Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 12.3, Problem 36P
Determine the equation of the elastic curve, the slope at A, and the deflection at B. El is constant.
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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 12 Solutions
Mechanics of Materials
Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope of end A of the cantilevered...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the slope of the simply supported beam...Ch. 12.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 12.2 - The L2 steel blade of the band saw wraps around...Ch. 12.2 - A picture is taken of a man performing a pole...Ch. 12.2 - A torque wrench is used to tighten the nut on a...
Ch. 12.2 - The pipe can be assumed roller supported at its...Ch. 12.2 - Determine the equations of the elastic curve for...Ch. 12.2 - Determine the equations of the elastic curve using...Ch. 12.2 - Determine the maximum deflection of the solid...Ch. 12.2 - Determine the equation of the elastic curve using...Ch. 12.2 - Determine the equations of the elastic curve using...Ch. 12.3 - The shaft supports the two pulley loads shown....Ch. 12.3 - Determine the equation of the elastic curve, the...Ch. 12.3 - Determine the equation of the elastic curve and...Ch. 12.3 - Determine the maximum deflection of the...Ch. 12.3 - Prob. 45PCh. 12.3 - Prob. 46PCh. 12.3 - Prob. 47PCh. 12.3 - Prob. 48PCh. 12.4 - Determine the slope and deflection of end A of the...Ch. 12.4 - Determine the slope and deflection of end A of the...Ch. 12.4 - Determine the slope and deflection of end A of the...Ch. 12.4 - Determine the slope and deflection at A of the...Ch. 12.4 - Prob. 11FPCh. 12.4 - Determine the maximum deflection of the simply...Ch. 12.4 - Determine the slope and deflection at C. El is...Ch. 12.4 - Prob. 54PCh. 12.4 - The composite simply supported steel shaft is...Ch. 12.4 - Determine the maximum deflection of the...Ch. 12.4 - Prob. 60PCh. 12.4 - Determine the slope at A and the maximum...Ch. 12.4 - Determine the displacement of the 20-mm-diameter...Ch. 12.4 - The two force components act on the tire of the...Ch. 12.4 - Determine the slope at B and deflection at C. El...Ch. 12.4 - Prob. 79PCh. 12.5 - The W10 15 cantilevered beam is made of A-36...Ch. 12.5 - The W14 43 simply supported beam is made of A992...Ch. 12.5 - The W14 43 simply supported beam is made of A992...Ch. 12.5 - The W14 43 simply supported beam is made of A-36...Ch. 12.7 - Determine the reactions at the supports A and B,...Ch. 12.7 - Determine the reactions at the supports A, B, and...Ch. 12.7 - Determine the reactions at the supports A and B,...Ch. 12.7 - The beam has a constant E1I1 and is supported by...Ch. 12.8 - Determine the reaction at the supports, then draw...Ch. 12.9 - Determine the reactions at the fixed support A and...Ch. 12.9 - Determine the reactions at the fixed support A and...Ch. 12.9 - Determine the reactions at the fixed support A and...Ch. 12.9 - Determine the reaction at the roller B. EI is...Ch. 12.9 - Determine the reaction at the roller B. EI is...Ch. 12.9 - Determine the reaction at the roller support B if...Ch. 12.9 - Determine the reactions at the journal bearing...Ch. 12.9 - Determine the reactions at the supports, then draw...Ch. 12.9 - Determine the reactions at the supports, then draw...Ch. 12.9 - The rim on the flywheel has a thickness t, width...Ch. 12.9 - Determine the moment developed in each corner....Ch. 12 - Determine the equation of the elastic curve. Use...Ch. 12 - Draw the bending-moment diagram for the shaft and...Ch. 12 - Determine the moment reactions at the supports A...Ch. 12 - Specify the slope at A and the maximum deflection....Ch. 12 - Determine the maximum deflection between the...Ch. 12 - Determine the slope at B and the deflection at C....Ch. 12 - Determine the reactions, then draw the shear and...Ch. 12 - El is constant.Ch. 12 - Using the method of superposition, determine the...
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