VM21

VM21
Tie Rod with Lateral Loading

Overview

Reference:	S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 42, article 6.
Analysis Type(s):	Static, Stress Stiffening Analysis (ANTYPE = 0)
Element Type(s):	3D 2 node beam (BEAM188)
Input Listing:	vm21.dat

Test Case

A tie rod is subjected to the action of a tensile force F and a uniform lateral load p. Determine the maximum deflection z_max, the slope Θ at the left-hand end, and the maximum bending moment M_max. In addition, determine the same three quantities for the unstiffened tie rod (F = 0).

Figure 27: Tie Rod Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

= 200 in

b = h = 2.5 in

F = 21,972.6 lb

p = 1.79253 lb/in

Analysis Assumptions and Modeling Notes

Due to symmetry, only one-half of the beam is modeled. The full load is applied for each iteration. The first solution represents the unstiffened case. The second solution represents the stiffened case.

Results Comparison

		Target	Mechanical APDL	Ratio
F neq 0 (stiffened)	Z_max , in	-0.19945	-0.19956	1.001
	Slope, rad	0.0032352	0.0032353	1.000
	M_max , in-lb	-4580.1	-4579.818	1.000
F = 0 (unstiffened)	Z_max , in	-0.38241	-0.38255	1.001
	Slope, rad	0.0061185	0.0061185	1.000
	M_max , in-lb	-8962.7	-8962.65	1.000