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. pp72-74

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, I_z = 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, F_x = 38.6 kips

Segmented linear function

Comparison

Result		Reference	STAAD.Pro*	Difference
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 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
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

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