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 10.3.14P
A propped cantilever beam of a length L is loaded by a concentrated moment M0at midpoint C Use the second-order differential equation of the deflection curve to solve for reactions at A and B. Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam.
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A propped cantilever beam of a length L isloaded by a concentrated moment M0 at midpoint C.Use the second-order differential equation of thedeflection curve to solve for reactions at A and B.Draw shear-force and bending-moment diagramsfor the entire beam. Also find the equations of thedeflection curves for both halves of the beam, anddraw the deflection curve for the entire beam.
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a-9 ft, b-6 ft and
w=10.5 kips/ft.
Calculate the reaction forces Ay and Cy 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 A, -0, it has been omitted from the free-body diagram.)
Answer:
(a) Vi
(b) V = i
(c) V-
a
Answers: A,
kips, Cy
Determine the shear force acting at each of the following locations:
(a) x = 0+ ft (i..., just to the right of support A)
(b) x-9 ft
(c)x=13ft
When entering your answers, use the shear force sign convention.
kips.
kips.
kips.
b
(a) M-
(b) M-
(c) M-i
С
Cy
The shear-force diagram crosses the V = 0 axis between points A and B. Determine the location x where V = 0 kips.
Answer:x-i
ft.
kip-ft.
kip-ft.
kip-ft.
kips.
Determine the maximum bending moment that acts anywhere in the beam. When entering your answer, use the bending moment
sign convention.…
can you help me on part 3, 4 and 5
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 is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.arrow_forwardA counterclockwise moment M0acts at the midpoint of a fixed-end beam ACB of length L (see figure). Beginning with the second-order differential equation of the deflection curve (the bendingmoment equation), determine all reactions of the beam and obtain the equation of the deflection curve for the left-hand half of the beam. Then construct the shear-force and bending-moment diagrams for the entire beam, labeling all critical ordinales. Also, draw the deflection curve for the entire beam.arrow_forward-13 Derive the equation of the deflection curve for a simple beam AB loaded by a couple M0at the left-hand support (see figure). Also, determine the maximum deflection max Use the second-order differential equation of the deflection curve.arrow_forward
- -22 Derive the equations of the deflection curve for a simple beam AB with a distributed load of peak intensity q0acting over the left-hand half of the span (see figure). Also, determine the deflection cat the midpoint of the beam. Use the second-order differential equation of the deflection curve.arrow_forward-10 Derive the equations of the deflection curve for beam AB with sliding support at A and roller support at B, supporting a distributed load of maximum intensity q0acting on the right-hand half of the beam (see figure). Also, determine deflection A, angle of rotation B , and deflection cat the midpoint. Use the fourth-order differential equation of the deflection curve (the load equation).arrow_forward-9 Derive the equations of the deflection curve for beam ABC with sliding support at A and roller support at B, supporting a uniform load of intensity q acting on the overhang portion of the beam (see figure). Also, determine deflection cand angle of rotation c. Use the fourth-order differential equation of the deflection curve (the load equation).arrow_forward
- A beam with a sliding support at B is loaded by a uniformly distributed load with intensity q. Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinales.arrow_forwardUse the method of superposition to find the angles of rotation 9Aand SBat the supports, and the maximum deflection for a simply supported beam subjected to symmetric loads P at distance a from each support. Assume that EI is constant, total beam length is L and a = U3. Hint: Use the formulas of Example 9-3.arrow_forwardA compound beam (see figure) has an internal moment release just to the left of B and a shear release just to the right of C Reactions have been computed at A, C, and D and are shown in the figure. First, confirm the reaction expressions using statics; then plot shear (V) and moment (W) diagrams. Label all critical Fand M values and also the distance to points where either V and/or M are zero.arrow_forward
- Beam AB has a pin support at A and a roller support at B Joint B is also restrained by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MBdue to rotation at B. Member AB has flexural rigidity EI. A moment M0acts counterclockwise at B. Use the method of superposition to solve for all reactions. Find an expression for joint rotation Ain terms of spring stiffness kR. What is Awhen kR 0? What is Awhen kR— ? What is Awhen kR= 6EI/L?arrow_forwardA 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 rotational spring with stiffness kR,which provides a resisting moment MBdue to rotation B . Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinates. Let kR= El/L.arrow_forward-20 Derive the equations of the deflection curve for a cantilever beam AB carrying a uniform load of intensity q over part of the span (see figure). Also, determine the deflection Bat the end of the beam. Use the second-order differential equation of the deflection curve.arrow_forward
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