Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 11.2, Problem 11.24P
To determine
The required minimum wall thickness t.
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(30 pts) Problem 1
A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. A
moment M
mgr
4
is applied to the rod. Assume that the bowl is fixed and its rim is in the
horizontal plane.
HINT: It will help you to find the length l of that portion of the rod that remains outside the
bowl.
M
2r
a) How many degrees of freedom does this system have?
b) Write an equation for the virtual work in terms of the angle 0 and the motion of the
center of mass (TF)
c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ)
a. HINT: Use the center of the bowl as the coordinate system origin for the problem.
d) In the case of no applied moment (i.e., M 0), derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation
e) In the case of an applied moment (i.e., M
=
mgr
= -) derive an equation that can be used to
4
solve for the equilibrium angle of the rod. DO NOT solve the equation.
f) Can…
Please show all work step by step
Chapter 11 Solutions
Mechanics of Materials
Ch. 11.2 - Determine the minimum dimension a to the nearest...Ch. 11.2 - of the rod to safely support the load. The rod is...Ch. 11.2 - The wood has an allowable normal stress of allow =...Ch. 11.2 - of the beam's cross section to safely support the...Ch. 11.2 - Determine the minimum dimension b to the nearest...Ch. 11.2 - The beam is made of steel having an allowable...Ch. 11.2 - Determine its dimensions if it is to be...Ch. 11.2 - Determine the minimum width of the beam to the...Ch. 11.2 - if P=10 kip.Ch. 11.2 - If the allowable bending stress is allow = 22 ksi...
Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - The allowable bending stress is allow = 22 ksi and...Ch. 11.2 - 11–7. Draw the shear and moment diagrams for the...Ch. 11.2 - *11–8. The simply supported beam is made of timber...Ch. 11.2 - The beam has an allowable normal stress of allow =...Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - 11–11. The timber beam is to be loaded as shown....Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...Ch. 11.2 - 11–13. Select the lightest steel wide-flange beam...Ch. 11.2 - 11–14. Select the lightest-weight steel...Ch. 11.2 - Prob. 11.15PCh. 11.2 - The beam has an allowable normal stress of allow....Ch. 11.2 - Determine the maximum cable force P that can...Ch. 11.2 - to safely support the load. The wood has an...Ch. 11.2 - and the wood has an allowable normal stress of...Ch. 11.2 - Prob. 11.20PCh. 11.2 - Prob. 11.21PCh. 11.2 - Prob. 11.22PCh. 11.2 - 11–23. The beam is constructed from three boards...Ch. 11.2 - Prob. 11.24PCh. 11.2 - Prob. 11.25PCh. 11.2 - Select the lightest-weight wide-flange beam from...Ch. 11.2 - Prob. 11.27PCh. 11.2 - * 11–28. The joist AB used in housing construction...Ch. 11.2 - If the maximum bending stress is not to exceed...Ch. 11.2 - 11–30. The simply supported beam supports a load...Ch. 11.4 - Determine the variation in the width was a...Ch. 11.4 - Prob. 11.32PCh. 11.4 - Prob. 11.33PCh. 11.4 - The beam is made from a plate that has a constant...Ch. 11.4 - Determine the variation in the depth d of a...Ch. 11.4 - Determine the variation of the radius r of the...Ch. 11.4 - Prob. 11.37PCh. 11.4 - Determine the variation in the width b as a...Ch. 11.4 - The tubular shaft has an inner diameter of 15 mm....Ch. 11.4 - Prob. 11.40PCh. 11.4 - Prob. 11.41PCh. 11.4 - Prob. 11.42PCh. 11.4 - Prob. 11.43PCh. 11.4 - Prob. 11.44PCh. 11.4 - Prob. 11.45PCh. 11.4 - Prob. 11.46PCh. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 11.49RPCh. 11 - Determine the shaft's diameter to the nearest...Ch. 11 - Select the lightest-weight wide-flange beam from...Ch. 11 - The simply supported joist is used in the...Ch. 11 - The simply supported joist is used in the...Ch. 11 - by 4-in. pieces of wood braced as shown. If the...
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