VM4

VM4
Deflection of a Hinged Support

Overview

Reference: S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 10, problem 2.
Analysis Type(s): Static Analysis (ANTYPE = 0)
Element Type(s): 3D Spar (or Truss) Elements (LINK180)
Input Listing: vm4.dat

Test Case

A structure consisting of two equal steel bars, each of length   and cross-sectional area A, with hinged ends is subjected to the action of a load F. Determine the stress, σ, in the bars and the deflection, δ, of point 2. Neglect the weight of the bars as a small quantity in comparison with the load F.

Figure 5: Hinged Support Problem Sketch

Hinged Support Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
= 15 ft
A = 0.5 in2
Θ = 30°
F = 5000 lb

Analysis Assumptions and Modeling Notes

Consistent length units are used. The dimensions a and b are calculated parametrically in the input as follows: a = 2  cos Θ, b =   sin Θ.

Results Comparison

TargetMechanical APDLRatio
Stress, psi10,000.10,000.1.000
Deflection, in-0.120-0.1201.000