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CFVR1713 - Eurocode 8-2004: Vertical type 2 elastic spectrum

Seismic Analysis on a 1 DOF beam according to Eurocode 8

This example compares spectrum accelerations given by CivilFEM to accelerations obtained when solving on a 1 DOF beam and to the correct Eurocode spectrum accelerations.
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.
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.
The spectrum is defined with the following parameters:
  • Vertical
  • Elastic
  • Type 2
  • Soil type C
  • 7% Damping
  • Base acceleration of 1.2753 cm/s2

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: CFVR1713.DAT


   FINISH
  ~CFCLEAR,,1
  NomFile='CFVR1713'
  /TITLE, %NomFile%, Eurocode 8-2004: Vertical type 2 elastic spectrum

! ----------------------------------------------------------------------
! Model definition
! ----------------------------------------------------------------------
! Setup: Code & Units
~UNITS,,LENG,CM
~UNITS,,TIME,S
~UNITS,,FORC,KP
~CODESEL,EC3-92,EC2-91,,,EC8-04
/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,IZZ,SECTION,1,MECHPROP,IZZ,,2   ! Izz  : Moment of inertia
  ~CFGET,IYY,SECTION,1,MECHPROP,IYY,,2   ! Iyy  : Moment of inertia

! Seismic Spectrum
  ~DEFSPEC,ALL,1.2753,C,ELASTIC,2,1,1,7

  pi=3.141592654

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

! Marix 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,TV,,II,2       ! Period
		 ! 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,0
   TYPE,2
   MAT, 1
   REAL,2
   EN,2,10
   FINISH
   /SOLU

 ! Solution
 ! ---------------------------------------------------------------------
 ! Displacements
   D, 1,,,,,,ALL,,,,,
   D,10,,,,,,UX,UZ,ROTX,ROTY,ROTZ,
   ~MODLSOL,1
   ~CMBMOD,NONE,VERTICAL,NONE,0,0.0001,
 ! Query results
   *GET,DispY,NODE,10,U,Y
 ! Correct values
   VALUE(20-II+1,1)=DispY*K/Mass ! Acceleration
 ! Obtained values
   ~CFGET,VALUE(20-II+1,2),SEISM,,SPEC,SDV,,II,2	 ! Y components of spectrum
   ~CFGET,VALUE(40-II+1,2),SEISM,,SPEC,SDV,,II,2	 ! Y components of spectrum
   ! 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
   /PREP7
   EDELE,2
*ENDDO

! Correct values
! ----------------------------------------------------------------------
   VALUE(21,1) = 0.7164  ! T=0.007s
   VALUE(22,1) = 0.8590
   VALUE(23,1) = 1.0015
   VALUE(24,1) = 1.1440
   VALUE(25,1) = 1.2866
   VALUE(26,1) = 1.4291
   VALUE(27,1) = 1.5716  ! TB=0.05s
   VALUE(28,1) = 1.5716  ! TC=0.15s
   VALUE(29,1) = 0.8083
   VALUE(30,1) = 0.5440
   VALUE(31,1) = 0.4100
   VALUE(32,1) = 0.3289
   VALUE(33,1) = 0.2747
   VALUE(34,1) = 0.2357  ! TD=1s
   VALUE(35,1) = 0.0377
   VALUE(36,1) = 0.0147
   VALUE(37,1) = 0.0078
   VALUE(38,1) = 0.0048
   VALUE(39,1) = 0.0033
   VALUE(40,1) = 0.0024  ! T=10s

! Warning and error tolerances
! ----------------------------------------------------------------------
  *DO,II,1,NComp
    TOLER(II, 1)= 1E-03 $ TOLER(II, 2)= 1E-03
  *ENDDO

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

Results

LabelTargetCivilFEMRatioTolerance
Sa(1)y 0.71642 0.716421.000 0.001
Sa(2)y 0.85896 0.858961.000 0.001
Sa(3)y 1.0015 1.00151.000 0.001
Sa(4)y 1.144 1.1441.000 0.001
Sa(5)y 1.2866 1.28661.000 0.001
Sa(6)y 1.4291 1.42911.000 0.001
Sa(7)y 1.5717 1.57161.000 0.001
Sa(8)y 1.5716 1.57161.000 0.001
Sa(9)y 0.80827 0.808281.000 0.001
Sa(10)y 0.54403 0.544031.000 0.001
Sa(11)y 0.41 0.411.000 0.001
Sa(12)y 0.32895 0.328951.000 0.001
Sa(13)y 0.27466 0.274661.000 0.001
Sa(14)y 0.23575 0.235751.000 0.001
Sa(15)y 0.03772 0.037721.000 0.001
Sa(16)y 0.014734 0.0147341.000 0.001
Sa(17)y 0.0077933 0.00779331.000 0.001
Sa(18)y 0.0048112 0.00481121.000 0.001
Sa(19)y 0.0032629 0.00326291.000 0.001
Sa(20)y 0.0023575 0.00235751.000 0.001
Sa(1)y 0.7164 0.716421.000 0.001
Sa(2)y 0.859 0.858961.000 0.001
Sa(3)y 1.0015 1.00151.000 0.001
Sa(4)y 1.144 1.1441.000 0.001
Sa(5)y 1.2866 1.28661.000 0.001
Sa(6)y 1.4291 1.42911.000 0.001
Sa(7)y 1.5716 1.57161.000 0.001
Sa(8)y 1.5716 1.57161.000 0.001
Sa(9)y 0.8083 0.808281.000 0.001
Sa(10)y 0.544 0.544031.000 0.001
Sa(11)y 0.41 0.411.000 0.001
Sa(12)y 0.3289 0.328951.000 0.001
Sa(13)y 0.2747 0.274661.000 0.001
Sa(14)y 0.2357 0.235751.000 0.001
Sa(15)y 0.0377 0.037721.000 0.001
Sa(16)y 0.0147 0.0147340.998 0.001
Sa(17)y 0.0078 0.00779331.001 0.001
Sa(18)y 0.0048 0.00481120.998 0.001
Sa(19)y 0.0033 0.00326291.011 0.001
Sa(20)y 0.0024 0.00235751.018 0.001


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