[VM] Beam Stresses and Deflections

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Reference: S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 2nd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 95, problem 4.

A standard WF beam, with a cross-sectional area A, is supported as shown below and loaded on the overhangs by a uniformly distributed load w. Determine the maximum bending stress σ in the middle portion of the beam and the deflection δ at the middle of the beam.

Video:

1. Calculated according to theory

• Geometry and Cross Section dimensions

Figure 1: Geometry and Cross Section dimensions

• Material and loads

Figure 2: Material and Loads

• Results

Figure 3: Max stress and Max deflection results

2. ANSYS Software

• Boundary conditions

Figure 4: Boundary conditions

This problem is performed in 3D analysis so some setup are required to convert it into 2D problem.

Where:

• • Fixed Rotation (Free Y direction - A) and Displacement (Free Y direction - C): to ensure the beam can translate (x-z direction) and rotate (y-direction) in XZ-plane.
  • Displacement (Fix X-Y-Z direction - E & F): make two points can only rotatable about Y-direction.
  • Line Pressure: Force distribure (lb/in)
• Results:
  • Deflection: max = 0.137in

Figure 5: Deflection result

• • Stress: max = 8556.7psi

Figure 6: Stress result

The results are similar to theory.

Download project: Google Drive

ANSYS Version: ANSYS 2020R2