Statics and Mechanics of Materials
2nd Edition
ISBN: 9780073398167
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4.4, Problem 97P
The cylinder shown is of weight W and radius r, and the coefficient of static fiction is the same at A and B. Determine the magnitude of the largest couple M that can be applied to the cylinder if it is not to rotate.
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Chapter 4 Solutions
Statics and Mechanics of Materials
Ch. 4.1 - For the beam and loading shown, determine (a) the...Ch. 4.1 - A 3200-lb forklift truck is used to lift a 1700-lb...Ch. 4.1 - A gardener uses a wheelbarrow to transport a 250-N...Ch. 4.1 - A load of lumber of weight W=25 kN is being raised...Ch. 4.1 - Three loads are applied as shown to a light beam...Ch. 4.1 - Three loads are applied as shown to a light beam...Ch. 4.1 - For the beam and loading shown, determine the...Ch. 4.1 - Prob. 8PCh. 4.1 - Prob. 9PCh. 4.1 - The lever BCD is hinged at C and attached to a...
Ch. 4.1 - The lever BCD is hinged at C and attached to a...Ch. 4.1 - A lever AB is hinged at C and attached to a...Ch. 4.1 - Determine the reactions at A and B when...Ch. 4.1 - Prob. 14PCh. 4.1 - Prob. 15PCh. 4.1 - Prob. 16PCh. 4.1 - A light bar AD is suspended from a cable BE and...Ch. 4.1 - Prob. 18PCh. 4.1 - Prob. 19PCh. 4.1 - Two slots have been cut in plate DEF, and the...Ch. 4.1 - A 6-m telephone pole weighing 1600 N is used to...Ch. 4.1 - Prob. 22PCh. 4.1 - For the and crate of Prob. 4.22 and assuming that...Ch. 4.1 - A tension of 20 N is maintained in a tape as it...Ch. 4.1 - The bracket ABC can be supported in the eight...Ch. 4.1 - Eight identical 500750-mm rectangular plates, each...Ch. 4.2 - Determine the reactions at B and C when a=30mm.Ch. 4.2 - Prob. 28PCh. 4.2 - A 12-ft wooden beam weighing 80 lb is supported by...Ch. 4.2 - Prob. 30PCh. 4.2 - One end of rod AB rests in the comer A and the...Ch. 4.2 - Using the method of Sec. 4.2B, solve Prob. 4.12.Ch. 4.2 - Prob. 33PCh. 4.2 - A 40-lb roller of 8-in. diameter, which is to be...Ch. 4.2 - Member ABC is supported by a pin and bracket at B...Ch. 4.2 - Prob. 36PCh. 4.2 - Prob. 37PCh. 4.2 - For the frame and loading shown, detennine the...Ch. 4.2 - For the boom and loading shown, determine (a) the...Ch. 4.2 - A slender rod BC of length L and weight W is held...Ch. 4.2 - Prob. 41PCh. 4.2 - Prob. 42PCh. 4.2 - Prob. 43PCh. 4.2 - Prob. 44PCh. 4.2 - Solve Prob. 4.44, assuming that the 170-N force...Ch. 4.2 - Prob. 46PCh. 4.2 - Prob. 47PCh. 4.2 - Prob. 48PCh. 4.2 - Prob. 49PCh. 4.2 - Prob. 50PCh. 4.3 - Two transmission belts pass over a double-sheaved...Ch. 4.3 - Solve Prob. 4.51, assuming that the pulley rotates...Ch. 4.3 - A 48-ft sheet of plywood weighing 40 lb has been...Ch. 4.3 - Prob. 54PCh. 4.3 - Prob. 55PCh. 4.3 - Prob. 56PCh. 4.3 - Prob. 57PCh. 4.3 - Prob. 58PCh. 4.3 - Prob. 59PCh. 4.3 - Prob. 60PCh. 4.3 - A 48-in. boom is held by a ball-and-socket joint...Ch. 4.3 - Prob. 62PCh. 4.3 - The 6-m pole ABC is acted upon by a 455-N force as...Ch. 4.3 - A 600-lb crate hangs from a cable that passes over...Ch. 4.3 - The horizontal platform ABCD weighs 60 lb and...Ch. 4.3 - Prob. 66PCh. 4.3 - Prob. 67PCh. 4.3 - Prob. 68PCh. 4.3 - A 10-kg storm window measuring 9001500 mm is held...Ch. 4.3 - Prob. 70PCh. 4.3 - Prob. 71PCh. 4.3 - Solve Prob. 4.69, assuming that the hinge at A has...Ch. 4.3 - Prob. 73PCh. 4.3 - Three rods are welded together to form a corner...Ch. 4.4 - Determine whether the block shown is in...Ch. 4.4 - Prob. 76PCh. 4.4 - Determine whether the block shown is in...Ch. 4.4 - Prob. 78PCh. 4.4 - Prob. 79PCh. 4.4 - Prob. 80PCh. 4.4 - Prob. 81PCh. 4.4 - Prob. 82PCh. 4.4 - Prob. 83PCh. 4.4 - Knowing that P=100N, determine the range of values...Ch. 4.4 - A 120-lb cabinet is mounted on casters that can be...Ch. 4.4 - Prob. 86PCh. 4.4 - A 40-kg packing crate must be moved to the left...Ch. 4.4 - A 40-kg packing crate is pulled by a rope as...Ch. 4.4 - Prob. 89PCh. 4.4 - Prob. 90PCh. 4.4 - Prob. 91PCh. 4.4 - Prob. 92PCh. 4.4 - Prob. 93PCh. 4.4 - Prob. 94PCh. 4.4 - Prob. 95PCh. 4.4 - Prob. 96PCh. 4.4 - The cylinder shown is of weight W and radius r,...Ch. 4.4 - Prob. 98PCh. 4 - A T-shaped bracket supports the four loads shown....Ch. 4 - Neglecting friction and the radius of the pulley,...Ch. 4 - Member ABC is supported by a pin and bracket at B...Ch. 4 - Prob. 102RPCh. 4 - Prob. 103RPCh. 4 - Prob. 104RPCh. 4 - Prob. 105RPCh. 4 - Prob. 106RPCh. 4 - Prob. 107RPCh. 4 - Prob. 108RPCh. 4 - Prob. 109RPCh. 4 - Two 10-lb blocks A and B are connected by a...
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- Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.arrow_forwardAn aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.arrow_forwardProblem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forward
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