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CFVR1706 - Eurocode 8-1994: Seismic Analysis (Elastic spectrum) Z-axis

Seismic Analysis on a 1 DOF beam according to Eurocode 8-1994

This example compares spectrum accelerations given by CivilFEM to accelerations obtained when solving on a one degree of freedom beam and to the correct Eurocode spectum accelerations.
The model is a single beam element with only one degree of freedom (the rest of the DOF are constrained). The beam has no mass. A punctual mass is applied at the free end of the beam.
After solving, the mass acceleration is obtained and compared to the CivilFEM spectrum acceleration and to the correct value. Therefore, this example checks the following results:

  • CivilFEM spectrum is defined correctly by comparing to the correct value.
  • CivilFEM spectrum is applied correctly and response acceleration is equal to spectrum acceleration.

Element types used in the model: BEAM4, MASS21

Needed CivilFEM Modules:
Geotechnical Module
Bridges and Civil Non Linearities Module
Advanced Prestressed Concrete Module

The example can be launched on an educational license.
KEYWORDS
Seismic
Eurocode 8

Model Statistics
Number of elements 1
Number of nodes 2
Number of civil materials 1
Number of cross sections 1
Number of shell vertices 0

Log file: CFVR1706.DAT


   FINISH
  ~CFCLEAR,,1
  NomFile='CFVR1706'
  /TITLE, %NomFile%, Eurocode 8-1994: Seismic Analysis (Elastic spectrum) Z-axis

! ----------------------------------------------------------------------
! Model definition
! ----------------------------------------------------------------------
! Setup: Code & Units
~UNITS,,LENG,CM
~UNITS,,TIME,S
~UNITS,,FORC,KP
~CODESEL,EC3-92,EC2-91,,,EC8-94
/PREP7
! Preprocessor
! ----------------------------------------------------------------------
! Materials: A-42
 ~CFMP,1,LIB,STEEL,EA,A42
! Modify density (Rho = 0)
 ~CFMP,1,USER
 ~CFMP,1,DatGen,RHO,,0
! Element Types
  ET,1,BEAM4   ! Type 1: 3D Beam
  ET,2,MASS21  ! Type 2: Mass
! Sections
 ~SSECLIB,1,1,1,1   ! IPE 80
 ~BMSHPRO,1,BEAM,1,1,,,4,,0,,

! Nodes
  L = 10              ! L    : Bar length
  N, 1
  N,10,L

! Elements
  TYPE,1
  MAT ,1
  REAL,1
  EN,1,1,10
  EPLOT
! Parameters
  *GET,EXX,EX,1                          ! Ex   : Elastic Modulus
  ~CFGET,BarAr,SECTION,1,MECHPROP,A,,2   ! Area : Bar area
  ~CFGET,IZZ,SECTION,1,MECHPROP,IZZ,,2   ! Izz  : Moment of inertia
  ~CFGET,IYY,SECTION,1,MECHPROP,IYY,,2   ! Iyy  : Moment of inertia

! Spectrum definition
  ~DEFSPEC,ALL,1.2753,A,ELASTIC,1,1,5,

  pi=3.141592654
  Direction= 3 ! Direction ( 1: X, 2: Y, 3: Z),1

! ----------------------------------------------------------------------
! DATA CHECK
! ----------------------------------------------------------------------
! Data comparison number
  NComp = 40
  NComp_ch = 0

! Matrix dim.
  *DIM,LABEL,CHAR,Ncomp,1
  *DIM,LABEL_CH,CHAR,Ncomp_ch,1
  *DIM,VALUE,,Ncomp,3
  *DIM,VALUE_CH,CHAR,Ncomp_ch,3
  *DIM,TOLER,,Ncomp,2

*DO,II,1,20
   /PREP7
   ~CFGET,Per,SEISM,,SPEC,TH,,II,2   ! Period
   *IF,Direction,EQ,1,THEN
    ! Labels
     LABEL(II,1) = 'Sa(%II%)x'
     LABEL(20+II,1) = 'Sa(%II%)x'
     K=EXX*BarAr/L
     Mass=K*(Per/(2*pi))**2  ! Mass applied at end
     R,2,Mass
   *ELSEIF,Direction,EQ,2,THEN
    ! Labels
     LABEL(II,1) = 'Sa(%II%)y'
     LABEL(20+II,1) = 'Sa(%II%)y'
     K=12*EXX*IZZ/L**3     ! Bending stiffness around Z axis
     Mass=K*(Per/(2*pi))**2  ! Mass applied at end
     R,2,0,Mass
   *ELSEIF,Direction,EQ,3,THEN
    ! Labels
     LABEL(II,1) = 'Sa(%II%)z'
     LABEL(20+II,1) = 'Sa(%II%)z'
     K=12*EXX*IYY/L**3     ! Bending stiffness around Y axis
     Mass=K*(Per/(2*pi))**2  ! Mass applied at end
     R,2,0,0,Mass
   *ENDIF
   TYPE,2
   MAT, 1
   REAL,2
   EN,2,10
   FINISH
   /SOLU

 ! Solution
 ! ---------------------------------------------------------------------
 ! Displacements
   D,1,,,,,,ALL,,,,,
   *IF,Direction,EQ,1,THEN
     D,10,,,,,,UY,UZ,ROTX,ROTY,ROTZ,
   *ELSEIF,Direction,EQ,2,THEN
     D,10,,,,,,UX,UZ,ROTX,ROTY,ROTZ,
   *ELSEIF,Direction,EQ,3,THEN
     D,10,,,,,,UX,UY,ROTX,ROTY,ROTZ,
   *ENDIF
    ~MODLSOL,1
   *IF,Direction,EQ,1,THEN
     ~CMBMOD,HORIZONT,NONE,NONE,0,0.0001,
   *ELSEIF,Direction,EQ,2,THEN
     ~CMBMOD,NONE,HORIZONT,NONE,0,0.0001,
   *ELSEIF,Direction,EQ,3,THEN
     ~CMBMOD,NONE,NONE,HORIZONT,0,0.0001,
   *ENDIF
 ! Query results
   *IF,Direction,EQ,1,THEN
     *GET,Displ,NODE,10,U,X
   *ELSEIF,Direction,EQ,2,THEN
     *GET,Displ,NODE,10,U,Y
   *ELSEIF,Direction,EQ,3,THEN
     *GET,Displ,NODE,10,U,Z
   *ENDIF
 ! Correct values
   VALUE(20-II+1,1)=Displ*K/Mass ! Acceleration
 ! Obtained values
   ~CFGET,VALUE(20-II+1,2),SEISM,,SPEC,SDH,,II,2	 ! Y components of elastic horizontal spectrum
   ~CFGET,VALUE(40-II+1,2),SEISM,,SPEC,SDH,,II,2	 ! Y components of elastic horizontal spectrum
   /PREP7
   ! CivilFEM gives the spectrum Normalized by gravity.
   ! To compare it must be changed to acceleration user units.
   VALUE(20-II+1,2) = VALUE(20-II+1,2)*981
   VALUE(40-II+1,2) = VALUE(40-II+1,2)*981
   EDELE,2
*ENDDO

! Correct values
! ----------------------------------------------------------------------
		 VALUE(40,1) = 0.3825E-01
		 VALUE(39,1) = 0.4250
		 VALUE(38,1) = 0.7286
		 VALUE(37,1) = 1.133
		 VALUE(36,1) = 1.569
		 VALUE(35,1) = 1.943
		 VALUE(34,1) = 2.550
		 VALUE(33,1) = 2.834
		 VALUE(32,1) = 3.188
		 VALUE(31,1) = 3.188
		 VALUE(30,1) = 3.188
		 VALUE(29,1) = 3.188
		 VALUE(28,1) = 2.951
		 VALUE(27,1) = 2.714
		 VALUE(26,1) = 2.478
		 VALUE(25,1) = 2.241
		 VALUE(24,1) = 2.004
		 VALUE(23,1) = 1.767
		 VALUE(22,1) = 1.531
		 VALUE(21,1) = 1.294

! Warning and error tolerances
! ----------------------------------------------------------------------
  *DO,II,1,40
   TOLER(II, 1)= 1E-3 $ TOLER(II, 2)= 1E-3
  *ENDDO

! ----------------------------------------------------------------------
! Results Comparison
! ----------------------------------------------------------------------
  COMPARA.MAC

Results

LabelTargetCivilFEMRatioTolerance
Sa(1)z 1.2944 1.29441.000 0.001
Sa(2)z 1.5312 1.53121.000 0.001
Sa(3)z 1.7679 1.76791.000 0.001
Sa(4)z 2.0046 2.00461.000 0.001
Sa(5)z 2.2413 2.24131.000 0.001
Sa(6)z 2.4781 2.47811.000 0.001
Sa(7)z 2.7148 2.71481.000 0.001
Sa(8)z 2.9515 2.95151.000 0.001
Sa(9)z 3.1883 3.18831.000 0.001
Sa(10)z 3.1882 3.18831.000 0.001
Sa(11)z 3.1883 3.18831.000 0.001
Sa(12)z 3.1883 3.18831.000 0.001
Sa(13)z 2.834 2.8341.000 0.001
Sa(14)z 2.5506 2.55061.000 0.001
Sa(15)z 1.9433 1.94331.000 0.001
Sa(16)z 1.5696 1.56961.000 0.001
Sa(17)z 1.1336 1.13361.000 0.001
Sa(18)z 0.72874 0.728741.000 0.001
Sa(19)z 0.4251 0.42511.000 0.001
Sa(20)z 0.038259 0.0382591.000 0.001
Sa(1)z 1.294 1.29441.000 0.001
Sa(2)z 1.531 1.53121.000 0.001
Sa(3)z 1.767 1.76791.000 0.001
Sa(4)z 2.004 2.00461.000 0.001
Sa(5)z 2.241 2.24131.000 0.001
Sa(6)z 2.478 2.47811.000 0.001
Sa(7)z 2.714 2.71481.000 0.001
Sa(8)z 2.951 2.95151.000 0.001
Sa(9)z 3.188 3.18831.000 0.001
Sa(10)z 3.188 3.18831.000 0.001
Sa(11)z 3.188 3.18831.000 0.001
Sa(12)z 3.188 3.18831.000 0.001
Sa(13)z 2.834 2.8341.000 0.001
Sa(14)z 2.55 2.55061.000 0.001
Sa(15)z 1.943 1.94331.000 0.001
Sa(16)z 1.569 1.56961.000 0.001
Sa(17)z 1.133 1.13361.000 0.001
Sa(18)z 0.7286 0.728741.000 0.001
Sa(19)z 0.425 0.42511.000 0.001
Sa(20)z 0.03825 0.0382591.000 0.001


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