V. Time History - Blast Loading
Determine the dynamic response of a tower subjected to blast loading.
Reference
Paz, Mario. 1985. Structural Dynamics Theory and Computation. 2nd Edition. New York, NY:Van Nostrand Reinhold. pp72-74Problem
- 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
Result | Reference | STAAD.Pro* | Difference | Comments | |
---|---|---|---|---|---|
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.
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\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
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass TITLE REF LOAD CASE 1
JOINT LOAD
2 FX 38.6
END DEFINE REFERENCE LOADS
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
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
REFERENCE LOAD
R1 1.0
TIME LOAD
2 FX 1 1 1.000000
PERFORM ANALYSIS
FINISH
STAAD.Pro Output
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