Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Textbook Question
Chapter 9.4, Problem 10FP
Determine the principal stresses at a point on the surface of the shaft.
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A beam of the cross section shown in Figure Q3 is made of a steel that is assumed to be elastic-
perfectectly plastic material with E = 200 GPa and σy = 240 MPa. Determine:
i.
The shape factor of the cross section
ii.
The bending moment at which the plastic zones at the top and bottom of the bar are 30
mm thick.
15 mm
30 mm
15 mm
30 mm
30 mm
30 mm
A torque of magnitude T = 12 kNm is applied to the end of a tank containing compressed air
under a pressure of 8 MPa (Figure Q1). The tank has a 180 mm inner diameter and a 12 mm
wall thickness. As a result of several tensile tests, it has been found that tensile yeild strength
is σy = 250 MPa for thr grade of steel used. Determine the factor of safety with respect to yeild,
using:
(a) The maximum shearing stress theory
(b) The maximum distortion energy theory
T
Figure Q1
An external pressure of 12 MPa is applied to a closed-end thick cylinder of internal diameter
150 mm and external diameter 300 mm. If the maximum hoop stress on the inner surface of the
cylinder is limited to 30 MPa:
(a) What maximum internal pressure can be applied to the cylinder?
(b) Sketch the variation of hoop and radial stresses across the cylinder wall.
(c) What will be the change in the outside diameter when the above pressure is applied?
[Take E = 207 GPa and v = 0.29]
Chapter 9 Solutions
Mechanics of Materials
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