Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 10, Problem 10.4.13P
-4-13 A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinates. Let k = 6EI/L3.
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A triangular distributed load of max intensity w acts on beam
AB. The beam is supported by a pin at A and member CD,
which is connected by pins at C and D respectively.
Determine the largest load intensity, Wmax, that can be
applied if the pin at D can support a maximum force of
18000 N. Also determine the reactions at A and C
and express each answer in Cartesian components. Assume
the masses of both beam and member ✓ are
negligible.
Dwas
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=
A
BY NC SA
2016 Eric Davishahl
C
D
-a-
Ур
-b-
X
B
W
Values for dimensions on the figure are given in the following
table. Note the figure may not be to scale.
Variable Value
a
6.6 m
b
11.88 m
C
4.29 m
The maximum load intensity is
=
wmax
N/m.
The reaction at A is A =
The reaction at C is
=
i+
Ĵ N.
ĴN.
12
i+
The beam is supported by a pin at B and a roller at C and is
subjected to the loading shown with w =110 lb/ft, and F
205 lb.
a.) If M
=
2,590 ft-lb, determine the support reactions at B
and C. Report your answers in both Cartesian components.
b.) Determine the largest magnitude of the applied couple M
for which the beam is still properly supported in equilibrium
with the pin and roller as shown.
2013 Michael Swanbom
CC
BY NC SA
M
ру
W
B⚫
C
F
ka
b
Values for dimensions on the figure are given in the following
table. Note the figure may not be to scale.
Variable Value
a
3.2 ft
b
6.4 ft
C
3 ft
a.) The reaction at B is B =
The reaction at C is C =
ĵ lb.
i+
Ĵ lb.
b.) The largest couple that can be applied is M
ft-lb.
==
i+
The beam ABC has a mass of 79.0 kg and is supported by
the rope BDC that runs through the frictionless pulley at D
. The winch at C has a mass of 36.5 kg. The tension in the
rope acts on the beam at points B and C and counteracts
the moments due to the beam's weight (acting vertically at
the midpoint of its length) and the weight of the winch
(acting vertically at point C) such that the resultant moment
about point A is equal to zero. Assume that rope segment
CD is vertical and note that rope segment BD is NOT
necessarily perpendicular to the beam.
a.) Compute the tension in the rope.
b.) Model the two forces the rope exerts on the beam as a
single equivalent force and couple moment acting at point B.
Enter your answer in Cartesian components.
c.) Model the two forces the rope exerts on the beam as a
single equivalent force (no couple) and determine the
distance from A to the point along the beam where the
equivalent force acts (measured parallel to the beam from A
). Enter your answer…
Chapter 10 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 10 - A propped cantilever steel beam is constructed...Ch. 10 - A fixed-end b earn is subjected to a point load at...Ch. 10 - A propped cantilever beam AB of a length L is...Ch. 10 - A fixed-end beam AB of a length L supports a...Ch. 10 - A cantilever beam AB of a length L has a fixed...Ch. 10 - A cantilever beam of a length L and loaded by a...Ch. 10 - A cantilever beam has a length L and is loaded by...Ch. 10 - A propped cantilever beam of a length L is loaded...Ch. 10 - A propped cantilever beam of a length L is loaded...Ch. 10 - A fixed-end beam of a length L is loaded by a...
Ch. 10 - A fixed-end b earn of a length L is loaded by a...Ch. 10 - A fixed-end beam of a length L is loaded by...Ch. 10 - A counterclockwise moment M0acts at the midpoint...Ch. 10 - A propped cantilever beam of a length L is loaded...Ch. 10 - A propped cantilever beam is subjected to uniform...Ch. 10 - Repeat Problem 10.3-15 using L = 3.5 m, max = 3...Ch. 10 - A two-span, continuous wood girder (E = 1700 ksi)...Ch. 10 - A fixed-end beam AB carries point load P acting at...Ch. 10 - A fixed-end beam AB supports a uniform load of...Ch. 10 - -4-4 A cantilever beam is supported at B by cable...Ch. 10 - A propped cantilever beam AB of a length L carries...Ch. 10 - A beam with a sliding support at B is loaded by a...Ch. 10 - A propped cantilever beam of a length 2L with a...Ch. 10 - The continuous frame ABC has a pin support at /l,...Ch. 10 - The continuous frame ABC has a pin support at A,...Ch. 10 - Beam AB has a pin support at A and a roller...Ch. 10 - The continuous frame ABCD has a pin support at B:...Ch. 10 - Two flat beams AB and CD, lying in horizontal...Ch. 10 - -4-13 A propped cantilever beam of a length 2L is...Ch. 10 - A propped cantilever beam of a length 2L is loaded...Ch. 10 - Determine the fixed-end moments (MAand MB) and...Ch. 10 - A continuous beam ABC wit h two unequal spans, one...Ch. 10 - Beam ABC is fixed at support A and rests (at point...Ch. 10 - A propped cantilever beam has flexural rigidity EI...Ch. 10 - A triangularly distributed 1oad with a maximum...Ch. 10 - A fixed-end beam is loaded by a uniform load q =...Ch. 10 - Uniform load q = 10 lb/ft acts over part of the...Ch. 10 - A propped cantilever beam with a length L = 4 m is...Ch. 10 - A cant i levé r b ea m i s supported by a tie rod...Ch. 10 - The figure shows a nonprismatic, propped...Ch. 10 - A beam ABC is fixed at end A and supported by beam...Ch. 10 - A three-span continuous beam A BCD with three...Ch. 10 - A beam rests on supports at A and B and is loaded...Ch. 10 - A propped cantilever beam is subjected to two...Ch. 10 - A propped cantilever beam is loaded by a...Ch. 10 - A fixed-end beam AB of a length L is subjected to...Ch. 10 - A temporary wood flume serving as a channel for...Ch. 10 - Two identical, simply supported beams AB and CD...Ch. 10 - The cantilever beam AB shown in the figure is an...Ch. 10 - The beam AB shown in the figure is simply...Ch. 10 - The continuous frame ABC has a fixed support at A,...Ch. 10 - The continuous frame ABC has a pinned support at...Ch. 10 - A wide-flange beam ABC rests on three identical...Ch. 10 - A fixed-end beam AB of a length L is subjected to...Ch. 10 - A beam supporting a uniform load of intensity q...Ch. 10 - A thin steel beam AB used in conjunction with an...Ch. 10 - Find an expression for required moment MA(in terms...Ch. 10 - Repeat Problem 10.4-41 for the loading shown in...Ch. 10 - A propped cantilever beam is loaded by two...Ch. 10 - A cable CD of a length H is attached to the third...Ch. 10 - A propped cantilever beam, fixed at the left-hand...Ch. 10 - Solve t he preceding problem by integrating the...Ch. 10 - A two-span beam with spans of lengths L and L/3 is...Ch. 10 - Solve the preceding problem by integrating the...Ch. 10 - Assume that the deflected shape of a beam AB with...Ch. 10 - (a) A simple beam AB with length L and height h...
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