VM180

VM180
Bending of a Curved Beam

Overview

Reference:

S. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd Edition, McGraw-Hill Book Co. Inc., New York, NY, 1970, pg. 73, article 29.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2D 8-Node Structural Solid Elements (PLANE183)

2D Elastic Beam Elements (BEAM188)

Input Listing:

vm180.dat

Test Case

A curved beam spans a 90° arc as shown. The bottom end is supported while the top end is free. For a bending moment M applied at the top end, determine the maximum tensile stress σ_t and the maximum compressive stress σ_cin the beam.

Figure 271: Curved Beam Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

υ = 0.0

r_i = 3.5 in

r_o = 4.5 in

h = 1.0 in

M = 100 in-lb

Analysis Assumptions and Modeling Notes

Beam elements with arbitrary properties are included at the free end of the curved beam for uniform transmission of the applied forces. This creates a pure bending situation except for the nodes at the free end at which stresses are ignored. POST1 is used to obtain the desired stress results.

Results Comparison

	Target	Mechanical APDL	Ratio
Stress_t , psi	655.0	674.5	1.030
Stress_c , psi	-555.0	-564.3	1.017