Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 5.4, Problem 58P
Assuming that the foundation exerts a linearly varying load distribution on its bottom, determine the load intensities w1, and w2 for equilibrium in terms of the parameters shown.
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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.
An 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.
Chapter 5 Solutions
Engineering Mechanics: Statics
Ch. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5PCh. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.4 - Determine the horizontal and vertical components...
Ch. 5.4 - Determine the horizontal and vertical components...Ch. 5.4 - The truss is supported by a pin at A and a roller...Ch. 5.4 - Determine the components of reaction at the fixed...Ch. 5.4 - The 25 kg bar has a center of mass at G. If it is...Ch. 5.4 - Determine the reactions at the smooth contact...Ch. 5.4 - Determine the horizontal and vertical components...Ch. 5.4 - Prob. 11PCh. 5.4 - Determine the components of the support reactions...Ch. 5.4 - Prob. 13PCh. 5.4 - Prob. 14PCh. 5.4 - Determine the horizontal and vertical components...Ch. 5.4 - Determine the components of reaction at the...Ch. 5.4 - Prob. 17PCh. 5.4 - Determine the tension in the cable and the...Ch. 5.4 - Prob. 19PCh. 5.4 - Prob. 20PCh. 5.4 - Prob. 21PCh. 5.4 - Prob. 22PCh. 5.4 - Prob. 23PCh. 5.4 - Prob. 24PCh. 5.4 - Determine the magnitude of force at the pin A and...Ch. 5.4 - Prob. 26PCh. 5.4 - Prob. 27PCh. 5.4 - Prob. 28PCh. 5.4 - Prob. 29PCh. 5.4 - Prob. 30PCh. 5.4 - Prob. 31PCh. 5.4 - Prob. 32PCh. 5.4 - Prob. 33PCh. 5.4 - Prob. 34PCh. 5.4 - Prob. 35PCh. 5.4 - Prob. 36PCh. 5.4 - The boom supports the two vertical loads. Neglect...Ch. 5.4 - The boom is intended to support two vertical loads...Ch. 5.4 - Prob. 39PCh. 5.4 - Prob. 40PCh. 5.4 - Prob. 41PCh. 5.4 - The cantilevered jib crane is used to support the...Ch. 5.4 - The cantilevered jib crane is used to support the...Ch. 5.4 - Prob. 44PCh. 5.4 - Prob. 45PCh. 5.4 - Three uniform books each having a weight W and...Ch. 5.4 - Prob. 47PCh. 5.4 - Prob. 48PCh. 5.4 - Prob. 49PCh. 5.4 - Prob. 50PCh. 5.4 - Prob. 51PCh. 5.4 - A boy stands out at the end of the diving board,...Ch. 5.4 - The uniform beam has a weight Wand length l and is...Ch. 5.4 - Determine the distance d for placement of the load...Ch. 5.4 - If d = 1 m, and = 30, determine me normal...Ch. 5.4 - Prob. 56PCh. 5.4 - Assuming that the foundation exerts a linearly...Ch. 5.4 - Assuming that the foundation exerts a linearly...Ch. 5.4 - Prob. 59PCh. 5.4 - The 30-N uniform rod has a length of l = 1 m. If s...Ch. 5.4 - The uniform rod has a length I and weight W. It is...Ch. 5.7 - The uniform plate has a weight of 500 lb....Ch. 5.7 - Determine the reactions at the roller support A,...Ch. 5.7 - The rod is supported by smooth journal bearings at...Ch. 5.7 - Determine the support reactions at the smooth...Ch. 5.7 - Determine the force developed in the short link...Ch. 5.7 - Determine the components of reaction that the...Ch. 5.7 - Determine the tension each rope and the force that...Ch. 5.7 - Determine the vertical reactions at the wheels C...Ch. 5.7 - Prob. 64PCh. 5.7 - If these components have weights WA = 45000 Wa =...Ch. 5.7 - Prob. 66PCh. 5.7 - Prob. 67PCh. 5.7 - Prob. 68PCh. 5.7 - Prob. 69PCh. 5.7 - Determine the components of reaction at hinges A...Ch. 5.7 - Prob. 71PCh. 5.7 - Prob. 72PCh. 5.7 - Prob. 73PCh. 5.7 - Prob. 74PCh. 5.7 - Prob. 75PCh. 5.7 - Prob. 76PCh. 5.7 - Determine the horizontal equilibrium force P that...Ch. 5.7 - Determine the components of reaction at A and the...Ch. 5.7 - Compute the x, y, z components of reaction at the...Ch. 5.7 - Determine the magnitude of F2 which will cause the...Ch. 5.7 - Determine the x, y, z components of reaction at...Ch. 5.7 - Prob. 82PCh. 5.7 - Determine the horizontal tension T in the belt on...Ch. 5.7 - Determine the horizontal tension T in the belt on...Ch. 5.7 - If the roller at 8 can sustain a maximum load of 3...Ch. 5.7 - Determine the normal reaction at the roller A and...Ch. 5.7 - Prob. 87RPCh. 5.7 - Prob. 88RPCh. 5.7 - I he uniform rod of length L and weight W is...Ch. 5.7 - Determine the x, y, z components of reaction at...Ch. 5.7 - Determine the x, y, z components of reaction at...Ch. 5.7 - Determine the reactions at the supports A and B...
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