OS-V: 0600 Simply Support Beam

OptiStruct is used to investigate the peak Displacement, Stress and Moment in the mid-span node of the beam. The width of the beam is 1.458 in.



Figure 1. Cross-section and Dimensions of Beam

Benchmark Model

Rectangular cross-section CBEAM elements are used to model the simply-supported beam which consists of 10 elements. The displacements in x, y, and z direction are fixed at the end A and the displacements in y and z direction and the x rotations are constrained at end B. A Spectrum input in terms of acceleration, velocity and displacement is applied in the vertical direction at both supports. The damping is specified as zero for this problem.

The material properties are:
Young's Modulus
30 x 106 psi
Density
0.0098 lb-s2/in4
Table 1. Response Spectra Input
Frequency (Hz) Displacement (inch) Velocity (inch/sec) Acceleration (inch/sec2)
0 0 0 0
5 0.783 24.599 772.80
6 0.4531 17.083 644.01
6.08 0.4316 16.538 633.66
7 0.2854 12.550 552.01
8 0.2222 11.1659 561.44

Response Spectrum Analysis Results

Model Spectrum Displacement

(in)

 Stress

(lb/in2)

 Moment

(lb-in)
Biggs 0.56 20100.00 959500.00
CBEAM Displacement 0.55 19520.38 929716.81
Normalized 1.018 1.0296 1.0320
CBEAM Velocity 0.55 19519.60 929679.68
Normalized 1.018 1.0297 1.0320
CBEAM Acceleration 0.55 19517.91 929599.25
Normalized 1.018 1.0298 1.0321

Model Files

The model files used in this problem include:

<install_directory>/hwsolvers/demos/optistruct/verification
  • /RSAdisp.fem
  • /RSAvel.fem
  • /RSAaccl.fem

Reference

J. M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Co., Inc., New York, NY, 1964, pg. 262, article 6.4.