Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
9th Edition
ISBN: 9781337594318
Author: Barry J. Goodno; James M. Gere
Publisher: Cengage Learning
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Textbook Question
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Chapter 5, Problem 5.8.8P
A beam of rectangular cross section (width/) and height supports a uniformly distributed load along its entire length L. The allowable stresses in bending and shear are and TaUow, respectively.
- If the beam is simply supported, what is the span length Lübelow which the shear stress governs the allowable load and above which the bending stress governs?
- If the beam is supported as a cantilever, what is the length L() below which the shear stress governs the allowable load and above which the bending stress governs?
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For
the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M
for any location in the beam. (Place the origin at point A.) Let a=2.50 m, b=4.25 m, PB = 45kN, and Pc = 90kN. Construct the shear-
force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO
exercise.
Answers:
Ay =
Dy=
Mi
i
B
Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the
red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.)
PB
a
PB
B
a
Pc
a
Pc
C
kN
b
KN
b
D
X
D₂
X
A rectangular beam of 100 mm wide is
subjected to maximum shear force of
50 kN, the corresponding maximum
shear stress being 3 N/mm?. The
depth of the beam is equal to
1.
A simple beam with an overhang is supported at points A and B. A uniform load of w = 6 kN/m
acts throughout the length of the beam, and a concentrated load P = 28 kN acts at a point 3 m
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Calculate the shear force V and bending moment M at cross section D located 5 m from the left
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Chapter 5 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
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