CFVR4403 - AASHTO LRFD: Seismic Analysis Z-axis

Seismic Analysis on a 1 DOF beam according to AASHTO LRFD

This example compares spectrum accelerations given by CivilFEM to accelerations obtained when solving on a 1 DOF beam and to the correct AASHTO LRFD spectum accelerations.
The model is 1 element beam with only 1 DOF, which direction the CivilFEM spectrum is set (the rest of the DOF are constrained). A different mass is applied at the free end of the beam for the beam period to be equal to the 20 CivilFEM spectrum points. 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:

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
AASHTO

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: CFVR4403.DAT


   FINISH
  ~CFCLEAR,,1
   NomFile='CFVR4403'
  /TITLE, %NomFile%, AASHTO LRFD: Seismic Analysis Z-axis
! ----------------------------------------------------------------------
! Model definition
! ----------------------------------------------------------------------
! CivilFEM Setup: Code & Units
~UNITS,,LENG,CM
~UNITS,,TIME,S
~UNITS,,FORC,KP
~CODESEL,,,,,AASHTO
/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,AR20,EX,1                            ! Ex   : Elastic Modulus
  ~CFGET,AR22,SECTION,1,MECHPROP,A,,2       ! Area : Bar area
  ~CFGET,AR23,SECTION,1,MECHPROP,IZZ,,2     ! Izz  : Moment of inertia
  ~CFGET,AR24,SECTION,1,MECHPROP,IYY,,2     ! Iyy  : Moment of inertia

! Spectrum definition
  ~DEFSPEC,ALL,1.2753,I,1,2/3

  pi=3.141592654

! ----------------------------------------------------------------------
! 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,ARG1,1,20
   /PREP7
   ~CFGET,AR26,SEISM,,SPEC,TH,,ARG1,1     ! Period
  ! Labels
   LABEL(ARG1,1) = 'Sa(%ARG1%)z'
   LABEL(20+ARG1,1) = 'Sa(%ARG1%)z'

   AR25=12*AR20*AR24/L**3      ! Bending rigidity around Y axis
   AR27=AR25*(AR26/(2*pi))**2  ! Mass applied at end
   R,2,0,0,AR27
   TYPE,2
   MAT, 1
   REAL,2
   EN,2,10
   FINISH
   /SOLU

 ! Displacements
   D,1,,,,,,ALL
   D,10,,,,,UX,UY,,ROTX,ROTY,ROTZ
   ~MODLSOL,1
   ~CMBMOD,NONE,NONE,HORIZONT,0,0.0001
 ! Query results
   *GET,ARG5,NODE,10,U,Z
 ! Correct values
   VALUE(20-ARG1+1,1)=ARG5*AR25/AR27 ! Acceleration
 ! Obtained values
   ~CFGET,VALUE(20-ARG1+1,2),SEISM,,SPEC,SDH,,ARG1,1	 ! Y components of horizontal spectrum
   ~CFGET,VALUE(40-ARG1+1,2),SEISM,,SPEC,SDH,,ARG1,1	 ! Y components of horizontal spectrum
   ! CivilFEM gives the spectrum Normalized by gravity.
   ! To compare it must be changed to acceleration user units.
   VALUE(20-ARG1+1,2) = VALUE(20-ARG1+1,2)*981
   VALUE(40-ARG1+1,2) = VALUE(40-ARG1+1,2)*981
   /PREP7
   EDELE,2
*ENDDO

! Correct values
! ----------------------------------------------------------------------
   VALUE(40,1) = 174.2
   VALUE(39,1) = 191.0
   VALUE(38,1) = 210.8
   VALUE(37,1) = 234.6
   VALUE(36,1) = 263.4
   VALUE(35,1) = 299.1
   VALUE(34,1) = 344.2
   VALUE(33,1) = 402.8
   VALUE(32,1) = 481.3
   VALUE(31,1) = 595.8
   VALUE(30,1) = 640.0
   VALUE(29,1) = 693.5
   VALUE(28,1) = 759.8
   VALUE(27,1) = 844.5
   VALUE(26,1) = 957.7
   VALUE(25,1) = 1118.
   VALUE(24,1) = 1370.
   VALUE(23,1) = 1835.
   VALUE(22,1) = 3128.
   VALUE(21,1) = 3128.

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

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

Results

LabelTargetCivilFEMRatioTolerance
Sa(1)z 3127.7 3127.71.000 1
Sa(2)z 3127.7 3127.71.000 1
Sa(3)z 1834.9 1834.91.000 1
Sa(4)z 1369.7 1369.71.000 1
Sa(5)z 1118.5 1118.51.000 1
Sa(6)z 957.75 957.751.000 1
Sa(7)z 844.55 844.551.000 1
Sa(8)z 759.78 759.791.000 1
Sa(9)z 693.51 693.511.000 1
Sa(10)z 640.03 640.031.000 1
Sa(11)z 595.78 595.781.000 1
Sa(12)z 481.28 481.281.000 1
Sa(13)z 402.78 402.781.000 1
Sa(14)z 344.24 344.241.000 1
Sa(15)z 299.13 299.131.000 1
Sa(16)z 263.43 263.431.000 1
Sa(17)z 234.58 234.581.000 1
Sa(18)z 210.83 210.831.000 1
Sa(19)z 190.99 190.991.000 1
Sa(20)z 174.21 174.211.000 1
Sa(1)z 3128 3127.71.000 1
Sa(2)z 3128 3127.71.000 1
Sa(3)z 1835 1834.91.000 1
Sa(4)z 1370 1369.71.000 1
Sa(5)z 1118 1118.51.000 1
Sa(6)z 957.7 957.751.000 1
Sa(7)z 844.5 844.551.000 1
Sa(8)z 759.8 759.791.000 1
Sa(9)z 693.5 693.511.000 1
Sa(10)z 640 640.031.000 1
Sa(11)z 595.8 595.781.000 1
Sa(12)z 481.3 481.281.000 1
Sa(13)z 402.8 402.781.000 1
Sa(14)z 344.2 344.241.000 1
Sa(15)z 299.1 299.131.000 1
Sa(16)z 263.4 263.431.000 1
Sa(17)z 234.6 234.581.000 1
Sa(18)z 210.8 210.831.000 1
Sa(19)z 191 190.991.000 1
Sa(20)z 174.2 174.211.000 1


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