VM12

VM12
Combined Bending and Torsion

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. 299, problem 2.
Analysis Type(s): Static Analysis (ANTYPE = 0)
Element Type(s):
Elastic Straight Pipe Element (PIPE16)
3D 2 Node pipe element (PIPE288)
Input Listing: vm12.dat

Test Case

A vertical bar of length   is subjected to the action of a horizontal force F acting at a distance d from the axis of the bar. Determine the maximum principal stress σmax and the maximum shear stress τmax in the bar.

Figure 15: Combined Bending and Torsion Problem Sketch

Combined Bending and Torsion Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
= 25 ft
d = 3 ft
Section modulus (I/c) = 10 in3
Outer Diameter = 4.67017 in
Wall Thickness = 2.33508 in
F = 250 lb
M = Fd = 9000 in-lb

Analysis Assumptions and Modeling Notes

Use consistent length units of inches. Real constants for PIPE16 and section properties for PIPE288 are used to define the pipe Outer Diameter and Wall Thickness. These values are calculated for a solid cross-section from the given section modulus. The offset load is applied as a centroidal force and a moment.

Results Comparison

Target[1]Mechanical APDLRatio
PIPE16
Principal stressmax, psi7527.7527.[2]1.000
Shear stressmax, psi3777.3777.[3]1.000
PIPE288
Principal stressmax, psi7527.75271.000
Shear stressmax, psi3777.37771.000

  1. Solution recalculated

  2. Corresponds to S1MX in element solution printout

  3. Calculated as SINTMX/2 (SINTMX from element solution printout) since SINTMX is defined as twice the maximum shear stress.