VM-LSDYNA-SOLVE-024

VM-LSDYNA-SOLVE-024
Deflection of a Hinged Support

Overview

Reference:	Timoshenko, S.P. (1995). Strength of materials: Part I: Elementary theory and problems. (3rd ed.). D. Van Nostrand Co. p10.
Analysis Type(s):	Explicit Dynamic Relaxation Analysis
Element Type(s):	Beam (Truss)

Test Case

A structure consisting of two equal steel bars—each of length L and cross-sectional area A with hinged ends— is subjected to the action of load F as shown in Figure 94. Determine the deflection 𝛅 of the hinged end. The weight of the bars, which is a small quantity in comparison with load F, is neglected.

This problem is also presented in test case VM4 in the Mechanical APDL Verification Manual.

Figure 94: Problem Sketch

Material Properties	Geometric Properties	Loading
E = 3e7 psi	L = 180 in A = 0.5 in² θ = 30	Force F = 5000 lbf

Material Properties

Geometric Properties

E = 3e7 psi

L = 180 in

A = 0.5 in²

θ = 30

Force F = 5000 lbf

Analysis Assumptions and Modeling Notes

The structure is modeled with truss beam element elform 3. An explicit dynamic relaxation analysis is performed with *CONTROL_DAMPLING (IDRFLG = 1). The analysis timestep is scaled by a factor of 0.3 using *CONTROL_TIMESTEP.

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

Results Comparison

Figure 95: Deflected Beams Calculated from LS-DYNA Model

Results	Target	LS-DYNASolver	Error (%)
Deflection at point 2 (in)	–0.12	–0.1197	0.25