F-09 (Response Spectrum Analysis of 2D Frame) |
  
|
F-09 (Response Spectrum Analysis of 2D Frame) |
|
Objective
To verify the results of response spectrum analysis on a 2D frame.
Problem Description
A 2-story concrete frame shown below [Ref 1] fixed at the bottom is subjected to ground motion characterized by the design spectrum specified.
Geometry: bay distance = 20 ft, each story height = 10 ft.
Material: E = 3000 ksi.
Section-1: Iz = 1000 in4; Section-2: Iz = 2000 in4. Other section properties are set to very large values to simulate bending only actions.
Masses: first floor center = 12.4368 kip-sec2/ft in X direction, second floor center = 6.2184 kip-sec2/ft in X direction.
The design response spectrum is defined below (from Create > Generate Loads > Response Spectra Library menu).
Period (sec) |
Spectral Acceleration (g) |
0.000 |
0.500 |
0.030 |
0.500 |
0.125 |
1.355 |
0.587 |
1.355 |
0.660 |
1.355 |
1.562 |
0.576 |
4.120 |
0.218 |
10.000 |
0.037 |
Results
The following lists different results by ENERCALC 3D against the reference [Ref. 1].
Time Periods (sec)
|
ENERCALC 3D |
Reference |
Mode 1 |
1.5621 |
1.562 |
Mode 2 |
0.5868 |
0.5868 |
Modal Displacements SRSS combination (in)
|
ENERCALC 3D |
Reference |
First story |
7.576e+000 |
7.566 |
Second story |
1.884e+001 |
18.81 |
Bending Moment (kip-ft)
Element |
Location |
ENERCALC 3D |
Reference |
||
Mode 1 |
Mode 2 |
Mode 1 |
Mode 2 |
||
First Floor Beam |
Left End |
-815.6 |
-56.54 |
-814 |
-57 |
Second Floor Beam |
Left End |
-396.9 |
178.5 |
-396 |
179 |
Bottom Column |
Top End |
425.9 |
372.9 |
425 |
374 |
Bottom End |
969.6 |
410.6 |
968 |
412 |
|
Top Column |
Top End |
396.9 |
-178.5 |
396 |
-179 |
Bottom End |
389.7 |
-316.4 |
389 |
-317 |
|
Comments
The results given by ENERCALC 3D are very close to the referenced values. The bending moments are from load combinations INERTIA_LOADCOMB_X_MODE_1 and INERTIA_LOADCOMB_X_MODE_2 which are generated automatically during the response spectrum analysis process.
Reference
[1]. pp 562, “Dynamics of Structures – Theory and Applications To Earthquake Engineering”, 2001, Second Edition, by Anil K. Chopra, Prentice Hall.
