E03: Beam Eigenvalues

A simply supported beam is subjected to its own weight. The span length is 80 inches and the beam is steel with 2 inches square cross section. The mass density of the beam is 0.000728 lb-sec2/in4. Determine the fundamental frequency of the beam.

The model of the beam has 5 joints and 4 beam elements. Joints 1 and 5 are pin supports. The joints 2, 3 and 4 represent the lateral dynamic degrees of freedom.


Modulus of Elasticity = 30,000,000 psi
Span Length = 80 inches
A = 4 in2
Izz = 1.3333 in4
Weight Density = 0.281 lb/in2 g = 386 in/sec2





Tested Features


Sources

  • LARSA 4D
  • Thomson, W.T., "Vibration Theory and Application," Prentice-Hall, Inc., Englewood Cliffs, N.Y., 2nd Printing, 1965, p.18.
  • Swanson Analysis Systems, Inc., "ANSYS Verification Manual".

Results Comparison

App Link:

https://openbrim.org/objid5prhn76b4bkpo2y9l29wc.project

Library Link:

https://openbrim.org/objid84jl4pxsn9jaol09lns71c.libobj

ModelOutput ParameterOpenBrIMLARSAThomsonSwansonOpenBrIM vs Larsa
Beamf1(hz)28.7628.7628.7728.771e-3%