VM18

VM18
Out-of-Plane Bending of a Curved Bar

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. 412, eq. 241.
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):
Elastic Curved Pipe Element (PIPE18)
3D 3 Node Pipe Element (PIPE289)
Input Listing:vm18.dat

Test Case

A portion of a horizontal circular ring, built-in at A, is loaded by a vertical (Z) load F applied at the end B. The ring has a solid circular cross-section of diameter d. Determine the deflection δ at end B, the maximum bending stress σBend, and the maximum torsional shear stress τ.

Figure 23: Curved Bar Problem Sketch

Curved Bar Problem Sketch

Figure 24: Curved Bar Finite Element Model

Curved Bar Finite Element Model

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
r = 100 in
d = 2 in
Θ = 90°
F = 50 lb

Analysis Assumptions and Modeling Notes

Node 10 is arbitrarily located on the radius of curvature side of the element to define the plane of the elbow when PIPE18 elements are used. The wall thickness is set to half the diameter for a solid bar. Since the section has no hole in the middle, ovalization cannot occur and PIPE289 elements can be used to determine the deflection and stresses.

Results Comparison

TargetMechanical APDLRatio
PIPE18
Deflection, in-2.648-2.6501.001
StressBend, psi63666366.198[1]1.000
Shear stress, psi-3183-3183.099[2]1.000
PIPE289
Deflection, in-2.648-2.6501.001
StressBend, psi63666446.6311.013
Shear stress, psi-3183-3199.4721.005

  1. Corresponds to maximum SAXL at 0° angle location in element solution output.

  2. Corresponds to SXH at 0° angle location in element solution output.