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 10.4.12P
Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both beams are simply supported. The lengths of beams AB and CD are LABand LCD, respectively.
What should be the ratio tABltCDof the thicknesses of the beams if all four reactions arc to be the same?
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Question 2 (40 Points)
Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have
angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is
perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is
defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can
also have a rate of extension or compression Ï2.
li
y
êr1
êe
12
χ
3
еф
er2
ده لج
1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any
extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points)
2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any
extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points)
3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y
directions, respectively. Also include the appropriate,…
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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