(LAMINATED STRIP UNDER THREE
POINT BENDING)
|
Reference:
|
NAFEMS Composite Tests. Laminated strip under three point
bending Test R0031/1
|
|
Analysis
Type(s):
|
Static
|
|
File:
|
VCF_1_0_08_02_04_00_001.xcf
|
A laminated
strip made of an orthotropic material with a length of 50 mm and a width of 10
mm is subjected to a three point bending load configuration. The load is
F=10N/mm. The strip has 7 layers of material, each one rotated 90 degrees from
the previous layer.
The strip is
simply supported at -15 and +15 mm. Displacement and stress is tested at the
central node, bottom layer.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E11 = 10000
MPa
E22 = 500MPa
E33 = 500MPa
ν12=0.4
ν23=0.3
|
ν31=0.015
G12=3000 MPa
G23=2000 MPa
G31=2000 MPa
|
Length=50 mm
Width=10mm
|
F =10 N/mm
|
Simple
supports in A and B
|
|
|
|
|
|
A shell element is modeled with the quadrangle
mesh type. The seven layers are modelled using shell elements with glue
contacts between them. Two orthotropic materials are defined with the same
properties, but two material axes are used to model the material orientation.
VCF_1_0_00_03_02_01_001
Description: (Laterally
Loaded Tapered Support Structure)
|
Reference:
|
S. H. Crandall, N. C. Dahl, An
Introduction to the Mechanics of Solids,
McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 342, problem 7.18.
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_03_02_01_001.xcf
|
A cantilever beam of thickness t and length ℓ has a depth
which tapers uniformly from d at the tip to 3d at the wall. It is loaded by
force F at the tip, as shown. Find the maximum bending stress at the mid-length
(X = ℓ) and the fixed end of the beam.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30 x 106 psi
υ = 0.0
|
ℓ = 50 in
d = 3 in
t = 2 in
|
F = 4000 lb
|
Node 1: u=v=w=0
|
Analysis
Assumption and Modeling Notes
The 2 inch thickness is incorporated by
using the plane stress with thickness option. Poisson's ratio is set to 0.0 to
agree with beam theory. Edges size is set at 0.5 m to get better results.
VCF_1_0_00_03_02_01_002
Description: (Bending
of a Solid Beam (Plane Elements)
|
Reference:
|
R. J. Roark, Formulas for Stress and
Strain, 4th Edition, McGraw-Hill Book Co.,
Inc., New York, NY, 1965, pp. 104, 106.
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_00_03_02_01_002.xcf
|
A beam of length ℓ and height h is built-in at one end and
loaded at the free end with:
- a moment M
- a shear force F
For each case, determine the deflection δ at the free end and the bending stress σBend a distance d from the wall at the
outside fibre.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30x 106 psi
υ = 0.0
|
ℓ = 10 in
h = 2 in
d = 1 in
|
Case 1, M = 2000 in-lb
Case2, F = 300 lb
|
Node 1: u=v=w=0
Node 11: u =v=w=0
|
Analysis
Assumption and Modeling Notes
Improved bending is check to be on. Local
mesh controls on lines (23 on ℓ and 6 on h).
VCF_1_0_00_03_04_01_001
Description: (Bending
of a Long Uniformly Loaded Rectangular Plate)
|
Reference:
|
S. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd Edition,
McGraw-Hill Book Co. Inc., New York, NY, 1970, pg. 73, article 29.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Solid,
stress, moment
|
|
File:
|
VCF_1_0_00_03_04_01_001.xcf
|
A curved beam with a span of 90° arc as
shown. The bottom end is supported while the top end is free. When bending
moment M applied at the top end, determine the maximum tensile stress σt and maximum compressive stress σc in
the beam.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30 x 106 psi
υ = 0.0
|
h= 1.0 in
ri= 3.5 in
ro = 4.5 in
|
M = 100 in-lb
|
Curve(8): u=v=w=0
|
Analysis
Assumption and Modeling Notes
Used improve
bending to get results. Average off. The Edges Size of the mesh controls is 0.1
in, for a more detailed mesh and thus better results.
VCF_1_0_00_04_00_01_001
Description: (Curved
frame)
|
Reference:
|
Arthur P. Boresi, Omar M. Sidebottom, Advanced Mechanics of
Materials, John Wiley & Sons, Inc., New
York, NY, 1984, pg. 361, Fourth Edition.
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_04_00_01_001.xcf
|
A curved frame, with dimension as shown below, is loaded by a linear
load P which is located 1 m from the center of curvature. Determine the
maximum tensile and compressive stresses in the frame.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Concrete C20/35 (Eurocode)
|
Height: 0.50m
Width: 0.50m
rA=0.3m
rB =0.8m
R (radius curved
frame axis)=0.55m
|
P=190kN/m
|
Surface S: u=0
Node A: v=w=0
Node B: w=0
|
Analysis
Assumption and Modeling Notes
The unit system
selected is International System. A curved concrete frame with solid element is
modeled.
; 
; 
;)
;
VCF_1_0_00_04_00_01_002
Description: (Solid
cylinder with cap)
|
Reference:
|
Any mechanics text book
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_00_04_00_01_002.xcf
|
A solid concrete cylinder is mounted in the top and subjected to the
action of its own weight. Calculate the increase in length and the normal
stress in the support.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 28847.60MPa (C20/25).
ρ = 2500 kg/ m3 (density).
|
H = 5 m
D = 0.8m.
|
W = self-weight
|
Surface A: w=0
Point 1 y 2: v=0
Center O: u=0
|
Analysis
Assumption and Modeling Notes
This is a solid
cylinder of concrete modeled as 3D Solid element embedded in the top and
subjected to self-weight. Hexahedral meshing with edge length 0.3 m is used for
each axis.
; 
; 
; 
VCF_1_0_00_04_00_01_003
Description: (Simply-supported
Thick Plate using Three-dimensional Elements)
|
Reference:
|
Roarks Formulas For Stress and Strain,
McGraw-Hill Book Co. Inc.
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_00_04_00_01_003.xcf
|
A simply-supported thick plate under uniform transverse pressure of
1.0 psi on top surface is elastically analyzed.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E = 20 x 106 psi
ν =
0.3
|
L= 30 in
T = 3 in
|
P= 1 psi
|
x= 30: u=
0
y= 30: v=
0
x=0 z=0,
y=0 z=0: w= 0
|
Analysis
Assumption and Modeling Notes
Only one-quarter of the plate (60x60x3 inches) is modeled since
there are two planes of symmetry in this problem. The thickness of the plate
was divided into four tiers of elements. Each tier was divided into a
five-by-five element pattern.
VCF_1_0_00_04_00_01_004
Description: (Beam
Plasticity)
|
Reference:
|
Any basic mechanics text book
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_00_04_00_01_004.xcf
|
Calculate the maximum principal stress in the fixed section. The
beam is subjected to a uniform surface load q.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Concrete HA-25
|
h = 0.30 m.
b = 0.15 m.
L = 10 m.
|
q = 66.66 kN/ m2
|
Node 1: u=v=0
θz =
0
|
Analysis
Assumption and Modeling Notes
The
beam is modelled with hexahedrical elements. Modelled with hexahedral size on
X and Y axis of 5 cm, and Z axis of 8 cm.
; 
; 
; 
; 
VCF_1_0_01_04_04_01_001
Description: (Deformation
in an orthotropic solid)
|
Reference:
|
S. H. Crandall, N. C. Dahl, An
Introduction to the Mechanics of Solids,
McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 225.
|
|
Analysis Type(s):
|
Static Linear Analysis
|
|
File:
|
VCF_1_0_01_04_04_01_001.xcf
|
A cube of side L, composed of an orthotropic material, is loaded with
forces FX and FY, as shown. Three orthogonal faces are supported and the three
opposite faces are free. Find the translational displacement of the free
surfaces through X, Y and Z axes.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E11 = 10 x 106
psi
E22 = 20 x 106
psi
E33 = 40 x 106
psi
ν 12 = 0.05
ν 23 = 0.1
ν 31 = 0.3
G12= G23 = G31
= 10 x 106 psi
|
L = 1 in
|
FX = 100 lb
FY = 200 lb
|
XY Plane: uz =0
YZ Plane: ux =0
XZ Plane: uy =0
|
Analysis
Assumption and Modeling Notes
The cube is
modeled with a single finite element, creating geometry by extruding a face.
You have to define a generic material, activating orthotropic properties and
using the data from the different modules in the three orthogonal axes.
VCF_1_0_03_02_04_01_001
Description: (Bending
of a Long Uniformly Loaded Rectangular Plate)
|
Reference:
|
S. Timoshenko, Strength of Material, Part II, Elementary Theory
and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg.
80, article 14.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Shell,
stress, nonlinear , pressure
|
|
File:
|
VCF_1_0_03_02_04_01_001.xcf
|
A rectangular plate whose length is large
compared to its width is subjected to uniform pressure p as shown. The shorter
edges are simply-supported. Determine the direct stress σx (MID) at the middle of the plate and the maximum combined stress
(direct plus bending) σx (BOT) at the bottom of
the plate.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
|
|
ℓ = 45 in
w = 9 in
t = 0.375 in
|
|
|
|
|
P = 10lb/in2
|
Node 11: u=v=w=0
Node 1: u =v=w=0
Node 15: u=v=w=0
Node 5: u =v=w=0
|
Large deflection and improve bending is on.
Edges size is set on 5 in to improve results.
TRUSS
VCF_1_0_00_01_02_00_001
Description: (Truss
)
|
Reference:
|
Adaptation
of R. Argüelles Álvarez, La
estructura metálica hoy, Librería técnica Bellisco, Madrid, 1975,
example V.B.4.2. pg. 297, Second Edition.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Truss,
axial stress, displacement
|
|
File:
|
VCF_1_0_00_01_02_00_001.xcf
|
A steel truss, shown below in sketch, is loaded by a punctual load P
located on every nodes of the bottom chord. Determine the maximum axial force
(tensile and compressive) and vertical displacement on node 3.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
steel
|
library
section, IPE 240
|
Punctual
loads on nodes of bottom chord P=58tnf
|
Node 1:
u=v=0
Node 2:
v=0
|
Truss elements
are used. Each structural element consists by only one element as parameter of
mesh control. Its necessary to deactivate average option to see the results on
the bars. Apply Castigliano Theorem.
The values of axial forces may be verify by applying equations of
equilibrium.
CF_1_0_00_01_02_01_001
Description: (Statically
Indeterminate Reaction Force Analysis)
|
Reference:
|
S. Timoshenko, Strength of Material, Part I, Elementary Theory and
Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York,
NY, 1955, pg. 26, problem 10.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Truss,
steel, cable, reaction
|
|
File:
|
VCF_1_0_00_01_02_01_001.xcf
|
A prismatic bar with built-in ends are
loaded axially at two intermediate cross-sections by forces F1 and F2.
Determine the reaction forces R1 and R2.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30x106 psi
|
ℓ=10 in
a=b=0.3 ℓ
|
 = =1000 lb
|
Node 1: u=v=w=0
Node 11: u =v=w=0
|
Nodes are defined where loads are to
be applied. Since stress results are not to be determined, a unit
cross-sectional area is arbitrarily chosen.
VCF_1_0_00_01_02_01_002
Description: (Deflection
of a Hinged Support)
|
Reference:
|
S. Timoshenko, Strength of Material, Part I, Elementary Theory and
Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York,
NY, 1955, pg. 10, problem 2.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Truss,
steel, stress, deflection
|
|
File:
|
VCF_1_0_00_01_02_01_002.xcf
|
A structure consisting of two equal steel bars, each of length
ℓ and cross-sectional area A, with hinged ends is subjected to the action
of load F. Determine the stress, σ, in the bars
and the deflection, δ, of point 2.
Neglect the weight of the bars as it is small in quantity in
comparison with the load F.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
|
|
ℓ = 15 ft
|
|
A = .05 in2
|
|
Θ = 30°
|
|
|
Node 1:
u=v=w=0
Node 3: u
=v=w=0
|
Consistent length units are used. The
dimensions a and b are calculated parametrically in the input as follows: a
= 2ℓ cos Θ, b = ℓ sinΘ
VCF_1_0_00_01_02_01_003
Description: (Cable
Supporting Hanging Loads)
|
Reference:
|
F. P. Beer, E. R. Johnston, Jr., Vector Mechanics for Engineers,
Statics and Dynamics, McGraw-Hill Book Co., Inc., New York,
NY, 1962, pg. 260, problem 7.8.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Truss,
steel, reaction, tension
|
|
File:
|
VCF_1_0_00_01_02_01_003.xcf
|
The cable AE supports three vertical loads from the points
indicated. For the equilibrium position shown, determine the horizontal 
and vertical 
reaction forces ay
point A and the maximum tension T in the cable.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
|
|
ℓ = 10 ft
|
|
A = 0.1 ft2
|
|
 = 5.56 ft
|
|
 = 5.83 ft
|
|
|
=
4000 lbf
|
|
 =
6000 lbf
|
|
|
Node 7:
u=v=w=0
Node 2: u
=v=w=0
|
Boundary conditions on element 2 are
needed to constrain rotation on Z.
VCF_1_0_00_08_16_01_001
Description: (BEAM-TRUSS
2D)
|
Reference:
|
Ingeciber
S.A.
|
|
Analysis
Type(s):
|
Static
Analysis.
|
|
Key words:
|
Truss, beam , displacement, axial force
|
|
File:
|
VCF_1_0_00_08_16_01_001.
cf
|
A simple beam AB is attached at its middle section to the CD cable
of the same material (concrete), as shown in figure.
Determine the vertical displacement of the beam at point C and cable
tension when the beam supports a uniformly distributed load q.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2.100.000 Kg/cm2
|
Beam:
L=5 m;
A=40cm2
Iz = 3000cm4
Cable:
ǿ = 2.2568 cm ; β = 30ş
|
q = 0.5 tn/m
|
A,D : All movements are
constrain in u and v.
B: Vertical movements
are constrain.
|
The model
consists of 50 beam element and cable of a single element. Its important for
the nodes to be merged at point B (cable-beam).
; Ncable 
VCF_1_0_00_08_29_12_001
Description: (Thermally
Loaded Support Structure)
|
Reference:
|
S. Timoshenko, Strength of Material, Part I, Elementary Theory and
Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York,
NY, 1955, pg. 30, problem 9.
|
|
Analysis
Type(s):
|
Static,
Thermal Stress Analysis
|
|
Key words:
|
Beam, truss, steel, cooper, stress
|
|
File:
|
VCF_1_0_00_08_29_12_001.xcf
|
Find the stresses in the copper and steel wire structure shown
below. The wires have a cross-sectional area of A. The structure is subjected
to a load Q and a temperature rise of ΔT after
assembly.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Ec = 16 x 106
psi
|
|
αc = 92 x 10-7
in/in-°F
|
|
Es = 30 x 106
psi
|
|
αs = 70 x 10-7
in/in-°F
|
|
A = 0.1 in2
|
|
Node 1:
u=v=w=0
Node 2: u
=v=w=0
Node 3: u
=v=w=0
|
Length of wires (20 in.), spacing between
wires (10 in.), and the reference temperature (70°F) are arbitrarily selected.
VCF_1_0_01_08_02_12_001
Description: (Two-dimensional
Braced Frame)
|
Reference:
|
Ingeciber
S.A.
|
|
Analysis
Type(s):
|
Static
Analysis
|
|
Key words:
|
Truss, steel, cable, axial force
|
|
File:
|
VCF_1_0_01_08_02_12_001.xcf
|
The structure consists of a simple frame that has two columns, a
beam and diagonal braces.
Two different structural elements are used to perform the diagonal
braces: cable for structure A and truss for structure B.
In structure A, diagonal 1 does not work so it is not consider in
structure B (with truss elements for diagonals) since otherwise it work in
compression.
The frame objects can carry axial loads only. This is achieved in
the model by pinning the ends of horizontal beams.
We have to compare the axial force of the diagonal, performed with
two different types of elements.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Steel for
beams: Fe 275
Steel for cable an
truss: S 500
|
L=5 m
B=5m
Beam section=IPE200
Column section= 2UPN120
Cable/Truss diameter=16mm
|
F = 5000N
|
Node 1, 2 3, 4: u=v= 0
|
Cable and truss
element are meshed with a single element. The relative tolerance for
convergence in forces has to be reduced (e.g. 0.001) in order to obtain more accurate
results.
VCF_1_0_03_01_04_04_001
Description: (Cable
net with punctual loads)
|
Reference:
|
John W. Leonard, Tension Structures, McGraw Hill Book
Company, pp. 115-117, 1988
|
|
Analysis
Type(s):
|
Static
non-linear analysis
|
|
Key words:
|
Cables,
non-linear, axial
|
|
File:
|
VCF_1_0_03_01_04_04_001.xcf
|
A cable net structure is subjected to vertical loads applied at
every interior node. Axial forces in several members and Ux, Uy, Uz
displacements are obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
|
|
ℓ = 60 ft (projected)
|
|
Z(2, 20, 10, 14) = -1.32 ft
Z(12, 18) = -1.76ft
Z(3, 7, 24, 28) = -1.98 ft
Z(5, 26) = -2.64 ft
A = 0.01 ft2
|
|
 = 10.5 ft (projected)
|
|
 = 12 ft (projected)
|
|
|
P= 13.608 kips in
every interior node
|
|
|
|
|
Node 1, 8,
9, 16, 22, 23, 20, 31, 33, 42, 44, 46, 47, 49: u=v=w=0
|
Large deflections option must be checked
to obtain correct results.
VON MISES
VCF_1_0_01_03_00_01_004
Description: (Plasticization
by compression forces in Von Mises)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Static Analysis
|
|
File:
|
VCF_1_0_01_03_00_01_004.xcf
|
Determine when this 2D concrete structure starts plasticizing when
it is submitted to a linear load on one side.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
C25/30. 7
days
|
|
Loads in
the scheme
|
0.001
m of displacement in (1,0) direction. $Curve(4)
$Curve
(2): constrains mov x.
$Curve
(1): constrains mov y.
|
Analysis Assumption and
Modeling Notes
Solid 2D plane
strain. Mesh controls: Edge length, quadrangle and edge sizes 1 m.
Structure starts plasticizing:
In the 4th step, structure has
not started plasticizing. 
In the 5th step, structure
starts plasticizing. 
In step 13 ŕ
TRANSIENT
VCF_1_3_00_00_00_03_001
Description: (SIMPLY
SUPPORTED BEAM SUBJECTED TO DYNAMIC LOADS)
|
Reference:
|
Biggs, J.M. Introduction to structural dynamics, McGraw-Hill
Book Co., New York, 1964, p. 50, Example E.
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_00_00_03_001.xcf
|
A steel beam is subjected to dynamic loads. The
weight is assumed to be zero. Determine the time at which the maximum
deflection occurs.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=30x106 psi
|
L=240 in
Mass=25.9067 lbf x sec2/in
Section depth: H=18 in
I=800.6 in4
|
See picture
|
Left support: Constrain
DY
Right support: Constrain
DY and DX
|
Two beam elements are used, with 30 elements each. A mass model util
is used to simulate the mass of the problem, and a transient load table is
defined.
VCF_1_3_00_00_02_04_001
Description: (Transient
response tower structure with harmonic load).
|
Reference:
|
Paz, Mario, Structural Dynamics ; Theory and
Computation, 3rd Edition, Van Nostrand Reinhold, New York, 1991, pages 84 to
87, Ex. 4.5
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
Key words:
|
Beam 2D,Harmonic Load, Generic Section, Lumped Mass, Step
fraction, Damping.
|
|
File:
|
VCF_1_3_00_00_02_04_001.xcf
|
Perform a time history analysis for a steel tower structure
subjected to a lateral harmonic excitation force applied at its top for 0.30
sec.
Determine the maximum lateral displacements respect
to time at t1 =0.1 sec, t2 = 0.2 sec, t3 = 0.3
sec.
The steel tower structure is modeled as a beam
element with rectangular equivalent flexural stiffness. A lumped mass is
located at the top of the structure.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2.0 × 107 psi
|
h = 100 inch.
Iyy = 1666.667 in4
|
Po = 100000 lbf
M = 100 lbf ⋅ sec2/in
ωF= 30.0 rad/sec
ξ = 0 (damping)
|
Node 1: u=v=0
θz =
0
Node 2: Free.
|
Analysis
Assumption and Modeling Notes
Modeled
with generic section. Use all the same step fraction to 0.01.
; 
; 
VCF_1_3_00_00_04_01_001
Description: (DEEP
SIMPLY SUPPORTED BEAM: TRANSIENT FORCED VIBRATION)
|
Reference:
|
NAFEMS Selected Benchmarks for Forced Vibration, R0016, March
1993, Test 5T
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_00_04_01_001.xcf
|
A suddenly applied transverse step load is applied to the beam and
the transient response is analyzed.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=200 Gpa
ν=0.3
Density=8000 kg/m3
|
L=10 m
Square section: 2m x 2m
|
A suddenly applied force
in all the beam of 1 MN/m value.
|
Left support: Constrain
all DF.
Right support: Constrain
Y movement
|
Analysis
Assumption and Modeling Notes
A beam element is used, with 20 elements. A transient load table is
defined, with an application time of 0.004 s for the force.
VCF_1_3_00_00_04_04_001
Description: (TRANSIENT
RESPONSE OF A SPRING-MASS SYSTEM WITH VISCOUS DAMPING)
|
Reference:
|
W.T. Thomson, Vibration Theory and Applications, 2nd
Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg.102, ex. 4.3.
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_00_04_04_001.xcf
|
A spring-mass system with viscous damping, initially at rest, is
subjected to a force N acting on the mass. Determine the maximum displacement v
at time t for the following damping ratios:
▪
ξ=0
(undamped)
▪
ξ=0.5
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
m = 0.5 lb sec2/in
k = 200 lb/in
|
Arbitrary
|
N = 200 lb
|
Node 2: u=v=0
Node 4: u=v=0
|
The spring has to be associated with a
structural element such a beam of massless generic section. The damping coefficient
c is calculated as c =2
. The maximum time
of 0.205 sec for de load case allows the masses to reach their largest
displacements. The step fraction time 0.0025 sec (T/120) allow to follow the
acceleration change for the theoretical comparison. The plot option Time plot
is used to show the displacement over time.
; ω
= 
; f = 
;
;
VCF_1_3_00_00_04_04_002
Description: (TRANSIENT
RESPONSE OF A SPRING-MASS-DAMPER SYSTEM WITH INITIAL DISPLACEMENT)
|
Reference:
|
W.T. Thomson, Vibration Theory and Applications, 2nd
Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg.41, ex. 2.2-1
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_00_04_04_002.xcf
|
A spring-mass system with viscous damping is initially held at rest
at the position Δ and then released. Determine
the displacement v at time t for the following damping ratios:
▪
ξ=2
▪
ξ=1
(critical)
▪
ξ=0.2
▪
ξ=0
(undamped)
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
w = 10 lb
m = w/g ≈ 0.026 lb sec2/in
k = 30 lb/in
|
Arbitrary
|
Initial Force N = 30 lb
g = 386 in/s2
|
Node 1, 3, 5, 7: u=v=0
|
The spring has to
be associated with a structural element such a beam of massless generic
section. The damping coefficient c is calculated as c =2 . The equivalent of
a displacement Δ is calculated as an
initial force kΔ = 30 lbs. The maximum time of
0.095 sec for de load case covers about ˝ the period. The step fraction time
0.001 sec (T/180) allow to follow the acceleration change for the theoretical
comparison.
; ω
= ; f = ;;
The plot option Time
plot is used to show the displacement over time.
VCF_1_3_00_00_04_04_003
Description: (TRANSIENT
ANALYSIS OF A SPRING-MASS SYSTEM WITH LOAD FUNCTION)
|
Reference:
|
R. K. Vierck, Vibration Analysis, 2nd Edition, Harper &
Row Publishers, New York, NY, 1979, sec. 5-8
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_00_04_04_003.xcf
|
A system containing two masses, m1 and m2, and two springs of
stiffness k1 and k2 is subjected to a pulse load F(t) on mass 1. Determine the
displacement response of the system for the load history shown.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
m1 = m2
=2.0 kg
k1 = 6.0 N/m
k2 = 16.0 N/m
|
Arbitrary
|
Fo = 50 N
(view graph)
td =1.8 sec.
|
u=v=ϕz=0
|
Load Function F(t)
The response of the
system is examined for an additional 0.6 seconds after the load is removed.
The displacements
are obtained with 0.010 s as time step.
ω = 
; f = 
;
;
The plot option Time plot is used to show
the displacement over time.
VCF_1_3_00_02_04_04_001
Description: (SIMPLY
SUPPORTED THIN SQUARE PLATE; TRANSIENT FORCED VIBRATION)
|
Reference:
|
Maguire, J., Dawswell, D.
J., & Gould, L. (1989). Selected
benchmarks for forced vibration. NAFEMS. Test 13-T
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_02_04_04_001.xcf
|
A square plate (E=200000MPa, ν=0.3, r=8000kg/m3) has
a length of 10m and is subjected to a suddenly applied pressure F0=100
N/m2 over the whole plate.
The damping factors are chosen as aR = 0.299 sec1 and bR= 1.339ž103 sec so that:
The edges of the plate are simply supported, and ux, uy
,qz = 0 at all nodes. Calculate the peak displacement and stress at
the center of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 200000MPa
ν=0.3
r = 8000kg/m3
ξ=2%
aR = 0.299 sec1
bR= 1.339ž103 sec
|
L=10m
t=0.05m
|
F0 =100N/m2
|
ux= uy
=θz =0 at all nodes
θx=0 along edges 1 and 3
θy=0 along edges 2 and 4
|
A shell element is modeled with a
quadrangle mesh type. The calculation time of the load case used is 0.5 sec.
The initial, minimum and maximum time step selected in the Global solution
controls is 0.02 so you obtain 50 result files. The peak result occurs in the
step nş 21 (0.21 sec)
VCF_1_3_00_02_04_04_002
Description: (SIMPLY
SUPPORTED THICK SQUARE PLATE; TRANSIENT FORCED VIBRATION)
|
Reference:
|
Maguire, J., Dawswell, D.
J., & Gould, L. (1989). Selected
benchmarks for forced vibration. NAFEMS. Test 21-T
|
|
Analysis
Type(s):
|
Transient
Analysis
|
|
File:
|
VCF_1_3_00_02_04_04_002.xcf
|
A square plate (E=200 GPa, ν=0.3, r=8000kg/m3) has
a length of 10m and is subjected to a suddenly applied pressure F0=1
MN/m2 over the whole plate.
The damping factors are chosen as aR = 0.299 sec1 and bR= 1.339ž103 sec so that:
The edges of the plate are simply supported, and ux, uy
,qz = 0 at all nodes. Calculate the peak displacement and stress at
the center of the plate.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 200 GPa
ν=0.3
r = 8000kg/m3
ξ=2%
aR = 0.299 sec1
bR= 1.339ž103 sec
|
L=10m
t=1m
|
F0 =1 MN/m2
|
ux= uy
=θz =0 at all nodes
θx=0 along edges 1 and 3
θy=0 along edges 2 and 4
|
A shell element is modeled with the
quadrangle mesh type. The calculation time of the load case used is 0.13 sec.
The initial, minimum and maximum time step selected in Global solution
controls is 0.005 so 200 result files are obtained. The peak result
occurs in step nş 17
VCF_1_3_01_01_02_01_001
Description: (CLAMPED
BEAM SUPPORTED BY A CABLE)
|
Reference:
|
INGECIBER
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_1_3_01_01_02_01_001.xcf
|
A steel beam is subjected both to static and dynamic
loads. The weight is assumed to be zero. Determine the beam
displacement.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=2.1414E10 Pa
|
L=240 in
Column section= 0.2 m
Cable section= 0.05 m
|
q= 1t
Vq= 5 m/iq
Step=5
Load Case (Time)= 2 iq
|
ux= uy
=θz =0
|
Two beam
elements are used, with 30 elements each.
Beam
section:
Cable
section:
MODAL ANALYSIS
VCF_1_1_00_00_00_02_001
Description: (BEAM
MASS MODAL ANALYSIS USING SECTIONS WITH DIFFERENT MECHANICAL PROPERTIES)
|
Reference:
|
Any basic dynamics text book
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_00_01_002.xcf
|
Determine the natural frequency of two vibration modes of four
cantilevers with different mechanical properties (Gross, Net, Homogenized, and
User concrete section) with a point mass at its end.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
Ec = 3.2x106 MPa
Es = 2.1x105 MPa
Density (ρ) = 0 kg/m3
|
l = 10 m
b=0.3m;h=0.4m
As=0.02m2
Net Section:
Area = 0.10 m2;
Inertia (Ix) =0.00106m4
Gross Section:
Area = 0.12 m2;
Inertia (Ix)=0.00160m4
User Section:
Area = 0.125 m2;
Inertia (Ix)=0.00270m4
Homogenized Section:
Area = 0.225 m2;
Inertia (Ix) =0.00287m4
|
Mass (m) =1 Kg
|
Node 1: u=v=θ=0
|
The cantilever is
modeled as 2D beam in a structural modal analysis.
ω = ; f = ; 
VCF_1_1_00_00_02_00_001
Description: (Natural
Frequency of a Spring-Mass System).
|
Reference:
|
Any basic dynamics text book
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_02_00_001.xcf
|
An instrument of weight W is set on a rubber mount
system having a stiffness k. Determine its natural frequency of vibration T.
|
Material
|
Geometry
section pipe
|
Loading
|
Boundary
Condition
|
|
E = 1*10-6
psi
Density = 1*10-6 psi
Steel Fe360.
k (spring) = 48 lb/in
|
Outer Diameter = 0.1
inch.
Wall thickness = 0.05
inch.
|
W = 2.5 lb
|
In point 1: Mov. X =
Mov. Y= 0.
In Point 2: Mov. X= 0.
|
The
spring length is arbitrarily selected. The density and the elastic modulus of
the material become practically zero to not affect the mass and stiffness of
the system. Beam structural element should be modeled with a single element.
The weight of the lumped mass element is divided by gravity in order to obtain
the mass. Mass = W/g = 2.5/386 = 0.006477 lb-sec2/in
VCF_1_1_00_00_02_01_001
Description: (Natural
Frequency of a Spring-Mass System of two degree of freedom).
|
Reference:
|
Any dynamics text book
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_02_01_001.xcf
|
Calculate the two first natural frequencies of vibration of the
following mass spring system.
|
Material
|
Geometry section cable
|
Loading
|
Boundary
Condition
|
|
E = 210000 MPa
Density=  Kg/m3.
K1 = 1.0 N/m
K1 = 1.0 N/m
|
Outer Diameter = cm
|
m1 = 1.0 kg
m2 = 1.0 kg
|
1: Mov.X= Mov.Y = Rot.Z
= 0.
2: Mov. Y= 0.
3: Mov. Y= 0.
|
1
2
3
Analysis
Assumption and Modeling Notes
The
density and the cable cross section of the material become practically zero to
not affect the mass and stiffness of the system.
;
VCF_1_1_00_00_02_01_002
Description: (VIBRATION
MODES OF A THIN PIPE ELBOW)
|
Reference:
|
NAFEMS Selected
Benchmarks for Forced Vibration, R0016, March
1993. Test 5H.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_02_01_002.xcf
|
This test is a modal analysis of a straight cantilever beam, and a
thin curved beam.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=2.1x1011 Pa
ν=0.3
Density=7800 kg/m3
|
L=0.6 m
Section=Tubular with di=0.016m,
de=0.020m.
Radius=1 m
|
N/A
|
Clamps at C and D,
supports at A and B.
|
Analysis
Assumption and Modeling Notes
Beam structural elements with 10 subdivisions are used. A pipe steel
section is defined and Fe360 is used as material.
VCF_1_1_00_00_04_01_001
Description: (EIGENVALUE
ANALYSIS OF A SLIM CIRCULAR RING FIXED BY 2 POINTS)
|
Reference:
|
P. Dellus, Résistance de matériaux, Paris, Technique and
Vulgarisation, 1958.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_01_001.xcf
|
This test is a modal analysis of a slim circular ring. 3
frequencies will be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=7.2x1010 Pa
ν=0.3
Density=2700 kg/m3
|
L=0.6 m
Section=Rectangular 0.010 m x 0.005
m
Radius=0.1 m
|
N/A
|
Clamps at two points
separated 120 degrees.
|
A beam
structural element with 74 subdivisions is used. A rectangular section and a
generic material are defined.
VCF_1_1_00_00_04_01_002
Description: (In-plane
vibration of a pin-ended cross)
|
Reference:
|
NAFEMS Finite Methods & Standards.
Abbassian, F., Dawswelll, D. J. , and Knowles, N.C. Selected Benchmarks
for Natural Frequency Analysis, Test Nş1. Glasgow: NAFEMS, Nov.,
1987.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_01_002.xcf
|
Find the first eight modes of natural frequency in a modal analysis of a pin-ended cross, by using beam elements.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=200e9 Pa
ν = 0.29
ρ = 8000 kg/m3
G=8.01e10 Pa
|
L= 5.0 m
a=b=0.125m
|
|
A,B,C,D: x = y =0
OA,OB,OC,OD: z=0; θx= θy= 0
|
Analysis
Assumption and Modeling Notes
One beam element per leg is modeled. Each beam is divided in four
elements.
VCF_1_1_00_00_04_04_001
Description: (BEAM
MASS MODAL ANALYSIS)
|
Reference:
|
Any basic dynamics text book
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_001.xcf
|
Determine the natural frequency and period of the first mode of
vibration of a cantilever subjected to a punctual mass at its end.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2.1x105 MPa
Density (ρ) = 0 kg/m3
|
l = 1 m
Area (A) = 10 cm2
Inertia y axis (Iz) = 83.33 cm4
|
Mass (m) =10 Kg
|
Node 1: u=v=θ=0
|
Analysis
Assumption and Modeling Notes
The cantilever is modeled as 2D beam in a
structural modal analysis. The first mode is used to analyze the results.
; ω = ; f = ;
VCF_1_1_00_00_04_04_002
Description: (Cantilever
with Off-Center Point Masses)
|
Reference:
|
National Agency for Finite Elements
Methods and Standards (U.K.): Test FV4 from NAFEMS publication TNSB, Rev.3,
The Standard NAFEMS Benchmarks, October 1990.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_002.xcf
|
A cantilever beam located horizontally with two
off-center lump masses of M1 = 10000 kg and M2 = 1000 kg
at right free ends. The beam is constrained in all DOFs at left end. Frequency
vibration analysis is performed on the model. Calculate the first six vibration
frequencies.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E1 = 2∙1011
Pa
ρ1= 8000 kg/m3
ν1= 0.3
E2 = 1∙1016
Pa
ρ2= 0 kg/m3
ν2= 0
|
D1
(diameter)= 0.50 m
L1 (length) =
10.0 m
D2
(diameter)= 2.0 m
L2 (length) =
4.0 m
|
M1(Lump
Mass)= 10000kg
M2 (lump
mass)= 1000 kg
|
Beam 1 (extreme
node): u=v=w=0
θx = θy
= θz = 0
|
Each
cantilever is modeled with generic material section, and beam 3D elements.
The
nodes shared by both beams must remain merged.
The
reference solution provided by the National Agency for Finite Elements Methods
and Standards (U.K.): Test FV4 from NAFEMS publication TNSB, Rev.3, The
Standard NAFEMS Benchmarks, October 1990.
VCF_1_1_00_00_04_04_003
Description: (Fundamental
Frequency of a Simply Supported Beam)
|
Reference:
|
W. T. Thomson, Vibration Theory and Applications,
2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 18, ex.
1.5-1
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_003.xcf
|
Determine the fundamental frequency of a simply-supported beam of
length ℓ with uniform cross-section as shown below.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30 x
106 psi
|
|
w = 1.124 lb/in
ρ = 0.000728 lb-sec2/in4
|
|
|
|
|
ℓ = 80 in
A = 4 in2
h = 2 in
I = 1.3333 in4
|
|
|
|
|
g = 386
in/ sec2
|
Node 1:
u=v=0
Node 2: u
=v=0
|
Three lateral master degrees of freedom are
selected.
VCF_1_1_00_00_04_04_004
Description: (Cantilever
Beam Modes and Frequencies).
|
Reference:
|
Huang, T. C.,
The Effect of Rotary Inertia and Shear Deformation on
the Frequency
and Normal Modes of Uniform Beams with Simple End
Conditions,
J. Applied Mechanics., Vol. 28, pp. 279-584 (December1961).
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_004.xcf
|
This problem is an illustration of the use of the
Timoshenko beam element. The first three modes of a square-section, cantilever
beam are extracted.
No load is imposed, since only modes and frequencies
are calculated.
All displacements and rotations are fixed.
|
Material
|
Geometry
section pipe
|
Loading
|
Boundary
Condition
|
|
E = 3*10-7
psi
Density (ρ) = 7.25*10-4
lbfˇsec2/in4
ν = 0.333
g = 386 in/ sec2
|
b= 1 inch.
h= 1 inch.
|
|
In node 1: u = v = φ= 0
|
Such elements are most commonly
used in dynamic problems, because of the importance of shear and rotational inertia
effects in high-frequency beam response. This particular example is chosen
because an exact Timoshenko beam solution is available.
To create the model is preferable
to use materials and generic section.
VCF_1_1_00_00_04_04_005
Description: (EIGENVALUE
ANALYSIS OF A SIMPLY SUPPORTED SHAFT)
|
Reference:
|
J. P. Den Hartog, Mechanical
Vibrations, 4th Edition, McGraw-Hill, New York, 1956, p. 432.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_005.xcf
|
This test is a modal analysis of a beam. 6 frequencies will
be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=30x106 psi
|
L=100 in
Section=Tubular with Ri=1
in, t=0.05 in.
|
Weight Dens=7.764x10-4
lbf x sec2/in4
g=1 in/sec2
|
Simple supports at both
ends.
|
A beam
structural element with 20 subdivisions is used. A tubular section and a
generic material are defined.
VCF_1_1_00_00_04_04_006
Description: (Natural
frequencies of a two-mass-spring system)
|
Reference:
|
W. T. Thomson, Vibration Theory and
Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965,
pg. 163, ex. 6.2-2.
|
|
Analysis Type(s):
|
Modal Analysis 2D
|
|
File:
|
VCF_1_1_00_00_04_04_006.xcf
|
Determine the first two natural frequencies of the system shown
below for the values of the masses and spring stiffnesses given.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
k1
= k2=200 lb/in
kc
= 4k1 = 800 lb/in
|
|
m2
= 2m1 = 1.0 lb-sec2/in
|
Node 1:
u=v=w=θ=0
Node 2:
v=0
Node 3:
v=0
Node 4:
u=v=w=θ=0
|
The spring lengths
are arbitrarily selected and are used only to define the spring direction.
;
VCF_1_1_00_00_04_04_007
Description: (Ten-bay,
nine-story, two-dimensional frame. Modal analysis.)
|
Reference:
|
Large Eigenvalue Problems in Dynamic
Analysis, Journal of the Eng. Mech. Div., ASCE,
Vol. 98, No. EM6, Proc. Paper 9433, Dec. 1972. Bathe, K. J. and Wilson, E. L.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_007.xcf
|
Find the first two modes of natural frequency in a modal analysis of a ten-bay nine story two dimensional frame,
with clamped supports.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=4.32x105 ksf
ρ = 3 kip-sec2/ft/ft
|
Ten bay, nine story frame
Horizontal spacing=20 ft
Vertical spacing=10 ft
Area of section=3 ft2
Moment of inertia=1 ft4
|
|
All supports: x = y =0, z=0; θx= θy= 0, θz= 0
|
One beam element per arm is modeled. Each beam is divided in five
elements. The included python script that generates the model should be run in
a new 2D modal case. The script performs the complete modeling, meshing and
solving of the model.
VCF_1_1_00_00_04_04_008
Description: (PIN-ENDED
DOUBLE CROSS: IN-PLANE VIBRATION)
|
Reference:
|
Test FV2. NAFEMS publication TNSB, Rev.
3, The Standard NAFEMS Benchmarks, October 1990.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_00_04_04_008.xcf
|
A modal analysis of a beam net is performed. 10 frequencies
will be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=200 GPa
ν=0.3
Dens=8000 kg/m3
|
L=10 m.
Square section, l=0.125
m
|
N/A
|
Pins in A, B, C, D, E,
F, G, H.
|
Analysis
Assumption and Modeling Notes
Eight beam structural elements with 10 subdivisions are used. A
generic section and material are defined.
VCF_1_1_00_02_02_01_001
Description: (Modal
Frequencies of a rectangular Shell)
|
Reference:
|
Marc (Volume C, Exercise 6.15).
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_02_02_01_001.xcf
|
Determine the first four frequencies of a shell
section as shown below. The one end is completely
constrained to represent the cantilever boundary conditions. The other
end is simply supported at its midpoint.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 28 x
106 psi
ν =
0.32
ρ =
0.000755 lb-sec2/in4
|
|
Length (L) = 0.6 inch
Width (w)= 0.25 inch
Thickness (t) = 0.003
inch
|
|
|
|
|
g = 386
in/ sec2
|
Side
1: All constrained
Side
2: δx=δy=δz=0
|
Analysis
Assumption and Modeling Notes
It is modeled
using a 28x14 mesh of linear elements.
VCF_1_1_00_02_02_01_002
Description: (Modal
Frequencies of a rectangular Plate)
|
Reference:
|
Blevins, Formula for Natural Frequency
and Mode Shape, Van Nostrand Reinhold Company Inc., 1979, Table 11-4, Case
11, pg. 256.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_02_02_01_002.xcf
|
A rectangular shell is simply supported (linear
boundary conditions) on both the smaller edges and fixed on the longer edge as
shown below. Find the first five modes of natural frequency.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2.0 x 1011 Pa
|
|
ν = 0.3
ρ = 7850 kg/m3
|
|
|
|
|
Length (L) = 0.25 m
Width (W)= 0.10 m
Thickness (t) = 0.005
m
|
|
|
|
|
g = 9.81 m/s2
|
Side 1 (longer edge):
All constrained.
Side 2 =Side 3: (smaller
edges): Only constrained δz (vertical).
|
Element size of
6.5 mm is applied on all the edges to get accurate results.
The first five natural
frequencies of the plate are described by the following equations:
f = dimensionless parameter associated with
the mode indices i, j.
i = number of half-waves in this mode shape
along the horizontal axis.
j = number of half-waves in this mode shape
along the vertical axis.
ν = Poissons ratio.
E = elastic modulus.
t = plate thickness.
γ = mass of material per unit area.
L = length of plate
W = width of plate
VCF_1_1_00_02_02_01_009
Description: (MODAL
ANALYSIS OF A CANTILEVER CYLINDRICAL VAULT)
|
Reference:
|
AFNOR (1990), Guide de Validation des Progiciels de
Calcul de Structures, SFM, Afnor Technique, France.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_02_02_01_009.xcf
|
A modal analysis of a cantilever vault, fixed at one end is
performed. 6 frequencies will be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=2.0658x105
MPa
ν=0.3
Dens=7.857x103
tf/m3
|
L=0.3048
m.
Angle=0.5
rad
Thickness=3.048x10-3
m
|
N/A
|
One side
is clamped.
|
A shell structural element is used, with a length of 0.01 m per
element.
VCF_1_1_00_02_04_01_001
Description: (MODAL
ANALYSIS OF A CANTILEVER PLATE)
|
Reference:
|
Harris, C. M. and Crede, C. E., Shock
and Vibration Handbook, McGraw-Hill, 1976
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_02_04_01_001.xcf
|
A modal analysis of a shell is performed. 5 frequencies will
be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=29.5x103
ksi
ν=0.3
Dens=2.835648x104
kips/in3
|
Square
plate, side=24 in.
Thickness=1.0
in
|
Gravity
|
Lower
side is clamped, all plate has constrains in X, Y directions and Z rotation
|
A shell structural element is used, using 19 divisions per side.
VCF_1_1_00_02_04_01_003
Description: (VIBRATION
OF A WEDGE)
|
Reference:
|
S. Timoshenko, D. H. Young, Vibration
Problems in Engineering, 3rd Edition, D. Van Nostrand Co., Inc., New York,
NY, 1955, pg. 392, article 62.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_02_04_01_003.xcf
|
A modal analysis of a triangular shell, fixed at its base is
performed. 1 frequency will be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=3x106 psi
ν=0
Dens= 0.000728 lb-sec2/in4
|
Triangle:
H=16 in
Semi Base (b) = 2 in
Thickness=1 in
|
N/A
|
Base is clamped.
|
A shell
structural element is used, with an edge size of 2 in.
VCF_1_1_00_02_04_01_004
Description: (THIN
RING PLATE CLAMPED ON A HUB)
|
Reference:
|
Societe Francaise des Mecaniciens. Guide de validation des
progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.
SDLS04/89.
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_00_02_04_01_004.xcf
|
A modal analysis of a thin ring plate clamped on a hub fixed at its
base is performed. 13 frequencies will be obtained.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E=2x1011
Pa
ν=0.3
Dens= 7800
kg/m3
|
Ring: Re=0.1 m
Ri=0.2 m
Thickness=0.01 m
|
N/A
|
Inner border of ring is clamped.
|
A 500 quadrangle shell structural element is used.
VCF_1_1_01_01_02_01_001
Description: (Modal
cable verification).
|
Reference:
|
Any dynamics text book
|
|
Analysis Type(s):
|
Modal Analysis
|
|
File:
|
VCF_1_1_03_01_04_04_001.xcf
|
This cable is submitted to a displacement in one end,
in which a punctual 75000 lbf load is applied. Calculate both the
nominal frequency and the elongation.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2ˇ104 N/m2
ρ = 8027.127 kg/m3
ν = 0
A= 0.5 m2
|
L= 120 m
|
P = 75000 lbf
|
Node 1: u=v=0
Node 2: v=0
|
Add a punctual displacement in end node equivalent to axial force
(P).
VCF_1_1_03_01_04_04_001
Description: (Vibrations
of a Truss).
|
Reference:
|
Any dynamics text book
|
|
Analysis Type(s):
|
Modal Analysis 2D
|
|
File:
|
VCF_1_1_03_01_04_04_001.xcf
|
The first two modal frequencies are computed for a
straight flexible and circular cable under tension.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 2.1ˇ1011 N/m2
ρ = 84.969 kg/m3
ν = 0.3
|
Radius (r) = 8.992 mm
L= 96.5 m
|
P = 49050 N
|
In node 1: u = v = φ= 0
 = 88.739 mm.
|
12 12
P
1
1
L
L 
Analysis
Assumption and Modeling Notes
Add a punctual displacement in end node equivalent to
axial force (P).
The mesh has 11 elements and 12 nodes.
The large deflections option is used to ensure that the
eigenmodes will include the effect of the stress stiffening induced by the
equivalent displacement.
The analytical formula for the
modal frequencies of a prestressed cable is (n = number of mode):
VCF_1_2_00_00_04_04_001
Description: (HARMONIC
RESPONSE OF A TWO-MASS-SPRING SYSTEM)
|
Reference:
|
W. T. Thomson, Vibration Theory and
Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965,
pg. 178, ex. 6.6-1.
|
|
Analysis Type(s):
|
Harmonic Analysis
|
|
File:
|
VCF_1_4_00_00_04_04_001.xcf
|
A two mass, two spring system is considered, with a
harmonic load of 200 lb mass applied in the leftmost mass. The X-displacements
at several frequencies are calculated.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
N/A.
|
m1=m2=lib-sec2/in
k1=k2=kc=200
lb/in
|
F=200 lb
|
Clamps at both ends.
|
Analysis
Assumption and Modeling Notes
As we need to model structural elements for defining the springs, a
fictitious material and structural elements are used.
VCF_1_2_00_00_04_04_002
Description: (DEEP
SIMPLY SUPPORTED BEAM: HARMONIC FORCED VIBRATION)
|
Reference:
|
NAFEMS Selected Benchmarks for Forced
Vibration, R0016, March 1993. Test 5H.
|
|
Analysis Type(s):
|
Harmonic Analysis
|
|
File:
|
VCF_1_2_00_00_04_04_002.xcf
|
A harmonic linear load is applied to the whole beam
shown in the figure. Frequencies and peak displacements are calculated.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=200 GPa
ν=0.3
Density=8000 kg/m3
|
L=10 m
Section=2x2 m
|
F= 1MN/m with
frequencies from 40 Hz to 45 Hz
|
Left side: Clamp.
Right side: Simple
support, x-disp unrestrained.
|
A generic
section and material are used. Meshing is performed with a beam structural
element with 20 subdivisions.
VCF_1_2_00_02_04_04_001
Description: (SIMPLY
SUPPORTED THIN SQUARE PLATE; HARMONIC FORCED VIBRATION)
|
Reference:
|
Maguire,
J., Dawswell, D. J., & Gould, L. (1989). Selected benchmarks for forced
vibration. NAFEMS.
Test 13-H
|
|
Analysis Type(s):
|
Harmonic Analysis
|
|
File:
|
VCF_1_2_00_02_04_04_001.xcf
|
A square plate has a length of 10m and is subjected to and harmonic
load function: F=F0 sin (ωt), with F0
=1 00 N/m2 over the whole plate:
ω = 2πf
f= 0 to 4.16 Hz.
The damping factors ξ=2%
The edges of the plate are simply supported, and ux, uy
,qz = 0 at all nodes. Calculate the peak displacement and stress at
the center of the plate and the frequency at which these peaks occur.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 200000MPa
ν=0.3
r = 8000kg/m3
ξ=2%
|
L=10m
t=0.05m
|
F=F0 sin (ωt)
F0 =100N/m2
ω = 2πf
f= 0 to 4.16 Hz.
|
ux= uy
=θz =0 at all nodes
θx=0 along edges 1 and 3
θy=0 along edges 2 and 4
|
A shell element is modeled with a
quadrangle mesh type (edges size 500mm). The load type is harmonic. The number
of frequencies tested is 50, between 0 to 4.16 Hz.
VCF_1_2_00_02_04_04_002
Description: (SIMPLY
SUPPORTED THICK SQUARE PLATE; HARMONIC FORCED VIBRATION)
|
Reference:
|
Maguire,
J., Dawswell, D. J., & Gould, L. (1989). Selected benchmarks for forced
vibration. NAFEMS.
Test 21-H
|
|
Analysis Type(s):
|
Harmonic Analysis
|
|
File:
|
VCF_1_2_00_02_04_04_002.xcf
|
A square plate has a length of 10m and is subjected to and harmonic
load function: F=F0 sin (ωt), with F0
=1 MN/m2 over the whole plate:
ω = 2πf
f= 0 to 78.17 Hz.
The damping factors ξ=2%
The edges of the plate are simply supported, and ux, uy
,qz = 0 at all nodes. Calculate the peak displacement and stress at
the center of the plate and the frequency at which these peaks occur.
|
Material
|
Geometry
|
Loading
|
Boundary Condition
|
|
E =
200000MPa
ν=0.3
r = 8000kg/m3
ξ=2%
|
L=10m
t=1m
|
F=F0
sin (ωt)
F0
=100N/m2
ω =
2πf
f= 0 to
78.17 Hz.
|
ux= uy =θz =0 at all nodes
θx=0 along edges 1 and 3
θy=0 along edges 2 and 4
|
A shell element
is modeled with a quadrangle mesh type (edges size 500mm). The load type is
harmonic. The number of frequencies tested is 50, between 40 to 60 Hz, as the
first modal frequency is around 50Hz
VCF_1_0_03_00_00_01_001
Description: (non-linear
buckling in concrete material)
|
Reference:
|
Ingeciber, S.A.
|
|
Analysis Type(s):
|
Buckling non-linear Analysis
|
|
File:
|
VCF_1_0_03_00_00_01_001.xcf
|
A beam is subjected to a P load in a buckling analysis. Calculate
the tension which makes the structure buckle in the outers section´s point.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
C45/55
E28=
|
L=10m.
e=0.10 m
|
P
|
u=v=w=0
θx=θy=θz=0
|
This beam is
modeled with 10 elements. Its section is a hole circular one.
The
deformed mesh, in buckling, is added to the static analysis. 
A P=163 is checked for the static analysis.
VCF_1_4_00_00_00_01_001
Description: (Buckling
Analysis Column)
|
Reference:
|
S. Timoshenko, J. M. Gere, Theory of
Elastic Stability, 2nd Edition, McGraw-Hill Book Co. Inc., New York, NY,
1961, pg. 78, article 2.7.
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_00_00_01_001.xcf
|
A slender square cross-sectional column of length L,
and dimensions bxh, is fixed at the base and free at the upper end. Determine
the critical buckling load in the first mode.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30*106 psi
|
h(height) = 0.5 in
b(width) = 0.5 in
L = 100 in
|
F (vertical load applied
in node 11).
|
Node 1: u=v=w=0
θx =
θy = θz = 0
|
The
column was modeled with ten elements. The number of modes that will be
extracted is one.
The
critical force, Fcr = 38.553 lb is used for calculation of the
applied load F.
VCF_1_4_00_00_04_01_001
Description: (BUCKLING
ANALYSIS OF A COLUMN)
|
Reference:
|
Gere & Timoshenko Mechanics of
Materials Chapter 11
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_00_04_01_001.xcf
|
Determine the buckling modes and the corresponding critical loads of
a column subjected to a vertical load with various boundary conditions: Pin-roller,
fixed-free, fixed-laterally guided, fixed-roller.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 10000 tonf/m2
|
L=15m
Section: Solid rectangular 0.25m x
0.25m
|
|
Pin-roller
Fixed-free
Fixed-laterally guided
Fixed-roller
|
A beam element
with 40 subdivisions is used. A generic material and section are defined and
four load cases are calculated, one for each boundary condition.
VCF_1_4_00_00_04_04_001
Description: (2D
linear buckling of a portal frame)
|
Reference:
|
Fundamentos para el cálculo y diseńo de estructuras
metálicas de acero laminado. Jaime Marco García. McGraw Hill. 1998. Página
624.
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_00_04_04_001.xcf
|
Calculate the buckling load of a portal frame, whose foundations are
all constrained degrees of freedom, with constant section and material
throughout the structure (columns and beams), with columns loaded with an axial
force P.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 210.000 MPa.
Density = 7.850 kg/m3
Poisson ratio = 0,3
|
Inertia Iy = 6,70133e-05 m4.
Inertia Iy = 6,70133e-05 m4.
Area = 1.0 m2.
L = 6 m.
|
P = 1,0 Kgf.
|
Node 1: u=v=0
θz =
0
Node 2: u=v=0
θz =
0
|
Ignore
the effects of axial deformation (with the cross sectional area of 1 m2
is sufficient).
Each of the structural elements (beams and columns) is modeled with
60 elements, with generic material and section.
Stiffness
matrix of the structure: Ks =
EI / L3 
- P / L 
= EI / L3 
with 
;
Solving
the eigenvalue problem associated with the above.
Matrix:
1.080
3 4.596λ2 + 5.136λ 1.008 = 0 ; λ1 = 0.248 ; Pcri =
0.248 ˇ30 EI / L2 = 7.44 EI / L2
VCF_1_4_00_02_02_01_001
Description: (PLASTIC
BUCKLING OF AN EXTERNALLY PRESSURIZED HEMISPHERICAL DOME)
|
Reference:
|
MSC Marc documentation. Volume E, problem 3.16.
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_02_02_01_001.xcf
|
A dome structure is analyzed to obtain its buckling
load factor. The model used is a hemispherical dome with a radius of 100 inches
and a thickness of 2 inches which is clamped at the edge. The material is
elastic-plastic, with a Youngs modulus of 21.8 x 106 psi, a
Poissons ratio of 0.32 and a yield stress of 20,000 psi.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E =21.8 x 106 psi
ν=0.32
Yield Stress=20.000 psi
|
R=100 in
Thickness=2 in
|
Superficial load: -540 psi
|
Clamped at edge.
|
A shell element is used, and only ź of the
hemispherical dome is modelled.
VCF_1_4_00_02_02_01_002
Description: (LATERAL
BUCKLING OF A SIMPLY SUPPORTED CRUCIFORM COLUMN SUBJECTED TO A CONCENTRIC AXIAL
LOAD)
|
Reference:
|
Timoshenko, S.P., and Gere, J.M., (1961).
Theory of Elastic Stability, McGraw-Hill, New York
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_02_02_01_002.xcf
|
A simply supported cruciform column consisting of narrow rectangular
fins undergoes a vertical load P applied at the centroid of the top end. The
buckling load factor is determined. The computed buckling load is then compared
with the analytical exact solution.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E =200 kN/mm2
ν=0.25
|
L=3 m
Cruciform shape,
thickness 6 mm, width 300 mm.
|
F=1 kN
|
Bottom end is pinned,
and top end is roller.
|
Four shell elements are used, with 40 by 4
division each.
VCF_1_4_00_02_02_01_003
Description: (LATERAL
BUCKLING OF A SIMPLY SUPPORTED RIGHT-ANGLE FRAME SUBJECTED TO BENDING MOMENTS
AT BOTH ENDS)
|
Reference:
|
Timoshenko, S.P., and Gere, J.M., (1961).
Theory of Elastic Stability, McGraw-Hill, New York
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_02_02_01_003.xcf
|
A simply supported right-angle frame is subjected to bending moments
M applied at the centroids of its ends. The buckling load factor is determined.
The computed buckling load is then compared with the analytical exact solution.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E =71240 N/mm2
ν=0.31
|
L= 240 mm
T= 0.6 mm
W=15 mm
H=15 mm
|
M=1 N x mm
F=1/30 N
|
Left end is pinned, and
right end is roller.
|
A shell element is used, with a total of 64
elements. The loads are modelled using two pair of punctual loads applied at
each end of the shell
VCF_1_4_00_02_04_01_001
Description: (BUCKLING
OF A CYLINDER TUBE)
|
Reference:
|
MSC Marc documentation. Volume E, problem 4.15.
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_02_04_01_001.xcf
|
The buckling load factors of a cylinder tube
subjected to a lateral load at one end of the tube are calculated. A horizontal
punctual load of 100 N is applied at the lower node and the nodes on the high
end of the tube are fixed.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E=3630 N/mm2
ν=0.3
|
L= 600 mm
T=1 mm
R=100 mm
|
N=100 N
|
Top ring is fixed.
|
Two shell
elements are used, one for the cylinder and one for the lower cone. The lower
cone is used to transmit the load to the cylinder, so its E is high to exclude
any collateral effects on the whole model.
VCF_1_4_00_02_04_01_002
Description: (BUCKLING
ANALYSIS OF A COLUMN)
|
Reference:
|
Gere & Timoshenko Mechanics of
Materials Chapter 11
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_02_04_01_002.xcf
|
Determine the buckling modes and the corresponding
critical loads of a column subjected to a vertical load with various boundary
conditions: Pin-roller, fixed-free, fixed-laterally guided, fixed-roller.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 10000 tonf/m2
|
L=15m
Section: Solid rectangular 0.25m x
0.25m
|
|
Pin-roller
Fixed-free
Fixed-laterally guided
Fixed-roller
|
A shell element
with 240 subdivisions is used. A generic material and section are defined and
four load cases are calculated, one for each boundary condition.
VCF_1_4_00_02_04_01_003
Description: (LATERAL
BUCKLING OF A RECTANGULAR CANTILEVER BEAM SUBJECTED TO A LOAD AT THE TIP)
|
Reference:
|
Timoshenko, S.P., and Gere, J.M., (1961).
Theory of Elastic Stability, McGraw-Hill, New York
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_00_02_04_01_003.xcf
|
A cantilever beam with a narrow rectangular section
is loaded by a vertical load P applied at the centroid of the free end. One end
of the beam is fixed and the other end is free.
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E =108 lb/in2
ν=2/3
|
L= 20 in
Section=0.05 x 1 in
|
P=1 lbf
|
Left end is fixed, and
right end is free.
|
A shell element is used, with a total of
324 elements.
VCF_1_4_03_00_00_01_001
Description: (Large
Deflection of a Buckled Column)
|
Reference:
|
S. Timoshenko, J. M. Gere, Theory of
Elastic Stability, 2nd Edition, McGraw-Hill Book Co. Inc., New York, NY,
1961, pg. 78, article 2.7.
|
|
Analysis Type(s):
|
Buckling Analysis
|
|
File:
|
VCF_1_4_03_00_00_01_001.xcf
|
A slender square cross-sectional bar of length L, and
area A, fixed at the base and free at the upper end, is loaded with a value
larger than the critical buckling load. Determine the displacement (ΔX, ΔZ, q) of the free end and display the deformed
shape of the bar at various loadings (loads step 3, 4, 5 and 6).
|
Material
|
Geometry
|
Loading
|
Boundary
Condition
|
|
E = 30*106 psi
|
h(height) = 0.5 in
b(width) = 0.5 in
L = 100 in
|
F/Fcr = 1.015; 1.063; 1.152; 1.293;
1.518 and 1.884
|
Node 1: u=v=w=0
θx =
θy = θz = 0
|
A
small perturbing force (Fx=0.5 lb is applied to the head of the
column) is introduced in the first load step to produce lateral (rather than
pure compressive) motion. The number of equilibrium iterations for convergence
increases significantly as the loading approaches the critical load (i.e. for
solutions with q near zero). The column was modeled with ten elements.
The critical force, Fcr is used for
calculation of the applied load F.
VCF_
2_0_00_03_00_04_001
Description: (2D Solid.
Steady State analysis)
|
Reference:
|
W. M. Rohsenow, H. Y. Choi, Heat,
Mass and Momentum Transfer, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs,
NJ, 1963, pg. 106, ex. 6.5.
ANSYS: VM58
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_03_00_04_001.xcf
|
Determine the surface temperature Ts of a bare
steel wire generating heat at the rate q. The surface convection
coefficient between the wire and the air (at temperature Ta) is h.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 13 Btu/hr-ft-°F
h
= 5 Btu/hr-ft2-°F
|
ro = 0.375 in = 0.03125 ft
|
Ta =
70°F
q=
111311.7 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
Since
the problem is axisymmetric, only a small sector is needed an angle Θ= 30°
is used for modeling the circular sector. Four mesh divisions are chosen
radially for accuracy considerations. Temperatures of the outer nodes are
coupled to ensure symmetry. The solution is based on a wire 1 foot long (Z
direction). Postprocessing is used to determine Tc, Ts, and q.
Being the green surface the termal flux applied
over the surface whereas the blue line performs the film coefficient boundary
condition.
VCF_
2_0_00_03_00_04_002
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 166, article 7-9.
ANSYS: VM102
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_03_00_04_002.xcf
|
A long hollow cylinder is
maintained at temperature Ti along its inner surface and To along its
outer surface. The thermal conductivity of the cylinder material is known to
vary with temperature according to the linear function k(T) = C0 +
C1 T. Determine the temperature distribution in the cylinder for case:
|
Material
|
Geometry
|
Boundary
Conditions
|
|
C0 = 50 Btu/hr-ft-°F
C1 = 0.5 Btu/hr-ft-°F2
|
ri = 1/2 in = (1/24) ft
ro = 1 in = (1/12) ft
|
Ti = 100°F
To = 0°F
|
Analysis Assumption and Modeling Notes
The axial length of the model is
arbitrarily chosen to be 0.01 ft. Note that axial symmetry is automatically
ensured by the adiabatic radial boundaries.
Being the red points the temperature
boundary conditions for both edges.
The material is thermal dependent,
following the next thermal function according to the law previously described
k(T) = C0 + C1 T :
Grid
Chart
VCF_
2_0_00_03_00_04_003
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 193, article 8-8
ANSYS: VM105
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_03_00_04_003.xcf
|
A long hollow generator coil has its inner and outer surface
temperatures maintained at temperature To while generating Joule heat at a
uniform rate q. The thermal conductivity of the coil material varies with
temperature according to the function k(T) = C0 + C1 T. Determine the
temperature distribution in the coil.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
C0 = 10 Btu/hr-ft-°F
C1 = 0.075 Btu/hr-ft-°F2
|
ri = 1/4 in = (1/48) ft
ro = 1 in = (1/12) ft
|
To = 0°F
q = 1 x 106 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric only a
symmetry sector (one-element wide) is needed. A small angle (Θ=10°) is
used for approximating the circular boundary with a straight-sided element.
Adiabatic boundary conditions are assumed at the symmetry edges. The
steady-state convergence procedures are used. Note that this problem can also
be modeled using the axisymmetric option
Being the red points the temperature boundary
conditions for both edges and the green surface the applied thermal flux.
The material is thermal dependent,
following the next thermal function according to the law previously described
k(T) = C0 + C1 T :
Grid
Chart
VCF
_2_0_00_03_04_04_001
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
F. Kreith, Principles of Heat
Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg.
57, ex. 2-13.
ANSYS: VM98
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_2_0_00_03_04_04_001.xcf
|
A tapered rectangular stainless steel cooling fin dissipates heat
from an air-cooled cylinder wall. The wall temperature is Tw, the air
temperature is Ta, and the convection coefficient between the fin and the air
is h. Determine the temperature distribution along the fin and the heat
dissipation rate q.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 15 Btu/hr-ft-°F
h = 15 Btu/hr-ft2-F
|
b = 1 in = (1/12) ft
l = 4 in = (4/12) ft
|
Tw = 1100°F
Ta = 100°F
|
Analysis Assumption and Modeling Notes
The solution is based on a fin of unit
depth (Z-direction). POST1 is used to extract results from the solution phase.
Being the red points the temperature
boundary conditions for that edge and the blue lines the applied film
coefficient.
VCF _
2_0_00_03_04_04_002
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 164, Article 7-8.
ANSYS: VM99
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_03_04_04_002.xcf
|
A rectangular cooling fin with a trapezoidal cross-section
dissipates heat from a wall maintained at a temperature Tw. The surrounding air
temperature is Ta and the convection coefficient between the fin and the
air is h. Determine the temperature distribution within the fin and the heat
dissipation rate q.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 18 Btu/hr-ft-°F
h = 500 Btu/hr-ft2°F
|
w = 0.96 in = 0.08 ft
|
Tw = 100°F
Ta =
0°F
|
Analysis Assumption and Modeling Notes
The finite element model is made the same
as the reference's relaxation model for a direct comparison. The solution is
based on a fin of unit depth (Z-direction). Only half of the fin is modeled due
to symmetry.
Being the red points the temperature
boundary conditions for that edge and the blue lines the applied film
coefficient.
VCF _
2_0_00_03_04_04_003
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
F. Kreith, Principles of Heat
Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 102,
ex. 3-4.
ANSYS: VM100
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_03_04_04_003.xcf
|
Determine the temperature distribution and the rate of heat flow q
per foot of height for a tall chimney whose cross-section is shown in the image
ahead. Assume that the inside gas temperature is Tg, the inside convection
coefficient is hi, the surrounding air temperature is Ta, and the outside
convection coefficient is ho.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k
= 18 Btu/hr-ft-°F
hi
= 12 Btu/hr-ft2°F
ho = 3 Btu/hr-ft2°F
|
a = 4 ft
b = 1 ft
|
Tw = 100°F
Ta = 0°F
|
Analysis Assumption and Modeling Notes
Due to symmetry, a 1/8 section is used. The
finite element model is made the same as the reference's relaxation model for a
direct comparison. The solution is based on a fin of unit depth (Z-direction).
POST1 is used to obtain results from the solution phase.
Being the blue lines the applied film
boundary conditions.
VCF _ 2_0_00_03_04_04_004
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
F. Kreith, Principles of Heat
Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg.
102, ex. 3-4.
ANSYS: VM118
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_03_04_04_004.xcf
|
Determine the temperature distribution and the rate of heat flow q
per foot of height for a tall chimney whose cross-section is shown in the image
ahead. Assume that the inside gas temperature is Tg, the inside convection
coefficient is hi, the surrounding air temperature is Ta, and the outside
convection coefficient is ho.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 13
Btu/hr-ft-°F
|
|
h = 5 Btu/hr-ft2°F
|
|
ro = 0.375 in=0.03125 ft
|
Ta =
70°F
q =
111311.7 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric, only a
one-element sector is needed. A small angle Θ = 10° is used for
approximating the circular boundary with a straight-sided element. Nodal
coupling is used to ensure circumferential symmetry. The solution is based on a
wire 1 foot long (Z-direction).
Being the blue lines the applied film
boundary conditions and the green surface the thermal flux.
VCF _
2_0_00_04_00_04_001
Description: (3D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 166, article 7-9.
ANSYS: VM102
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_04_00_04_001.xcf
|
A long hollow cylinder is
maintained at temperature Ti along its inner surface and To along its
outer surface. The thermal conductivity of the cylinder material is known to
vary with temperature according to the linear function k(T) = C0 +
C1 T. Determine the temperature distribution in the cylinder for the case
ahead:
|
Material
|
Geometry
|
Boundary
Conditions
|
|
C0 = 50 Btu/hr-ft-°F
|
|
C1 = 0.5 Btu/hr-ft-°F2
|
|
|
ri = 1/2 in = (1/24) ft
|
|
ro = 1 in = (1/12) ft
|
|
|
Analysis Assumption and Modeling Notes
The axial length of the model is
arbitrarily chosen to be 0.01 ft. Note that axial symmetry is automatically
ensured by the adiabatic radial boundaries. The problem is solved in two load
steps. The first load step uses the constant k.
Being the red points the temperature for
those edges. These boundary conditions are applied over the inner and the
outter edges both in the top and bottom soil surfaces.
The material is thermal dependent,
following the next thermal function according to the law previously described
k(T) = C0 + C1 T :
Grid
Chart
VCF _
2_0_00_04_00_04_002
Description: (3D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 193, article 8-8
ANSYS: VM105
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_04_00_04_002.xcf
|
A long hollow generator coil has its inner and outer surface
temperatures maintained at temperature To while generating Joule heat at a
uniform rate q. The thermal conductivity of the coil material varies with
temperature according to the function k(T) = C0 + C1 T. Determine the
temperature distribution in the coil.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
C0 = 10 Btu/hr-ft-°F
|
|
C1 = 0.075 Btu/hr-ft-°F2
|
|
|
ri = 1/4 in = (1/48) ft
|
|
ro = 1 in = (1/12) ft
|
|
|
Ti = 0°F
|
|
q= 1 x 106 Btu/hr-ft3
|
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric only a
symmetry sector (one-element wide) is needed. A small angle (Θ=10°) is
used for approximating the circular boundary with a straight-sided element.
Adiabatic boundary conditions are assumed at the symmetry edges. The
steady-state convergence procedures are used.
Being the red points the temperature for
those edges. These boundary conditions are applied over the inner and the
outter edges both in the top and bottom soil surfaces. Beside, the green color
all over the solid performs the temperature on the volume boundary condition.
The material is thermal dependent,
following the next thermal function according to the law previously described
k(T) = C0 + C1 T :
Grid
Chart
VCF _ 2_0_00_04_00_04_003
Description: (3D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 193, article 8-8
ANSYS: VM96
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_04_00_04_003.xcf
|
A short, solid cylinder is subjected to the surface temperatures
shown. Determine the temperature distribution within the cylinder.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 1.0
Btu/hr-ft-°F
|
r = l = 0.5 ft
|
Ttop = 40°F
Tbot = Twall = 0°F
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric, the
entire cylinder geometry is not required. An angle Θ = 45° is arbitrarily
chosen. Postprocessing is used to print temperatures at the centerline in
geometric order.
Being the red points the temperature for
those edges. This boundary condition is applied not only in the top and bottom
surfaces but also contour surface. Being 40°F in the top and bottom surfaces
and 0°F in the wall.
VCF _
2_0_00_04_04_04_001
Description: (3D
Solid. Steady State analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 193, article 8-8
ANSYS: VM110
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_04_04_04_001.xcf
|
A short solid cylinder is subjected to the surface temperatures shown.
Determine the temperature distribution within the cylinder.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 1.0
Btu/hr-ft-°F
|
r = l = 0.5 ft
|
Ttop = 40°F
Tbot = Twall = 0°F
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric only a sector (one element wide)
is modeled. A small angle Θ=10° is used for approximating the circular
boundary with a straight-sided element. Note that circumferential symmetry is
automatically ensured due to default adiabatic boundary conditions.
Being the red points the temperature for
those edges. This boundary condition is applied not only in the top and bottom
surfaces but also contour surface. Being 40°F in the top and bottom surfaces
and 0°F in the wall.
VCF _
2_0_00_04_04_04_002
Description: (3D
Solid. Steady State analysis)
|
Reference:
|
W. M. Rohsenow, H. Y. Choi, Heat,
Mass and Momentum Transfer, 2nd Printing, Prentice-Hall, Inc., Englewood
Cliffs, NJ, 1963, pg. 106, ex. 6.5.
ANSYS: VM118
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 2_0_00_04_04_04_002.xcf
|
Determine the centerline temperature Tc and the surface
temperature Ts of a bare steel wire generating heat at the rate q.
The surface convection coefficient between the wire and the air (at temperature
Ta) is h. Also determine the heat dissipation rate q.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k = 13
Btu/hr-ft-°F
|
|
h = 5 Btu/hr-ft2-°F
|
|
ro = 0.375 in
= 0.03125 ft
|
|
Ta = 70°F
|
|
q = 111311.7 Btu/hr-ft3
|
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric, only a
one-element sector is needed. A small angle Θ = 10° is used for
approximating the circular boundary with a straight-sided element. Nodal
coupling is used to ensure circumferential symmetry. The solution is based on a
wire 1 foot long (Z-direction).
The green color shapes the thermal flux
boundary condition. This will be applied in every surface but the curved surface,
that is, the Solid 3D contour. Over that contour will be established a film
condition with a 70°F temperature and the h coefficient of 5 Btu/hr-ft2-°F
previously detailed.
VCF _
2_0_00_03_18_04_001
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
Collection of proposed and solved
problems of heat transference. Sevila Politecnic University. Page 25.
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_2_0_00_03_18_04_001.xcf
|
Considering a wal made out of two layers with the caracteristics
ahead:
ˇ
First layer: Thickness 0.4 m, Kt1=0.9(1+T)
[W/mˇK]
ˇ
Second layer: Thickness 0.05 m,
Kt2=0.04 [W/mˇK]
The outter layer is subjected to a sun termal flux of 300 W/m2.
This layer is in touch with air at 40°C (convective outter coefficient 10W/m2ˇK).
The inner layer is in touch with air at 20°C (convective outter coefficient 5/m2ˇK).
|
Material
|
Geometry
|
Boundary
Conditions
|
|
Concrete:
Kt1=0.9(1+T)
Soil:
Kt2=0.04
|
Th1= 0.4 m
Th1=
0.05 m
|
Ta1 = 40°C, h1=10
J/(sˇm2ˇ∆C)
Ta2 = 20°C, h2=5 J/(sˇm2ˇ∆C)
q = 300 J/s/m2
|
Analysis Assumption and Modeling Notes
Variables in order to calculate:
-Heat flux per area: q; Surfaces
temperature: T1,T2 and T3.
Both sides are subjected to film boundary
conditions and, in addition, the left side is also submitted to a thermal flux
per area. That is, a thermal flux on a curve.
Explanation:
Heat flux per area throught the wall
The heat flux per are has to be cte. The
conductivity varies with temperature, following the next statement:
If this equation is integrated in the first
layer:
Now, both boundary conditions will be
entered into this formulation:
In the other contour, the boundary
condition will be:
Thus, there are three equations and three
variables ŕ(T1, T2, q):
Now it is available to obtain the values
from T1, T2 and q:
ˇ
T1=67.33; T2=58.72; q = 26.7W/m2
So, by last, the T3 values would
be easy to calculate due to the application of this equation:
VCF _
2_3_00_01_04_04_001
Description: (2D
Bar. Transient analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pp. 274-275, article 11-2, eq. 11-9.
ANSYS: VM114
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 2_3_00_01_04_04_001.xcf
|
A semi-infinite solid, initially at a temperature To, is subjected
to a linearly rising surface temperature Ts = 3600 t, where Ts is in
°F and t is time in hours. Determine the temperature distribution in the solid
at t = 2 min.
|
Material
|
Boundary
Conditions
|
|
k = 10 Btu/hr-ft-°F
γ
= 500 lb/ft3
c
= 0.2 Btu/lb-°F
|
To = 0°F
@ t = 0
Ts = 120°F @ t = 2 (ramped)
|
Analysis Assumption and Modeling Notes
A nonuniform mesh is used to model the
nonlinear thermal gradient through the solid. An arbitrary area of 1
ft2 is used for the elements. The length of the model is taken as 0.3 ft
assuming that no significant temperature change occurs at the interior end
point (Node 2) during the time period of interest (2 min). This assumption is
validated by the temperature of node 2 at the end of the transient analysis.
Automatic time stepping is used with an
initial integration time step (0.03333/20 = 0.001666 hr) greater
than δ2/4α, where δ = minimum element conducting length
(0.0203 ft) and α = thermal diffusivity ( = k/ γc =
0.1 ft2/hr).
Note that the KBC key (not input) defaults
to zero, resulting in the surface temperature load being ramped linearly to its
final value.
The problem is shaped by an initial
condition on which the temperature is 0°F. This condition is only fulfilled in
the initial state, therefore, a temperature dependent of time will be applied.
The next table detail how the temperature varies with respect time:
Grid
Chart
VCF_
2_3_00_03_04_04_001
Description: (2D Solid.
Transient analysis)
|
Reference:
|
V4.23.303 TTLP303 de Code Aster 13: TTLP303 - Transfert de
chaleur dans une plaque ort[...]
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
2_3_00_03_04_04_001.xcf
|
A modeled 2D solid, with an initial temperature To, is subjected to
a contour ABCD temperature all along the perimeter. Determine the temperature
distribution in the solid at t = 1.2 h on points (0.6, 1.5), (1.5, 3.0) and
(0.0, 0.0).
|
Material
|
Boundary Conditions
|
|
kx = 10 W/m°C
ky
= 0.659 W/m°C
c
=1899.1 J/m3°C
|
Contour ABCD : T=−17.778° C
To (t=0)=−1.111° C
|
The previous image represents the countour
boundary condition of temperature, which value is, as formely detailed,
17.778°C. The initial condition may be applied whether with a nodal temperature
on every node with value 1.111 °C or with the initial condition utility,
available on the loads ribbon.
Contour BC:
Grid
The time has been provided in hours while
the temperature has been detailed in °C.
The method of calculation has followed
the equation ahead:
Where 
:
Next table pretends to be a scheme of all
the amount of temperatures in the model. X and Y distances are detailed on it
along with the temperatures for every point. Temperatures have been provided
into Celsius, however, the model has been developed in S.I so CivilFEm will
come out these temperatures in Kelvin.
The values of reference are obtained with
n=j=1000.
VCF _ 2_3_00_03_04_04_002
Description: (2D Sold.
Transient analysis)
|
Reference:
|
F. Kreith, Principles of Heat
Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg.
143, ex. 4-5.
ANSYS: VM111- VM112
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 2_3_00_03_04_04_002.xcf
|
Determine the temperature at the center of a spherical body,
initially at a temperature To, when exposed to an environment having a
temperature Te for a period of 6 hours. The surface convection coefficient
is h.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
K=(1/3) BTU/hr-ft-°F
γ
= 62 lb/ft3
c
= 1.075 Btu/lb-°F
h
= 2 Btu/hr-ft2-°F
|
ro = 2 in = (1/6) ft
|
To = 65°F
Te = 25°F
|
Analysis Assumption and Modeling Notes
Since the problem is axisymmetric, only a
one-element sector is needed. A small angle Θ = 15° is used for
approximating the circular boundary with a straight-side element. Nodal
coupling is used to ensure circumferential symmetry. Automatic time stepping is
used. The initial integration time step (6/40 = 0.15 hr) is based
on δ2/4 α, where δ is the element characteristic
length (0.0555 ft) and α is the thermal diffusivity (k/γc =
0.005 ft2/hr).
The problem is shaped by an initial
condition on which the temperature is 65°F. This condition is only fulfilled in
the initial state, therefore, a temperature dependent of time will be applied.
The second boundary condition consists on a
film condition (The blue line plotted in the previous image) on which the ambient
temperature is defined as 25°F and the h coefficient as 0.2
Btu/hr-ft2-°F. Both the ambient temperature and the h coefficient do not vary
along time. That is, final time is 6 hours.
VCF _
2_3_00_03_04_04_003
Description: (2D
Sold. Transient analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 261, ex. 10-7.
ANSYS: VM113
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 2_3_00_03_04_04_003.xcf
|
A long metal bar of
rectangular cross-section is initially at a temperature To and is then
suddenly quenched in a large volume of fluid at temperature Tf. The material
conductivity is orthotropic, having different X and Y directional properties.
If the surface convection coefficient is h, determine the temperature
distribution in the slab after 3 seconds in the following locations of the bar:
- center
- corner edge
- face centers of the bar
|
Material
|
Geometry
|
Boundary
Conditions
|
|
kx = 20
Btu/hr-ft-°F
ky = 3.6036
Btu/hr-ft-°F
γ = 400 lb/ft3
c = 0.009009 Btu/lb-°F
h = 240 Btu/hr-ft2-°F
|
a = 2 in = (2/12) ft
b = 1 in = (1/12) ft
|
To = 500°F
Tf = 100°F
|
Analysis Assumption and Modeling Notes
A nonuniform grid (based on a geometric
progression) is used in both X and Y directions to model a quarter of the bar
cross-section. Automatic time stepping is used. The initial integration time
step = (3/3600)(1/40) is greater than (δ2/4α), where δ is
the shortest element length (0.0089 ft) and α is the thermal
diffusivity (ky/γc = 1.0 ft2/hr).
The problem is shaped by an initial
condition on which the temperature is 500°F. This condition is only fulfilled
in the initial state, therefore, a temperature dependent of time will be
applied.
The second boundary condition consists on a
film condition (those blue lines plotted in the previous image) on which the ambient
temperature is defined as 100°F and the h coefficient as 240
Btu/hr-ft2-°F. Both the ambient temperature and the h coefficient do not vary
along time. That is, final time is 3 seconds.
VCF _
2_3_00_03_04_04_004
Description: (2D
Sold. Transient analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 283, article 11-4, eq. (11-21) and pg. 309, article 12-8.
ANSYS: VM115
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 2_3_00_03_04_04_004.xcf
|
An infinite plate of thickness l, initially at a uniform
temperature To, is subjected to a sudden uniformly distributed heat generation rate q and
a surface temperature Ts. Determine the temperature distribution in the plate
after 12 minutes.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k =
20 Btu/hr-ft-°F
γ
= 500 lb/ft3
c= 0.2 Btu/lb-°F
|
L= 1 ft
|
To = 60°F
Ts = 32°F (t>0)
q = 4 x 104 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
A 1 ft2 area is used for the
conduction elements. Due to symmetry only half of the plate is modeled.
Automatic time stepping is used. The initial integration time step (0.01 hr) is
based on δ2/4α, where δ is the element length (0.1 ft)
and α is the thermal diffusivity (k/γc = 0.2 ft2/hr).
The problem is shaped by an initial
condition on which the temperature is 60°F. This condition is only fulfilled in
the initial state, therefore, a BC dependent of time will be applied.
The second boundary condition consists both
on a thermal flux and on a temperature on a curve conditions. The temperature
on nodes is shaped by means of those red points while the thermal flux is
applied all over the surface due to the green color. Both the temperature and
the thermal flux are applied constantly along the whole period of time. The
calculation time goes to 720 seconds.
VCF_ 2_3_00_03_04_04_005
Description: (2D Sold. Transient analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 283, article 11-4, eq. (11-21) and pg. 309, article 12-8.
ANSYS: VM115
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 2_3_00_03_04_04_005.xcf
|
An infinite plate of thickness l, initially at a uniform
temperature To, is subjected to a sudden uniformly distributed heat generation
rate q and a surface temperature Ts. Determine the temperature
distribution in the plate after 12 minutes.
This problem is similar to the VCF_ 2_3_00_03_04_04_004, however,
there is a dependency in respect to time from both the thermal conductivity and
the specific heat.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k =
1 Btu/hr-ft-°F
γ
= 500 lb/ft3
c= 1 Btu/lb-°F
|
L= 1 ft
|
To = 60°F
Ts =
32°F (t>0)
q =
4 x 104 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
A 1 ft2 area is used for the
conduction elements. Due to symmetry only half of the plate is modeled.
Automatic time stepping is used. The initial integration time step (0.01 hr) is
based on δ2/4α, where δ is the element length (0.1 ft)
and α is the thermal diffusivity (k/γc = 0.2 ft2/hr).
The problem is shaped by an initial
condition on which the temperature is 60°F. This condition is only fulfilled in
the initial state, therefore, a BC dependent of time will be applied.
The second boundary condition consists both
on a thermal flux and on a temperature on a curve conditions. The temperature
on nodes is shaped by means of those red points while the thermal flux is
applied all over the surface due to the green color. Both the temperature and
the thermal flux are applied constantly along the whole period of time. The
calculation time goes to 720 seconds.
AS previously detailed, this problem is
very similar to the VCF_ 2_3_00_03_04_04_004. Nevertheless, these will
be the dependency tables from the thermal conductivity and the specific heat
with respect the time:
Thermal conductivity:
Grid
Specific Heat:
Grid
Both thermal conductivity and specific heat
coefficients have to be entered as 1 due to the fact that these ones will
multiply to the table values.
VCF _
2_3_00_04_04_04_001
Description: (2D
Sold. Transient analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 283, article 11-4, eq. (11-21) and pg. 309, article 12-8.
ANSYS: VM115
|
|
Analysis Type(s):
|
Transient State Analysis
|
|
File:
|
VCF_ 2_3_00_04_04_04_001.xcf
|
An infinite plate of thickness l, initially at a uniform
temperature To, is subjected to a sudden uniformly distributed heat generation
rate q and a surface temperature Ts. Determine the temperature
distribution in the plate after 12 minutes.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k =
20 Btu/hr-ft-°F
γ
= 500 lb/ft3
c= 0.2 Btu/lb-°F
|
L= 1 ft
|
To = 60°F
Ts = 32°F (t>0)
q = 4 x 104 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
A 1 ft2 area is used for the
conduction elements. Due to symmetry only half of the plate is modeled.
Automatic time stepping is used. The initial integration time step (0.01 hr) is
based on δ2/4α, where δ is the element length (0.1 ft)
and α is the thermal diffusivity (k/γc = 0.2 ft2/hr).
The problem is shaped by an initial
condition on which the temperature is 60°F. This condition is only fulfilled in
the initial state, therefore, a BC dependent of time will be applied.
The second boundary contents both a thermal
flux on a volume and a surface temperature that will be applied both in the top
and bottom surfaces.
Temperatures are plotted by nodes so, it is
therefore the surface temperature keeps represented by these red points. One
red point by each node. The thermal flux is applied in the whole volume. The
green color corresponds to the thermal fluxes.
Both the temperature and the thermal flux
are applied constantly along the whole period of time. The calculation time goes
to 720 seconds.
VCF_ 2_3_00_04_04_04_002
Description: (2D Sold. Transient analysis)
|
Reference:
|
P. J. Schneider, Conduction Heat
Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA,
1957, pg. 283, article 11-4, eq. (11-21) and pg. 309, article 12-8.
ANSYS: VM115
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 2_3_00_04_04_04_002.xcf
|
An infinite plate of thickness l, initially at a uniform
temperature To, is subjected to a sudden uniformly distributed heat generation
rate q and a surface temperature Ts. Determine the temperature
distribution in the plate after 12 minutes.
This problem is similar to the VCF_ 2_3_00_04_04_04_001, however,
there is a dependency in respect to time from both the thermal conductivity and
the specific heat.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
k =
1 Btu/hr-ft-°F
γ
= 500 lb/ft3
c= 1 Btu/lb-°F
|
L= 1 ft
|
To = 60°F
Ts = 32°F (t>0)
q = 4 x 104 Btu/hr-ft3
|
Analysis Assumption and Modeling Notes
A 1 ft2 area is used for the
conduction elements. Due to symmetry only half of the plate is modeled.
Automatic time stepping is used. The initial integration time step (0.01 hr) is
based on δ2/4α, where δ is the element length (0.1 ft)
and α is the thermal diffusivity (k/γc = 0.2 ft2/hr).
The problem is shaped by an initial
condition on which the temperature is 60°F. This condition is only fulfilled in
the initial state, therefore, a BC dependent of time will be applied.
The second boundary contents both a thermal
flux on a volume and a surface temperature that will be applied both in the top
and bottom surfaces.
Temperatures are plotted by nodes so, it is
therefore the surface temperature keeps represented by these red points. One
red point by each node. The thermal flux is applied in the whole volume. The
green color corresponds to the thermal fluxes.
Both the temperature and the thermal flux
are applied constantly along the whole period of time. The calculation time
goes to 720 seconds.
AS previously detailed, this problem is
very similar to the VCF_ 2_3_00_03_04_04_004. Nevertheless, these will
be the dependency tables from the thermal conductivity and the specific heat
with respect the time:
Thermal conductivity:
Grid
Specific Heat:
Grid
Both thermal conductivity and specific heat
coefficients have to be entered as 1 due to the fact that these ones will
multiply to the table values.
VCF _
3_0_00_00_02_01_001
Description: (2D Link
and Beam. Thermal-Structural analysis)
|
Reference:
|
INGECIBER verification example
|
|
Analysis Type(s):
|
Thermal-Structural Analysis
|
|
File:
|
VCF_ 3_0_00_00_02_01_001.xcf
|
Determine the component stress the beam is subjected to as a result
of the application of a 75°C temperature and the detailed structural boundary
conditions.
|
Material
|
Geometry
|
Boundary Conditions
|
|
E=2.1E11 Pa
k=60.5 J/(sˇmˇ∆C)
|
A=B
A= Link SE
B= Beam SE
|
Thermal:
T = 75°C
Structural:
Node 1: u=v=0
Node 2: u=v=0; θz = 0
|
Analysis Assumption and Modeling Notes
The problem is based in two unidimensional structural
elements: one link and one; subjected to different boundary conditions which
make the structure get stressed as a result of the applied nodal temperature in
the junction of both of the spans. Stress component will be measured in node 2.
VCF _
3_0_00_01_04_01_001
Description: (2D
Link. Thermal-Structural analysis)
A link, with no internal stresses, is
pinned between two solid structures at a reference temperature of 0 C (273 K).
One of the solid structures is heated to a temperature of 75 °C (348 K). As
heat is transferred from the solid structure into the link, the link will
attemp to expand. However, since it is pinned this cannot occur and as such,
stress is created in the link. A steady-state solution of the resulting stress
will be found to simplify the analysis.
Loads will not be applied to the link, only a temperature change of
75 degrees Celsius. The link is steel with a modulus of elasticity of 200 GPa,
a thermal conductivity of 60.5 W/m*K and a thermal expansion coefficient of
12e-6 /K.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Generic
material:
E=200 GPa
k=60.5 J/(sˇmˇ∆C)
|
L=1m
|
Thermal:
Node
1: T = 75°C
Structural:
Node 1: u=v=0
Node 2: u=v=0
|
Analysis Assumption and Modeling Notes
In order to simplify the example,
solidswill not be modeled due to the fact that qhen the solid is subjected to
the detailed temperature, this one will be transferred to the link so, that
is, the temperature will be attached to one of the enddings of this link. For
instance, on the left.
VCF_
4_0_01_03_03_00_001
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground Water
Verification.Problem: Confined flow under dam foundation. Page-11
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 4_0_01_03_03_00_001.xcf
|
Determine the total head H both for the equipotential
lines 1-1 and 2-2. The soil will be completely satured, being its hydraulic
conductivity 1.0e-05 m/s. Dimensions are specified in the scheme ahead.
|
Material
|
Geometry
|
Boundary
Conditions
|
|
Soil
Material:
ks = 1.0e-05m/s
Satured soil
|
H=10 m
L=40
m
|
-TH1 = 5m
-TH2 =
0m
|
Analysis Assumption and Modeling Notes
The
problem has been modeled with the dimensions previously described. It is based
on a satured soil being upstream the total head 5 m but 0 m downstream.
The
flow is considered to be two-dimensional with negligible flow in the lateral
direction. The flow equation for isotropic soil can be expressed as:
The
accuracy of numerical solutions for the problem is dependent on how the
boundary conditions are applied. For the particular example in this document,
two boundary conditions are applied:
ˇ
No flow occurs across the
impermeable base, and
ˇ
The pressure heads at the
ground surface upstream and downstream of the dam are solely due to water
pressure.
This plot pretends to locate where the
total head boundary conditions have been imposed.
VCF_
4_0_01_03_03_00_004
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground
Water Verification.Problem: Steady-State Seepage Analysis through
Saturated-Unsaturated
Soils.
Page-23
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 4_0_01_03_03_00_004.xcf
|
Determine the pressure head in this model of a dam,
whose water table is located at 10 m from the base. Solution will be evaluated along
the line 1-1.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Soil
Material:
ks = 1 m/s
Unsatured soil: Ks dependent (see
table 1)
|
H= 12 m
L=
52 m
|
-TH1 = W= 10m
-Horizontal
Drain = TH2 = 0 m
|
Problem
description scheme
Horizontal
drain distribution
Analysis Assumption and Modeling Notes
The seepage model has been
developed with an Unsatured/Satured hydraulic property. That is, the
conductivity factor has been established variable with respect the pressure
head. The permeability function used in the analysis will be visualized ahead:
In CivilFEM, it is mandatory to
introduce the matric suction in m instead of kPa. Conversion will be got by appliying
the next conversion:
This problem require the next
table (table 1) to be introduced as the dependency hydraulic
conductivity-Pressure Head.
This plot pretends to locate where the water
table and the drainboundary conditions have been imposed.
The results of finite-element
analysis by Lam (1984) [2] are presented in [1] in the form of two-dimensional
contour charts.
VCF_ 4_0_01_03_03_00_005
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground Water
Verification.Problem: Isotropic earth dam under steady-state
infiltration. Page-31
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_4_0_01_03_03_00_005.xcf
|
Determine the pressure head in this model of a dam,
whose water table is located at 10 m from the base. Beside, the dam model is
subjected to a 1e-08 m3/s infiltration on its top. Solution will be
evaluated along the line 1-1.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Soil
Material:
ks = 1 m/s
Unsatured soil: Ks dependent (see
table 1)
|
H= 12 m
L=
52 m
|
-TH1= W= 10m
-Horizontal
Drain = TH2 = 12 m
-q=1e-08
m3/s
|
Problem
description scheme
Horizontal
drain distribution
Analysis Assumption and Modeling Notes
The seepage model has been
developed with an Unsatured/Satured hydraulic property. That is, the
conductivity factor has been established variable with respect the pressure
head. The permeability function used in the analysis will be visualized ahead:
In CivilFEM, it is mandatory to
introduce the matric suction in m instead of kPa. Conversion will be got by
appliying the next conversion:
This problem require the next
table (table 1) to be introduced as the dependency hydraulic
conductivity-Pressure Head.
This plot represents the location the water
table, the rainfall and the horizontal drain, have been set.
VCF_
4_0_01_03_03_00_006
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground Water
Verification.Problem: Anisotropic earth dam with a horizontal drain.
Page-27
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 4_0_01_03_03_00_006.xcf
|
Determine the pressure head in this model of a dam,
whose water table is located at 10 m from the base. Beside, the dam has been
developed with an anisotropic material. That is, the water coefficient
permeability in the horizontal direction is assumed to be nine times larger
than in the vertical direction. Solution will be evaluated along the line
1-1.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Soil
Material:
Ksx = 9 m/s
Ksy= 1 m/s
Unsatured soil: Dependency table
(table 1)
|
H= 12 m
L=
52 m
|
-TH1 = W= 10m
-Horizontal
Drain = TH2 =0 m
|
Problem
description scheme
Horizontal
drain distribution
Analysis Assumption and Modeling Notes
The seepage model has been
developed with an Unsatured/Satured hydraulic property. That is, the
conductivity factor has been established variable with respect the pressure
head. The permeability function used in the analysis will be visualized ahead:
In CivilFEM, it is mandatory to
introduce the matric suction in m instead of kPa. Conversion will be got by
appliying the next conversion:
This problem require the next
table (table 1) to be introduced as the dependency hydraulic
conductivity-Pressure Head.
This plot represents the location the water
table, the rainfall and the horizontal drain, have been set.
VCF_
4_0_01_03_03_00_007
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground
Water Verification.Problem: Seepage from Trapezoidal Ditch into Deep
Horizontal Drainage
Layer.
Page-59
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_ 4_0_01_03_03_00_007.xcf
|
Seepage from a trapezoidal ditch
into a deep horizontal drainage layer is analyzed in this section.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Soil
Material:
Ks = 1.0e-05 m/s
|
Ditch half-width = 25 m
Ditch
depth = 10 m
Bank
angle = 45°
|
-Contour bank line: TH1 = 50 m
-Bottom
soil line: TH2 = 0 m
|
Problem
description scheme
Analysis Assumption and Modeling Notes
Vedernikov (1934) proposed a direct method to solve for the seepage
from such a ditch. He proposed the following equation for calculating the flow:
Where A is a function of B/H and cot α. In this example we will
use B=50 m, H=10 m and α= 45° which will yield a value of A = 3.
He also proposed the following
equation for calculation the width of the flow at an infinite distance under
the bottom of the ditch:
Usin the above equation, the flow
though the system was calculated to be 0.0008 m3/s. The width of the
seepage zona was calculated to be 80 m.
The analytical solution used for
total head is a flow net drawn by hand using Vedernikovs boundary conditions
(width of seepage zone, depth to horizontal equipotential lines).
|
ELEVATION
|
TOTAL HEAD
|
|
40
|
50
|
|
35
|
42.64
|
|
30
|
35.85
|
|
25
|
29.77
|
|
20
|
22.69
|
|
15
|
16.94
|
|
10
|
11.42
|
|
5
|
5.49
|
|
0
|
-0.31
|
The total head
solution has been measured all along the border line, which establishes the
symmetry.
VCF_
4_0_01_03_03_00_008
Description: (2D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground Water
Verification.Problem: Isotropic earth dam with seepage face.
Page-33
|
|
Analysis Type(s):
|
Steady State Analysis
|
|
File:
|
VCF_4_0_01_03_03_00_008.xcf
|
Determine the pressure head in this model of a dam,
whose water table is located at 10 m from the base. The statement is based on
setting a seepage face review boundary condition, in the downstream wall.
Solution will be evaluated along the line 1-1.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Soil
Material:
Ks = 1 m/s
Unsatured soil: Dependency table
(table 1)
|
H= 12 m
L=
52 m
|
-TH1 = W= 10m.
-Seepage
face review =Q= 0 m3 on downstream wall
nodes.
-TH2
= 0 m on downer node of the downstream wall.
|
Problem
description scheme
Analysis Assumption and Modeling Notes
The seepage model has been
developed with an Unsatured/Satured hydraulic property. That is, the
conductivity factor has been established variable with respect the pressure
head. The permeability function used in the analysis will be visualized ahead:
In CivilFEM, it is mandatory to
introduce the matric suction in m instead of kPa. Conversion will be got by
appliying the next conversion:
This problem require the next
table (table 1) to be introduced as the dependency hydraulic
conductivity-Pressure Head.
On the
other hand, a seepage face review boundary condition has been imposed all along
the downstream wall. The seepage face review boundary condition allows to
establish the condition H=y over a list of selected nodes, being H their total
head value and y their height. Thus, we now that in case H=y=0, this implys
that those nodes would belong to the water table.
This plot visualizes the total head of 10 m
besides the seepage face review condition. By last, the downer node from the
downstream wal l would simulate a sink behavior, being its total head 0 m.
VCF_ 4_0_01_04_03_00_003
Description: (3D
Solid. Steady State analysis)
|
Reference:
|
1989-2011 RocScience Inc. Ground Water
Verification.Problem: Isotropic earth dam with seepage face.
Page-33
|
|
Analysis Type(s):
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Steady State Analysis
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File:
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VCF_ 4_0_01_04_03_00_003.xcf
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Determine the
pressure head in this model of a dam, whose water table is located at 10 m from
the base. The statement is based on setting a seepage face review boundary
condition, in the downstream wall. Solution will be evaluated along the line
1-1.
This problem fulfills the same hypothesis than the Test
Case VCF_4_0_01_03_03_00_008, nevertheless in this case it has been
modeled in a 3D model view.
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Material
|
Geometry
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Boundary Conditions
|
|
Soil
Material:
Ks = 1 m/s
Unsatured soil: Dependency table (table 1)
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H= 12 m
L=
52 m
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-TH1 = W= 10m.
-Seepage
face review =Q= 0 m3 on downstream wall
nodes.
-TH2
= 0 m on downer node of the downstream wall.
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Problem
description scheme
Analysis Assumption and Modeling Notes
The seepage model has been
developed with an Unsatured/Satured hydraulic property. That is, the
conductivity factor has been established variable with respect the pressure
head. The permeability function used in the analysis will be visualized ahead:
In CivilFEM, it is mandatory to
introduce the matric suction in m instead of kPa. Conversion will be got by
appliying the next conversion:
This problem require the next
table (table 1) to be introduced as the dependency hydraulic
conductivity-Pressure Head.
On the
other hand, a seepage face review boundary condition has been imposed all along
the downstream wall. The seepage face review boundary condition allows to
establish the condition H=y over a list of selected nodes, being H their total
head value and y their height. Thus, we now that in case H=y=0, this implys
that those nodes would belong to the water table.
This plot visualizes the total head of 10 m
besides the seepage face review condition. By last, the downer edge from the
downstream wal l would simulate a sink behavior, being its total head 0 m.
The image helps when visualizing the
difference with the Test case VCF_4_0_01_03_03_00_008. The 3D model would
apply the total head of 10 m into a surface besides, the 0 m total head from
the bottom part or the downstream wall, into a line. The seepage face review is
now applied over a surface, as well.
On the other hand, the width of the dam is
not a variable. In this problem a 20 m width dam were modeled.
VCF_
4_3_01_04_03_00_001
Description: (3D
Solid. Steady State analysis)
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Reference:
|
1989-2011 RocScience Inc. Ground Water
Verification.Problem: Radial Flow to a Well in a Confined Aquifer.
Page-75
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Analysis Type(s):
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Steady State Analysis
|
|
File:
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VCF_ 4_3_01_04_03_00_001.xcf
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The problem concerns the radial
flow towards a pumping well through a confined homogeneous, isotropic aquifer.
The problem is axisymmetric. Solution will be evaluated along the radious.
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Material
|
Geometry
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Boundary Conditions
|
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Soil
Material:
Ks = 0.002 m/s
Satured soil
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Well radious rw= 0.15 m
Boundary
radious re= 40 m
Aquifer
depth = b= 5 m
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-TH1= H = 16 m
-Volumetric
pumping rate = Q =0.125 m3/s
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Problem
description scheme
Analysis Assumption and Modeling Notes
According to Davis (1966) [1] the
head h at any radius r is given by the analytical solution [1]:
Where H is the head at the far boundary, re
is the radious of the far boundary, b is the thickness of the aquifer, k, is
the permeability in the aquifer and Q is the volumetric pumping rate.
This problem may be carried out in a 2D model, however,
it is important to remark that it consist on an axisymmetric problem so, a 3D
model has been developed in order to simplify this circumnstance.
This plot visualizes the total head of 16 m
all over the wall of the well. The second image represents the hydraulic flux,
which corresponds with the volumetric pumping rate.
The pumping boundary condition was
simulated by applying a negative normal infiltration of q along the length of
the well. The magnitude of q was calculated by dividing the volumetric pump
rate (Q) by the surface area of the well:
Where l represents the length of the well. In
this case it fully penetrates the reservoir so l=b.
VCF_
4_3_01_03_03_00_002
Description: (2D
Solid. Transient analysis)
|
Reference:
|
1989-2011 RocScience Inc. Transient
Ground Water Verification. Problem: Transient Seepage through a
Fully Confined Aquifer. Page-11
|
|
Analysis Type(s):
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Transient Analysis
|
|
File:
|
VCF_ 4_3_01_03_03_00_002.xcf
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This problem deals with transient
seepage through a fully confined aquifer. The aquifer has an initial pore water
distribution of five feet of hydraulic head from the left to the right side of
the aquifer. Seepage is then examined in the x-direction with time. The aquifer
is 100 feet long and five feet thick.
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Material
|
Geometry
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Boundary
Conditions
|
|
Soil
Material:
ks = 4.0 ft/hr
mv=0.1
Satured soil
|
H=5 ft
W=100
ft
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-Initial condition = 5 ft
-TH
= 10 ft on the left edge
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Analysis Assumption and Modeling Notes
The equation for transient seepage
through a fully confined aquifer can be expressed through the J.G. Ferris
Formula [1] as:
Where h(x,t) is the hydraulic head
at position x at time t; ΔH is the head difference between the initial
pore-water distribution and the introduced hydraulic head; and erfc is the
complimentary error function.
First of all, an initial boundary condition
of 5 ft is applied on the aquifer. From this point, a new boundary condition is
applied on the left edge. This boundary condition consist of a total head of 10
ft. This will be evaluated into time along the next instants:
ˇ
1
h, 12 h, 24 h, 48 h, 72 h, 120 h, 240 h, 600 h.
A load case for every time step will be
created so as to evaluate the inner development on the aquifer.
The solution will be evaluated through the
edge that joins the middle node of the left edge with the middle node of the
right edge. That is, the edge which stablishes the vertical symmetry.
VCF_
4_3_01_03_03_00_004
Description: (2D
Solid. Transient analysis)
|
Reference:
|
Geo Studio 2018_SEEP W. Example Files.
Problem: Leakage from a Pond with a Clay Liner.
|
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Analysis Type(s):
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Transient Analysis
|
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File:
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VCF_ 4_3_01_03_03_00_004.xcf
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The objective of this example is
to illustrate how to model the effect of leakage from a lined pond on a
groundwater flow system. The transient analysis is ued to model the response of
the water table from the time of filling the pond to when the system approaches
a steady state.
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Material
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Geometry
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Boundary Conditions
|
|
Embankment:
ks = 1 m/d
Unsatured soil: Dependency table
Clay Liner:
ks = 1 m/d
Unsatured soil: Dependency table
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Detailed on scheme ahead
|
-Initial condition = 4 m
--Seepage
face review =Q= 0 m3
-Total
head of 10.5 m
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Analysis Assumption and Modeling Notes
Two materials have been defined,
shaped both of them by an unsatured hydraulic property. This means that
conductivity factor is dependent from the pressure head, as well as the
volumetric water content. Thus, permeability and volumetric water content
function used both for the clay liner and the embankment material will be
visualized ahead:
Clay Liner:
Embankment:
First of all, detail that we have a leakage
from a pond with a clay liner, whose model is described on the images above.
The left image locate the initial condition, which value is 4m, on the bottom
part of the downstream wall. On the other hand, the right image visualizes the
boundary conditions fixed in order to analyse in a transient model. First of
all, seepage faces review on the slope and a total head of 10.5 m in the clay
liner so as to modelate the wate leakage.
The seepage face review boundary condition
allows to establish the condition H=y over a list of selected nodes, being H
their total head value and y their height. Thus, we now that in case H=y=0,
this implys that those nodes would belong to the water table.
Although the transient analysis has been
solved with different times, visualized ahead:
ˇ
1d,
2.12d, 3.37d, 4.78d, 6.35d, 8.11d, 10.1d, 12.3d, 14.8d, 17.55d, 20.63d, 24.1d,
28d, 32.33d, 37.2d, 42.6d, 48.75d, 55.59d, 63.25d, 71.82d, 81.42d, 92.1d,
104.2d, 117.67d, 132.75d, 149.61d, 168.56d, 189.74d 213.45d and 240d.
A load case for every time step will be
created so as to evaluate the inner development on the aquifer. The solution
will be evaluated all along the left edge. In addition, the solution will be
referenced to the last load case, that is, the 240 d load case.
VCF_
4_3_01_04_03_00_002
Description: (3D
Solid. Transient analysis)
|
Reference:
|
RocScience Inc. Transient Ground
Water Analysis. Problem: Transient Groundwater Analysis.
|
|
Analysis Type(s):
|
Transient Analysis
|
|
File:
|
VCF_ 4_3_01_04_03_00_002.xcf
|
A transient groundwater analysis
may be important when there is a time-dependent change in pore pressure. In
this case, it will take a finite amount of time to reach steady state flow
conditions. The transient pore pressures may have a large effect on slope
stability. The problem pretends to describe how this affects slope stability
calculations with the boundary conditions imposed.
|
Material
|
Geometry
|
Boundary Conditions
|
|
Soil Material:
ks = 1 m/s
Unsatured soil: Dependency tables
|
Detailed on scheme ahead
|
-TH = 10 m
-Seepage face review =Q= 0 m3
-Horizontal drain. TH =0 m
|
Problem
description
Analysis Assumption and Modeling Notes
The seepage model has been
developed with an Unsatured/Satured hydraulic property. That is, both the
conductivity factor and the volumetric water content have been established
variable with respect the pressure head. The permeability function used in the
analysis will be visualized ahead:
Soil Material:
This transient model has been carried out
in order to evaluate the pore pressure change with respect time. We are
evaluating the model along with their boundary conditions until the steady
state is almost reached.
In the previous image, bouyndary conditions
are visualized. First of all, it is noticeable that the water level is located
to the left side, reaching a height of 10 m. In other instance, the right side
of the dam shares two boundary conditions. Firstly, a horizontal drain, which
function woul be to move out the necessary amount of water in case of being
mandatory. The drain would be 12 meters long, being located in the bottom part
of the dam with a total head of 0 m. By last, a seepage face review boundary
condition has been created in order to make sure the water table is properly
found.
The seepage face review boundary condition
allows to establish the condition H=y over a list of selected nodes, being H
their total head value and y their height. Thus, we now that in case H=y=0,
this implys that those nodes would belong to the water table. Although the
transient analysis has been solved with different times, visualized ahead:
ˇ
10
h, 50 h, 100 h, 500 h and 10000 h.
A load case for every time step will be
created so as to evaluate the pressure head change along time until the model
reach to a steady state flow condition.
The solution will be evaluated on a point
located almost in the middle part of the section, for instance the point (25,
0, 5).
On the other hand, some particular solution
controls have been modified. A value of 0.01m was entered for the tolerance
∆m. This will make more precise when calculating the water table
solution.
