VM-LSDYNA-SOLVE-033

VM-LSDYNA-SOLVE-033
Combined Bending and Torsion of Beam

Overview

Reference:	Timoshenko, S. (1955). Strength of material, Part I: Elementary theory and problems (3rd ed.). D. Van Nostrand Co. p.299, problem 2.
Analysis Type(s):	Static Structural Analysis
Element Type(s):	Beam

Test Case

As shown in Figure 120, a vertical bar of length L and radius r is subjected to the action of a horizontal force F acting at distance d from the axis of the bar. Determine the maximum principal stress σ_max.

This test case also appears in the Workbench Verification Manual. See VM-WB-MECH-049.

Figure 120: Problem Sketch

Material Properties	Geometric Properties	Loading
E = 3e7 psi ν = 0.3 ρ = 0.0007345 lbf·s2/in	L = 300 in r = 2.33508 in d = 3 ft	F = 250 lb (Y direction) M = 9000 lbf-in (Z direction)

Material Properties

Geometric Properties

E = 3e7 psi

ν = 0.3

ρ = 0.0007345 lbf·s2/in

L = 300 in

r = 2.33508 in

d = 3 ft

F = 250 lb (Y direction)

M = 9000 lbf-in (Z direction)

Analysis Assumptions and Modeling Notes

When setting boundary conditions, keyword BOUNDARY_SPC_SET is used to restrict the movements and rotations of the node at the ends of the beam (node 1) in the X, Y, and Z directions.

In LS-DYNA, a beam-type model, using the SECTION_BEAM keyword, is used by selecting the section type, with a value for ELFORM of 1 (using the Hughes-Liu formulation with cross-section integration) and a value for QR/IRID of 2 (2 x 2 Gauss quadrature). Figure 121 shows the mesh model (B).

Figure 121: Problem setup (A) and Mesh model (B)

Results Comparison

The LS-DYNA results are nearly identical to the theoretical results.

Results	Target	LS-DYNASolver	Error (%)
Principal stress_min (psi)	-7527	-7460	0.89%
Principal stress_max (psi)	7527	7460	0.89%