## Reference

Paz, Mario. 1985. Structural Dynamics Theory and Computation. 2nd Edition. New York, NY:Van Nostrand Reinhold. pp72-74

## Problem

• Material modulus of elasticity (assumed steel), E = 29,000 ksi and Poisson's ratio, ν = 0.3
• Length (assumed) = 10 ft
• Section moment of inertia, Iz = 1,986.4 in4 (given K = 100 kip/in, rearrange K = 3EI/L3 to solve for I = KEL3/3
• Horizontal weight applied at top of 10' tower, Fx = 38.6 kips

## Comparison

Nodal displacement at top (in.) at t = 0 0.000 0.000 none
0.02 0.078 0.078 none
0.04 0.512 0.512 none
0.06 1.134 1.134 none
0.08 1.395 1395 none
0.10 1.117 1.117 none

* The STAAD.Pro results are taken from the text data output file with the extension .tim.

Note: Apart from .tim file, time-displacement graphs in postprocessing also display the results graphically.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\08 Dynamic Analysis\Time History - Blast Loading.STD is typically installed with the program.

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 07-Mar-17
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 10 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT FEET KIP
PRISMATIC
CANTILEVER
1e+009 0.095785 0.001 0.001 0.001 0.001 0.5 0.5
END
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+006
POISSON 0.3
DENSITY 0.489024
ALPHA 6e-006
DAMP 1.1e-006
TYPE STEEL
STRENGTH FY 5184 FU 8352 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 UPTABLE 1 CANTILEVER
CONSTANTS
MATERIAL STEEL MEMB 1
SUPPORTS
1 FIXED
2 FX 38.6
CUT OFF MODE SHAPE 0
CUT OFF TIME 0.1999
CUT OFF FREQUENCY 1000
DEFINE TIME HISTORY DT 0.0001
TYPE 1 FORCE SAVE
0 0 0.02 120 0.04 120 0.06 0 0.08 0 0.1 0 0.2 0
ARRIVAL TIME
0
DAMPING 1.1e-006
R1 1.0
2 FX 1 1 1.000000
PERFORM ANALYSIS
FINISH
``````

### Horizontal displacement vs time graph in Postprocessing workflow

```               CALCULATED FREQUENCIES FOR LOAD CASE       1
MODE            FREQUENCY(CYCLES/SEC)         PERIOD(SEC)
1                       5.033                  0.19867
MODAL WEIGHT (MODAL MASS TIMES g) IN KIP          GENERALIZED
MODE           X             Y             Z              WEIGHT
1       3.860000E+01  0.000000E+00  0.000000E+00    3.860000E+01
MASS PARTICIPATION FACTORS
MASS  PARTICIPATION FACTORS IN PERCENT
--------------------------------------
MODE    X     Y     Z     SUMM-X   SUMM-Y   SUMM-Z
1   100.00   0.00   0.00  100.000    0.000    0.000
A C T U A L  MODAL  D A M P I N G  USED IN ANALYSIS
MODE       DAMPING
*WARNING* Damping Ratio reset from .0000011 to 0.0 for modes
1      0.00000000
TIME STEP USED IN TIME HISTORY ANALYSIS = 0.00010 SECONDS
NUMBER OF MODES WHOSE CONTRIBUTION IS CONSIDERED =    1
TIME DURATION OF TIME HISTORY ANALYSIS =      0.200 SECONDS
NUMBER OF TIME STEPS IN THE SOLUTION PROCESS =     1999
55. FINISH
BASE SHEAR UNITS ARE -- KIP  FEET
MAXIMUM BASE SHEAR  X=   1.395310E+02  Y=   0.000000E+00  Z=   0.000000E+00
AT TIMES               0.178900           0.000000           0.000000
STAAD SPACE                                              -- PAGE NO.    4
```