VM70

VM70
Seismic Response of a Beam Structure

Overview

Reference: J. M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Co., Inc., New York, NY, 1964, pg. 262, article 6.4.
Analysis Type(s): Mode-frequency, Seismic Analysis (ANTYPE = 2)
Element Type(s): 3D 3 Node Beam (BEAM189)
Input Listing: vm70.dat

Test Case

A simply supported beam of length , mass per unit length m, and section properties shown below is subjected to a vertical motion of both supports. The motion is defined in terms of a seismic displacement response spectrum. Determine the fundamental displacement δ, and the corresponding maximum bending stress σmax.

Figure 95: Beam Structure Problem Sketch

Beam Structure Problem Sketch

Material PropertiesGeometric Properties
E = 30 x 106 psi
m = 0.2 lb-sec2/in2
Response Spectrum
Frequency, Hz Displacement, in
    0.1                    0.44 
  10.0                    0.44 
I = (1000/3) in4
A = 273.9726 in2
= 240 in
h = 14 in

Analysis Assumptions and Modeling Notes

The beam geometry data is modeled using ASEC subtype (SECTYPE,1,BEAM,ASEC).

The bending stem is calculated using:

SByB = -Mz * ymin / Izz

Where:

Mz is the bending moment.

ymin is the height of the beam (minimum y coordinate in the cross section measured from the centroid).

Izz is the moment of inertia.

Results Comparison

TargetMechanical APDLRatio
f, Hz 6.09796.095941.000
Deflection, in0.560000.560161.000
Stressmax, psi20158.20399.015871.012