CFVR1709 - Eurocode 8-2004: Horizontal 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.
- Horizontal
- 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: |
|
| 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: CFVR1709.DAT
FINISH ~CFCLEAR,,1 NomFile='CFVR1709' /TITLE, %NomFile%, Eurocode 8-2004: Horizontal 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,TH,,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,HORIZONT,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,SDH,,II,2 ! Y components of spectrum ~CFGET,VALUE(40-II+1,2),SEISM,,SPEC,SDH,,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) = 2.2633 ! T=0.014s VALUE(22,1) = 2.6137 VALUE(23,1) = 2.9641 VALUE(24,1) = 3.3145 VALUE(25,1) = 3.6649 VALUE(26,1) = 4.0153 VALUE(27,1) = 4.3657 ! TB=0.1s VALUE(28,1) = 4.3657 ! TC=0.25s VALUE(29,1) = 2.6729 VALUE(30,1) = 1.9260 VALUE(31,1) = 1.5054 VALUE(32,1) = 1.2356 VALUE(33,1) = 1.0478 VALUE(34,1) = 0.9095 ! TD=1.2s VALUE(35,1) = 0.1842 VALUE(36,1) = 0.0767 VALUE(37,1) = 0.0418 VALUE(38,1) = 0.0262 VALUE(39,1) = 0.0180 VALUE(40,1) = 0.0131 ! 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
| Label | Target | CivilFEM | Ratio | Tolerance |
| Sa(1)y | 2.2633 | 2.2633 | 1.000 | 0.001 |
| Sa(2)y | 2.6137 | 2.6137 | 1.000 | 0.001 |
| Sa(3)y | 2.9641 | 2.9641 | 1.000 | 0.001 |
| Sa(4)y | 3.3145 | 3.3145 | 1.000 | 0.001 |
| Sa(5)y | 3.6649 | 3.6649 | 1.000 | 0.001 |
| Sa(6)y | 4.0153 | 4.0153 | 1.000 | 0.001 |
| Sa(7)y | 4.3657 | 4.3657 | 1.000 | 0.001 |
| Sa(8)y | 4.3657 | 4.3657 | 1.000 | 0.001 |
| Sa(9)y | 2.6729 | 2.6729 | 1.000 | 0.001 |
| Sa(10)y | 1.926 | 1.926 | 1.000 | 0.001 |
| Sa(11)y | 1.5054 | 1.5054 | 1.000 | 0.001 |
| Sa(12)y | 1.2356 | 1.2356 | 1.000 | 0.001 |
| Sa(13)y | 1.0478 | 1.0478 | 1.000 | 0.001 |
| Sa(14)y | 0.90952 | 0.90952 | 1.000 | 0.001 |
| Sa(15)y | 0.18418 | 0.18418 | 1.000 | 0.001 |
| Sa(16)y | 0.076661 | 0.076661 | 1.000 | 0.001 |
| Sa(17)y | 0.041764 | 0.041764 | 1.000 | 0.001 |
| Sa(18)y | 0.026227 | 0.026227 | 1.000 | 0.001 |
| Sa(19)y | 0.017986 | 0.017986 | 1.000 | 0.001 |
| Sa(20)y | 0.013097 | 0.013097 | 1.000 | 0.001 |
| Sa(1)y | 2.2633 | 2.2633 | 1.000 | 0.001 |
| Sa(2)y | 2.6137 | 2.6137 | 1.000 | 0.001 |
| Sa(3)y | 2.9641 | 2.9641 | 1.000 | 0.001 |
| Sa(4)y | 3.3145 | 3.3145 | 1.000 | 0.001 |
| Sa(5)y | 3.6649 | 3.6649 | 1.000 | 0.001 |
| Sa(6)y | 4.0153 | 4.0153 | 1.000 | 0.001 |
| Sa(7)y | 4.3657 | 4.3657 | 1.000 | 0.001 |
| Sa(8)y | 4.3657 | 4.3657 | 1.000 | 0.001 |
| Sa(9)y | 2.6729 | 2.6729 | 1.000 | 0.001 |
| Sa(10)y | 1.926 | 1.926 | 1.000 | 0.001 |
| Sa(11)y | 1.5054 | 1.5054 | 1.000 | 0.001 |
| Sa(12)y | 1.2356 | 1.2356 | 1.000 | 0.001 |
| Sa(13)y | 1.0478 | 1.0478 | 1.000 | 0.001 |
| Sa(14)y | 0.9095 | 0.90952 | 1.000 | 0.001 |
| Sa(15)y | 0.1842 | 0.18418 | 1.000 | 0.001 |
| Sa(16)y | 0.0767 | 0.076661 | 1.000 | 0.001 |
| Sa(17)y | 0.0418 | 0.041764 | 1.001 | 0.001 |
| Sa(18)y | 0.0262 | 0.026227 | 0.999 | 0.001 |
| Sa(19)y | 0.018 | 0.017986 | 1.001 | 0.001 |
| Sa(20)y | 0.0131 | 0.013097 | 1.000 | 0.001 |
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