Laterally Loaded Tapered Beam

Description

A cantilever beam of width 2" and length 50" has a depth which tapers uniformly from 3" at the tip to 9" at the wall. The cantilever beam is loaded by a 4000 lb force at the tip. Find the maximum bending stress at the mid-span of the cantilever.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_19.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Solid mesh/shell mesh.

Meshing Parameters

Use the default Global Size for Solid Mesh and a Global Size of 0.3 in for Shell Mesh.

Material Properties

Modulus of elasticity = 3 X 107 psi, Poisson's ratio = 0.

Results

Bending stress at midspan (SX), psi

Solid mesh

Shell mesh

Theory 8333 8333
SOLIDWORKS Simulation 8373 8318

Moment (mid-span): MX = F * L/2

Bending stress (mid-span): SX = MX * ( (Dm /2) / I )

where:
  • F: Force at tip
  • I: Moment of inertia
  • L: Beam length
  • Dm: Beam depth at mid-span

Reference

Crandall, S. H., and Dahl, N. C., “An Introduction to the Mechanics of Solids,” McGraw-Hill Book Co., Inc., New York, l959, pp. 342.