CFVR1704 - Eurocode 8-1994: Seismic Analysis (Elastic spectrum) X-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: |
|
| 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: CFVR1704.DAT
FINISH ~CFCLEAR,,1 NomFile='CFVR1704' /TITLE, %NomFile%, Eurocode 8-1994: Seismic Analysis (Elastic spectrum) X-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= 1 ! 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 ! 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(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) = 2.833 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,NComp TOLER(II, 1)= 1E-03 $ TOLER(II, 2)= 1E-03 *ENDDO ! ---------------------------------------------------------------------- ! Results Comparison ! ---------------------------------------------------------------------- COMPARA.MAC |
Results
| Label | Target | CivilFEM | Ratio | Tolerance |
| Sa(1)x | 1.2944 | 1.2944 | 1.000 | 0.001 |
| Sa(2)x | 1.5312 | 1.5312 | 1.000 | 0.001 |
| Sa(3)x | 1.7679 | 1.7679 | 1.000 | 0.001 |
| Sa(4)x | 2.0046 | 2.0046 | 1.000 | 0.001 |
| Sa(5)x | 2.2413 | 2.2413 | 1.000 | 0.001 |
| Sa(6)x | 2.4781 | 2.4781 | 1.000 | 0.001 |
| Sa(7)x | 2.7148 | 2.7148 | 1.000 | 0.001 |
| Sa(8)x | 2.9515 | 2.9515 | 1.000 | 0.001 |
| Sa(9)x | 3.1883 | 3.1883 | 1.000 | 0.001 |
| Sa(10)x | 3.1883 | 3.1883 | 1.000 | 0.001 |
| Sa(11)x | 3.1882 | 3.1883 | 1.000 | 0.001 |
| Sa(12)x | 3.1883 | 3.1883 | 1.000 | 0.001 |
| Sa(13)x | 2.834 | 2.834 | 1.000 | 0.001 |
| Sa(14)x | 2.5506 | 2.5506 | 1.000 | 0.001 |
| Sa(15)x | 1.9433 | 1.9433 | 1.000 | 0.001 |
| Sa(16)x | 1.5696 | 1.5696 | 1.000 | 0.001 |
| Sa(17)x | 1.1336 | 1.1336 | 1.000 | 0.001 |
| Sa(18)x | 0.72874 | 0.72874 | 1.000 | 0.001 |
| Sa(19)x | 0.4251 | 0.4251 | 1.000 | 0.001 |
| Sa(20)x | 0.038259 | 0.038259 | 1.000 | 0.001 |
| Sa(1)x | 1.294 | 1.2944 | 1.000 | 0.001 |
| Sa(2)x | 1.531 | 1.5312 | 1.000 | 0.001 |
| Sa(3)x | 1.767 | 1.7679 | 1.000 | 0.001 |
| Sa(4)x | 2.004 | 2.0046 | 1.000 | 0.001 |
| Sa(5)x | 2.241 | 2.2413 | 1.000 | 0.001 |
| Sa(6)x | 2.478 | 2.4781 | 1.000 | 0.001 |
| Sa(7)x | 2.714 | 2.7148 | 1.000 | 0.001 |
| Sa(8)x | 2.951 | 2.9515 | 1.000 | 0.001 |
| Sa(9)x | 3.188 | 3.1883 | 1.000 | 0.001 |
| Sa(10)x | 3.188 | 3.1883 | 1.000 | 0.001 |
| Sa(11)x | 3.188 | 3.1883 | 1.000 | 0.001 |
| Sa(12)x | 3.188 | 3.1883 | 1.000 | 0.001 |
| Sa(13)x | 2.833 | 2.834 | 1.000 | 0.001 |
| Sa(14)x | 2.55 | 2.5506 | 1.000 | 0.001 |
| Sa(15)x | 1.943 | 1.9433 | 1.000 | 0.001 |
| Sa(16)x | 1.569 | 1.5696 | 1.000 | 0.001 |
| Sa(17)x | 1.133 | 1.1336 | 1.000 | 0.001 |
| Sa(18)x | 0.7286 | 0.72874 | 1.000 | 0.001 |
| Sa(19)x | 0.425 | 0.4251 | 1.000 | 0.001 |
| Sa(20)x | 0.03825 | 0.038259 | 1.000 | 0.001 |
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