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 10.4.43P
A propped cantilever beam is loaded by two different load patterns (see figures a and b). Assume that El is constant and the total beam length is L. Find expressions for reactions at  and B for each beam. Plot shear and moment diagrams. Assume that a = L/B.
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Figure 1 below shows a 5 m length of beam with a pinned support at A and roller
support at E. The beam carries three concentrated loads of 10 kN, 5 kN and 15 kN
at B, C and D, respectively.
а.
Show the Free Body Diagram (FBD) of the beam then determine the reaction
force.
b.
Calculate the shear force, V. Draw Shear Force Diagram (SFD).
Calculate the bending moment, M. Draw the Bending Moment Diagram (BMD).
10 kN
5 kN
15 kN
A
E
B
C
D
1m
1m
1 m
2 m
Figure 1
C.
SHOW THE FOLLOWING:
1. COMPUTATION OF REACTIONS
2. SHEAR AND MOMENT DIAGRAM
3. MAXIMUM BENDING MOMENT @ THE LOACTION OF THE MAXIMUM DEFLECTION
4. VALUE OF THE MAXIMUM DEFLECTION
(A/B). A beam 7 m long is simply supported at its ends and loaded as follows: 120 kN at 1 m from one end A,
20kN at 4 m from A and 60 kN at 5 m from A. Calculate the position and magnitude of the maximum deflection. The
second moment of area of the beam section is 400 x 10-m* and E for the beam material is 210 GN/m².
1. The cantilever beam in Figure 1 is fixed at A, and is loaded with a distributed load from A
to B and a concentrated moment at C.
Use the GRAPHICAL METHOD to plot the shear force and bending moment diagrams for the
entire length of the beam. Label values at all key locations on the plots (at changes in loads,
maxima, minima, and zeroes).
Annotate your diagrams to explain how they were drawn (e.g. "AQAB = (-12 kN/m)(1 m) =
-12 kN" and "(dQ/dx)AB = -12 kN/m").
12 kN/m
5 kNm
ZA
B
D
1 m
0.5 m
0.5 m
Figure 1.
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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