VM43

VM43
Bending of an Axisymmetric Thick Pipe

Overview

Reference:	R. J. Roark, Formulas for Stress and Strain, 4th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1965, pg. 112, no. 33.
Analysis Type(s):	Static Analysis (ANTYPE = 0)
Element Type(s):	Axisymmetric-Harmonic 4-Node Structural Solid Elements (PLANE25)
Input Listing:	vm43.dat

Test Case

A long thick-walled pipe is rigidly supported at its ends between two walls. Determine the maximum deflection in the pipe due to gravity loading. Determine the maximum tensile stress σ_max at the outer surface of the pipe at Y = 4.16666 in.

Figure 58: Axisymmetric Thick Pipe Sketch Problem

Material Properties

Geometric Properties

E = 30 x 10⁶

ρ = .00073 lb-sec²/in⁴

υ = 0.0

L = 200 in

d_o = 2 in

d_i = 1 in

g = 386 in/sec²

Analysis Assumptions and Modeling Notes

The loading g, which is constant in magnitude and direction around the circumference of the pipe, is applied as the sum of two harmonically varying loads. Each load has one wave around the circumference and is 90° out of phase with the other.

Results Comparison

	Target	Mechanical APDL	Ratio
Deflection_x, in (angle = 0°)	-0.12524	-0.12529	1.000
Deflection_z, in (angle = 90°)	0.12524	0.12530	1.000
Stress_max , psi (angle = 0°)	2637.8	2652.4	1.006

Figure 59: Displacement Displays

Window 1 Shows a Circumferential Angle of 0°
Window 2 Shows a Circumferential Angle of 90°