# V. Time History - Ground Acceleration

Determine the response of a two-story portal frame subjected to suddenly applied constant acceleration of 0.28 g at its base.

## Reference

Paz, Mario. 1985. Structural Dynamics Theory and Computation. 2nd Edition. New York, NY:Van Nostrand Reinhold. pp196-201, 213, & 217-219.

## Problem

• Material modulus of elasticity, E = 30,000 ksi and Poisson's ratio, ν = 0.3
• Section moment of inertia, Iz1 = 248.6 in4, Iz2 = 106.3 in4
• Mass at first story above ground, Fx = 52.5 kips, at roof story Fx = 25.5 kips
• Constant ground acceleration = 0.28g = 9.03917 ft/sec2

The ground acceleration is applied as a time vs. acceleration function with the data pairs supplied up to t = 2 sec.

## Comparison

Max. displacement at first floor (in); node 2 1.426 1.42605 negligible
Max. displacement at roof (in); node 5 1.789 1.78064 negligible

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

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 15 0; 3 30 15 0; 4 30 0 0; 5 0 25 0; 6 30 25 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 3 6; 6 5 6;
START USER TABLE
TABLE 1
UNIT FEET KIP
PRISMATIC
COLUMN1
1e+009 0.011989 0.001 0.001 0.001 0.001 0.5 0.5
COLUMN2
1e+009 0.005126 0.001 0.001 0.001 0.001 0.5 0.5
TABLE 2
UNIT FEET KIP
PRISMATIC
BEAM
0.001 1e+009 0.001 0.001 0.001 0.001 0.5 0.5
END
DEFINE MATERIAL START
ISOTROPIC XYZSTEEL
E 4.32e+006
POISSON 0.3
DENSITY 0.489024
ALPHA 6e-006
DAMP 0.03
G 1.60615e+006
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 3 UPTABLE 1 COLUMN1
4 5 UPTABLE 1 COLUMN2
2 6 UPTABLE 2 BEAM
CONSTANTS
MATERIAL XYZSTEEL MEMB 1 2 2 TO 6
SUPPORTS
1 4 FIXED
2 FX 52.5
5 FX 25.5
FLOOR DIAPHRAGM
DIA 3 TYPE RIG HEI 15
DIA 4 TYPE RIG HEI 25
DEFINE TIME HISTORY DT 0.0013888
TYPE 1 ACCELERATION SAVE
0 9.03917 0.1 9.03917 0.2 9.03917 0.3 9.03917 0.4 9.03917 0.5 9.03917
0.6 9.03917 0.7 9.03917 0.8 9.03917 0.9 9.03917 1 9.03917
1.1 9.03917 1.2 9.03917 1.3 9.03917 1.4 9.03917 1.5 9.03917
1.6 9.03917 1.7 9.03917 1.8 9.03917 1.9 9.03917 2 9.03917
ARRIVAL TIME
0
DAMPING 1.1e-006
R1 1.0
GROUND MOTION X 1 1 1.000000
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 2 5
FINISH
``````

```   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE