V. Column Pushover Displacement
Compare theoretical solution to a pushover analysis to the STAAD.Pro solution.
Reference
Hand calculation.
Problem
A transverse load P is applied to a cantilever member and increased until the member fails.
Member length = 24 inch
Section = Wide flange W16X77
Material = Steel
Expected yield strength = 36 ksi
Results from STAAD.Pro
The analysis results are saved at an interval of 0.1 inch deflection of the cantilever tip. The following results are displayed in the Postprocessing workflow by selecting the Dynamics group on the Results ribbon tab.
tool in theLoad Step | Displacement in | Base Shear kip |
---|---|---|
1 | 0 | 0.153 |
2 | 0.001 | 1.153 |
3 | 0.078 | 57.837 |
4 | 0.136 | 61.953 |
5 | 0.243 | 63.979 |
6 | 0.349 | 65.979 |
7 | 0.455 | 67.979 |
8 | 0.562 | 69.979 |
9 | 0.668 | 71.979 |
10 | 0.774 | 73.979 |
11 | 0.880 | 75.979 |
12 | 0.986 | 77.979 |
13 | 1.065 | 79.479 |
14 | 1.065 | 21.510 |
Results from hand calculation
At Load Step 3
At Load Step 13
Plastic rotation = 0.04 radian.
Since STAAD.Pro assumes small displacements (sinθ = θ), plastic deformation at cantilever tip
Total deflection = δz elastic + δz plastic = 0.108 + 0.96 = 1.068 inch
Comparison
Load Step | Force P (free end) kips | Deflection (free end) in | Percent Difference | |
---|---|---|---|---|
STAAD.Pro Advanced Analysis | Hand Calculation | |||
3 | 57.837 | 0.078 | 0.078 | none |
13 | 79.479 | 1.065 | 1.068 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\07 Nonlinear Analysis\Column Pushover Displacement.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 20-Jul-07
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 0 24 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W16X77
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
DEFINE PUSHOVER DATA
FRAME 2
FYE 36.000000 ALL
HINGE PROPERTY MOMENT
TYPE 1
A 0 0 B 1 1 C 11 1.3 D 11 0.32 E 15 0.32 YM 1480 YR 0.004
IO 2 LS 7 CP 10.5
HINGE TYPE 1 ALL
GNONL 1
DISP Z 2 JOINT 2
LOADING PATTERN 1
LDSTEP 1
SPECTRUM PARAMETERS
DAMPING 2.0000
SC 4
SS 1.1
S1 1.6
SAVE LOADSTEP RESULT DISP 0.100000
END PUSHOVER DATA
LOAD 1 LOADTYPE Gravity
SELFWEIGHT Z 1
LOAD 2 LOADTYPE Push
JOINT LOAD
2 FZ 1
PERFORM PUSHOVER ANALYSIS
FINISH
STAAD Output
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 2 NUMBER OF MEMBERS 1
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 1
Using 64-bit analysis engine.
SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 6
TOTAL LOAD COMBINATION CASES = 0 SO FAR.
MORE MODES WERE REQUESTED THAN THERE ARE FREE MASSES.
NUMBER OF MODES REQUESTED = 6
NUMBER OF EXISTING MASSES IN THE MODEL = 3
NUMBER OF MODES THAT WILL BE USED = 3
*** EIGENSOLUTION : ADVANCED METHOD ***
STAAD SPACE -- PAGE NO. 3
CALCULATED FREQUENCIES FOR LOAD CASE 3
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)
1 306.367 0.00326
2 544.518 0.00184
3 1865.405 0.00054
MODAL WEIGHT (MODAL MASS TIMES g) IN KIP GENERALIZED
MODE X Y Z WEIGHT
1 0.000000E+00 0.000000E+00 7.674960E-02 7.674960E-02
2 7.674960E-02 0.000000E+00 0.000000E+00 7.674960E-02
3 0.000000E+00 7.674960E-02 0.000000E+00 7.674960E-02
MASS PARTICIPATION FACTORS
MASS PARTICIPATION FACTORS IN PERCENT
--------------------------------------
MODE X Y Z SUMM-X SUMM-Y SUMM-Z
1 0.00 0.00 100.00 0.000 0.000 100.000
2 100.00 0.00 0.00 100.000 0.000 100.000
3 0.00 100.00 0.00 100.000 100.000 100.000
***WARNING: MEMBER # 1 HAS FAILED IN " DEFORMATION-CONTROLLED ACTION.
*** WARNING : STRUCTURE HAS REACHED AN UNSTABLE STATE WHERE
A VERY SMALL INCREASE IN PUSH LOAD IS CAUSING LARGE DISPLACEMENT.