CFVR1712 - Eurocode 8-2004: Vertical type 1 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.
- Vertical
- Elastic
- Type 1
- Soil type B
- 5% 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: CFVR1712.DAT
FINISH ~CFCLEAR,,1 NomFile='CFVR1712' /TITLE, %NomFile%, Eurocode 8-2004: Vertical type 1 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,B,ELASTIC,1,1,1,5 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) = 1.4757 ! T=0.007s VALUE(22,1) = 1.8036 VALUE(23,1) = 2.1316 VALUE(24,1) = 2.4595 VALUE(25,1) = 2.7874 VALUE(26,1) = 3.1154 VALUE(27,1) = 3.4433 ! TB=0.05s VALUE(28,1) = 3.4433 ! TC=0.15s VALUE(29,1) = 1.7708 VALUE(30,1) = 1.1919 VALUE(31,1) = 0.8983 VALUE(32,1) = 0.7207 VALUE(33,1) = 0.6017 VALUE(34,1) = 0.5165 ! TD=1s VALUE(35,1) = 0.0826 VALUE(36,1) = 0.0323 VALUE(37,1) = 0.0171 VALUE(38,1) = 0.0105 VALUE(39,1) = 0.0071 VALUE(40,1) = 0.0052 ! 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 | 1.4757 | 1.4757 | 1.000 | 0.001 |
| Sa(2)y | 1.8036 | 1.8036 | 1.000 | 0.001 |
| Sa(3)y | 2.1316 | 2.1316 | 1.000 | 0.001 |
| Sa(4)y | 2.4595 | 2.4595 | 1.000 | 0.001 |
| Sa(5)y | 2.7874 | 2.7874 | 1.000 | 0.001 |
| Sa(6)y | 3.1154 | 3.1154 | 1.000 | 0.001 |
| Sa(7)y | 3.4433 | 3.4433 | 1.000 | 0.001 |
| Sa(8)y | 3.4433 | 3.4433 | 1.000 | 0.001 |
| Sa(9)y | 1.7708 | 1.7708 | 1.000 | 0.001 |
| Sa(10)y | 1.1919 | 1.1919 | 1.000 | 0.001 |
| Sa(11)y | 0.89825 | 0.89825 | 1.000 | 0.001 |
| Sa(12)y | 0.72069 | 0.72069 | 1.000 | 0.001 |
| Sa(13)y | 0.60174 | 0.60174 | 1.000 | 0.001 |
| Sa(14)y | 0.5165 | 0.5165 | 1.000 | 0.001 |
| Sa(15)y | 0.082639 | 0.082639 | 1.000 | 0.001 |
| Sa(16)y | 0.032281 | 0.032281 | 1.000 | 0.001 |
| Sa(17)y | 0.017074 | 0.017074 | 1.000 | 0.001 |
| Sa(18)y | 0.010541 | 0.010541 | 1.000 | 0.001 |
| Sa(19)y | 0.0071487 | 0.0071487 | 1.000 | 0.001 |
| Sa(20)y | 0.005165 | 0.005165 | 1.000 | 0.001 |
| Sa(1)y | 1.4757 | 1.4757 | 1.000 | 0.001 |
| Sa(2)y | 1.8036 | 1.8036 | 1.000 | 0.001 |
| Sa(3)y | 2.1316 | 2.1316 | 1.000 | 0.001 |
| Sa(4)y | 2.4595 | 2.4595 | 1.000 | 0.001 |
| Sa(5)y | 2.7874 | 2.7874 | 1.000 | 0.001 |
| Sa(6)y | 3.1154 | 3.1154 | 1.000 | 0.001 |
| Sa(7)y | 3.4433 | 3.4433 | 1.000 | 0.001 |
| Sa(8)y | 3.4433 | 3.4433 | 1.000 | 0.001 |
| Sa(9)y | 1.7708 | 1.7708 | 1.000 | 0.001 |
| Sa(10)y | 1.1919 | 1.1919 | 1.000 | 0.001 |
| Sa(11)y | 0.8983 | 0.89825 | 1.000 | 0.001 |
| Sa(12)y | 0.7207 | 0.72069 | 1.000 | 0.001 |
| Sa(13)y | 0.6017 | 0.60174 | 1.000 | 0.001 |
| Sa(14)y | 0.5165 | 0.5165 | 1.000 | 0.001 |
| Sa(15)y | 0.0826 | 0.082639 | 1.000 | 0.001 |
| Sa(16)y | 0.0323 | 0.032281 | 1.001 | 0.001 |
| Sa(17)y | 0.0171 | 0.017074 | 1.002 | 0.001 |
| Sa(18)y | 0.0105 | 0.010541 | 0.996 | 0.001 |
| Sa(19)y | 0.0071 | 0.0071487 | 0.993 | 0.001 |
| Sa(20)y | 0.0052 | 0.005165 | 1.007 | 0.001 |
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