Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 10, Problem 10.4.25P
A beam ABC is fixed at end A and supported by beam DE at point B (sec figure). Both beams have the same cross section and are made of the same material.
- Determine all reactions due to the load P.
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A beam is loaded as shown in the figure. What is the angle of inclination of the resultant reaction at A below the horizontal reference line?
Home Work:
1. Determine the maximum deflection d in a simply supported beam of length L
carrying a uniformly distributed load of intensity w, applied over its entire length.
2. For the beam loaded as shown in the Figure, compute the moment of area of the
M diagrams between the reactions about both the left and the right reaction. (Hint:
Draw the moment diagram by parts from right to left).
500 N
2 m
1 m
1 m
400 N/m
B
R1
R2
Please solve according to
the exporters of a typical
solution.
1
M
E*I
3. Moment Diagram by Parts
but
ds = pd0
M
de
M
ds
E*I
1
The construction of moment diagram by parts depends on two basic principles:
1) The resultant bending moment at any section caused by any load system is the
algebraic sum of the bending moment at that section caused by each load acting
separately.
= de =
%3D
E*I
ds
but
ds = dx
(Flat curve)
M
Σ
. de =
-) M. =
MR
M =
E * I
1
(M * dx
EML,EMR : Sum of the moment caused by all the forces to the left and right
section respectively.
.. 0 =
E * I
2)…
Home Work:
1. Determine the maximum deflection d in a simply supported beam of length L
carrying a uniformly distributed load of intensity w, applied over its entire length.
2. For the beam loaded as shown in the Figure, compute the moment of area of the
M diagrams between the reactions about both the left and the right reaction. (Hint:
Draw the moment diagram by parts from right to left).
500 N
2 m
1 m
1 m
400 N/m
R1
R2
Please solve according to
the exporters of a typical
solution.
1
E*I
3. Moment Diagram by Parts
but
ds = pd0
M
de
M
ds
E*I
1
The construction of moment diagram by parts depends on two basic principles:
1) The resultant bending moment at any section caused by any load system is the
= de =
%3D
E*I
ds
algebraic sum of the bending moment at that section caused by each load acting
separately.
but
ds = dx
(Flat curve)
M
=) M2 =
Σ
= OP **
E * I
MR
1
[M * dx
EM,EMR : Sum of the moment caused by all the forces to the left and right
section respectively.
:. 0 =
E * I
2) The…
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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- A fixed-end beam AB of a length L supports a uniform load of intensity q (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the shear-force and bending-moment diagrams, Labeling all critical ordinales.arrow_forwardCantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and a downward uniform load of intensity q from x = L/2 to L. Find q1in terms of q if the resulting moment at A is zero. Draw V and M diagrams for the case of both q and qtas applied loadings. Repeat part (a) for the case of an upward triangularly distributed load with peak intensity q0(see Fig. b). For part (b), find q0, instead of q1arrow_forwardA propped cantilever beam is subjected to two triangularly distributed loads, each with a peak load intensity equal to q0(see figure), lind the expressions for reactions at A and C using superposition. Plot shear and moment diagrams.arrow_forward
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