Mechanics Of Materials, Si Edition
9th Edition
ISBN: 9789810694364
Author: Russell C Hibbeler
Publisher: Pearson Education
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Chapter 13, Problem 13.131RP
The square structural A992 steel tubing has outer dimensions of 8 in. by 8 in. Its cross-sectional area is 14.40 in2 and its moments of inertia are lx = ly = 131 in4. Determine the maximum load P it can support. The column can be assumed fixed at its base and free at its top.
R13−4
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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 13 Solutions
Mechanics Of Materials, Si Edition
Ch. 13.3 - A 50-in long steel rod has a diameter of 1 in....Ch. 13.3 - A 12-ft wooden rectangular column has the...Ch. 13.3 - The A992 steel column can be considered pinned at...Ch. 13.3 - A steel pipe is fixed supported at its ends. If it...Ch. 13.3 - Determine the maximum force P that can be...Ch. 13.3 - The A992 steel rod BC has a diameter of 50 mm and...Ch. 13.3 - 13-1. Determine the critical buckling load for the...Ch. 13.3 - The column consists of a rigid member that is...Ch. 13.3 - The aircraft link is made from an A992 steel rod....Ch. 13.3 - Rigid bars AB and BC are pin connected at B. If...
Ch. 13.3 - 13-5. A rod made from polyurethane has a...Ch. 13.3 - 13–6. A rod made from polyurethane has a...Ch. 13.3 - Prob. 13.7PCh. 13.3 - Prob. 13.8PCh. 13.3 - Prob. 13.9PCh. 13.3 - Prob. 13.10PCh. 13.3 - The A992 steel angle has a cross-sectional area of...Ch. 13.3 - *13–12. The control linkage for a machine consists...Ch. 13.3 - 13–13. An A992 steel column has a length of 5 m...Ch. 13.3 - Prob. 13.14PCh. 13.3 - Prob. 13.15PCh. 13.3 - Prob. 13.16PCh. 13.3 - The 10-ft wooden rectangular column has the...Ch. 13.3 - The 10-fl wooden column has the dimensions shown....Ch. 13.3 - Determine the maximum force P that can be applied...Ch. 13.3 - Prob. 13.20PCh. 13.3 - 13-21. The A992 steel tube has the cross-sectional...Ch. 13.3 - Prob. 13.22PCh. 13.3 - 13-23. The linkage is made using two A992 steel...Ch. 13.3 - *13–24. An L-2 tool steel link in a forging...Ch. 13.3 - The W14 30 A992 steel column is assumed pinned at...Ch. 13.3 - The A992 steel bar AB has a square cross section....Ch. 13.3 - Prob. 13.27PCh. 13.3 - *13–28. The strongback is made of an A992 steel...Ch. 13.3 - Prob. 13.29PCh. 13.3 - Prob. 13.30PCh. 13.3 - The steel bar AB has a rectangular cross section....Ch. 13.3 - Prob. 13.32PCh. 13.3 - 13–33. Determine the greatest load P the frame...Ch. 13.3 - Prob. 13.34PCh. 13.3 - Prob. 13.35PCh. 13.3 - The members of the truss are assumed to be pin...Ch. 13.3 - Solve Prob. 1336 for member AB, which has a radius...Ch. 13.3 - The truss is made from A992 steel bars, each of...Ch. 13.3 - The truss is made from A992 steel bars, each of...Ch. 13.3 - Prob. 13.40PCh. 13.3 - The ideal column has a weight w (force/length) and...Ch. 13.3 - The ideal column is subjected to the force F at...Ch. 13.3 - The column with constant El has the end...Ch. 13.3 - Consider an ideal column as in Fig.13-10 c, having...Ch. 13.3 - Consider an ideal column as in Fig. 13-10d, having...Ch. 13.5 - The wood column is fixed at its base and free at...Ch. 13.5 - Prob. 13.47PCh. 13.5 - Prob. 13.48PCh. 13.5 - Prob. 13.49PCh. 13.5 - Prob. 13.50PCh. 13.5 - Assume that the wood column is pin connected at...Ch. 13.5 - Prob. 13.52PCh. 13.5 - Prob. 13.53PCh. 13.5 - A W14 30 structural A-36 steel column is pin...Ch. 13.5 - The wood column is pinned at its base and top. If...Ch. 13.5 - Prob. 13.56PCh. 13.5 - The 6061-T6 aluminum alloy solid shaft is fixed at...Ch. 13.5 - The 6061-T6 aluminum alloy solid shaft is fixed at...Ch. 13.5 - Prob. 13.59PCh. 13.5 - The wood column is pinned at its base and top. If...Ch. 13.5 - Prob. 13.61PCh. 13.5 - Prob. 13.62PCh. 13.5 - Prob. 13.63PCh. 13.5 - Prob. 13.64PCh. 13.5 - Prob. 13.65PCh. 13.5 - Prob. 13.66PCh. 13.5 - Prob. 13.67PCh. 13.5 - The W14 53 structural A992 steel column is fixed...Ch. 13.5 - The W14 53 column is fixed at its base and free...Ch. 13.5 - Prob. 13.70PCh. 13.5 - Prob. 13.71PCh. 13.5 - The aluminum rod is fixed at its base and free and...Ch. 13.5 - The stress-strain diagram for the material of a...Ch. 13.5 - Construct the buckling curve, P/A versus L/ r, for...Ch. 13.5 - The stress-strain diagram of the material can be...Ch. 13.5 - The stress-strain diagram of the material can be...Ch. 13.5 - Prob. 13.77PCh. 13.6 - Determine the largest length of a W10 12...Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Take Y = 50 ksi.Ch. 13.6 - Determine the longest length of a W8 31...Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 13.83PCh. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 13.85PCh. 13.6 - Prob. 13.86PCh. 13.6 - Prob. 13.87PCh. 13.6 - Prob. 13.88PCh. 13.6 - Using the AISC equations, check if a column having...Ch. 13.6 - Prob. 13.90PCh. 13.6 - Prob. 13.91PCh. 13.6 - Prob. 13.92PCh. 13.6 - Prob. 13.93PCh. 13.6 - Prob. 13.94PCh. 13.6 - Prob. 13.95PCh. 13.6 - Prob. 13.96PCh. 13.6 - Prob. 13.97PCh. 13.6 - Prob. 13.98PCh. 13.6 - The tube is 0.25 in. thick, is made of 2014-T6...Ch. 13.6 - Prob. 13.100PCh. 13.6 - A rectangular wooden column has the cross section...Ch. 13.6 - Prob. 13.102PCh. 13.6 - Prob. 13.103PCh. 13.6 - The bar is made of aluminum alloy 2014-T6....Ch. 13.6 - Prob. 13.105PCh. 13.6 - Prob. 13.106PCh. 13.7 - Prob. 13.107PCh. 13.7 - Prob. 13.108PCh. 13.7 - Prob. 13.109PCh. 13.7 - Prob. 13.110PCh. 13.7 - The W8 15 wide-flange A992 steel column is fixed...Ch. 13.7 - The W8 15 wide-flange A992 steel column is fixed...Ch. 13.7 - Prob. 13.113PCh. 13.7 - Prob. 13.114PCh. 13.7 - Prob. 13.115PCh. 13.7 - Prob. 13.116PCh. 13.7 - Prob. 13.117PCh. 13.7 - Prob. 13.118PCh. 13.7 - The 2014-T6 aluminum hollow column is fixed at its...Ch. 13.7 - The 2014-T6 aluminum hollow column is fixed at its...Ch. 13.7 - Prob. 13.121PCh. 13.7 - Prob. 13.122PCh. 13.7 - Prob. 13.123PCh. 13.7 - Prob. 13.124PCh. 13.7 - The 10-in.-diameter utility pole supports the...Ch. 13.7 - Using the NFPA equations of Sec 13.6. and Eq....Ch. 13.7 - Prob. 13.127PCh. 13 - The wood column has a thickness of 4 in. and a...Ch. 13 - The wood column has a thickness of 4 in. and a...Ch. 13 - A steel column has a length of 5 m and is free at...Ch. 13 - The square structural A992 steel tubing has outer...Ch. 13 - If the A-36 steel solid circular rod BD has a...Ch. 13 - If P = 15 kip, determine the required minimum...Ch. 13 - The steel pipe is fixed supported at its ends. If...Ch. 13 - The W200 46 wide-flange A992-steel column can be...Ch. 13 - The wide-flange A992 steel column has the cross...Ch. 13 - The wide-flange A992 steel column has the cross...
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Column buckling; Author: Amber Book;https://www.youtube.com/watch?v=AvvaCi_Nn94;License: Standard Youtube License