Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 4.6, Problem 37P
The rod has a weight of 6 lb/ft. If it is supported by a ball-and-socket joint at C and a journal bearing at D, determine the x, y, z components of reaction at these supports and the moment M that must be applied along the axis of the rod to hold it in the position shown.
Prob.4-37
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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.
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Chapter 4 Solutions
Statics and Mechanics of Materials (5th Edition)
Ch. 4.4 - Draw the free-body diagram of each object. Prob....Ch. 4.4 - Determine the horizontal and vertical components...Ch. 4.4 - Determine the horizontal and vertical components...Ch. 4.4 - The truss is supported by a pin at A and a roller...Ch. 4.4 - Determine the components of reaction at the fixed...Ch. 4.4 - The 25-kg bar has a center of mass at G. If it is...Ch. 4.4 - Determine the reactions at the smooth contact...Ch. 4.4 - Determine the components of the support reactions...Ch. 4.4 - Determine the reactions at the supports. Prob. 4-2Ch. 4.4 - Determine the horizontal and vertical components...
Ch. 4.4 - Determine the reactions at the supports. Prob. 4-4Ch. 4.4 - Determine the reactions at the supports. Prob. 4-5Ch. 4.4 - Determine the reactions at the supports. Prob. 4-6Ch. 4.4 - Determine the magnitude of force at the pin A and...Ch. 4.4 - The dimensions of a jib crane are given in the...Ch. 4.4 - The dimensions of a jib crane are given in the...Ch. 4.4 - The smooth pipe rests against the opening at the...Ch. 4.4 - The beam is horizontal and the springs are...Ch. 4.4 - The 10-kg uniform rod is pinned at end A. If it is...Ch. 4.4 - The man uses the hand truck to move material up...Ch. 4.4 - Three uniform books, each having a weight W and...Ch. 4.4 - Determine the reactions at the pin A and the...Ch. 4.4 - If rope BC will fail when the tension becomes 50...Ch. 4.4 - Prob. 17PCh. 4.4 - Prob. 18PCh. 4.4 - The cantilever footing is used to support a wall...Ch. 4.4 - Prob. 20PCh. 4.4 - A boy stands out at the end of the diving board,...Ch. 4.4 - Prob. 22PCh. 4.4 - Prob. 23PCh. 4.4 - Prob. 24PCh. 4.4 - Prob. 25PCh. 4.4 - The man attempts to pull the four wheeler up the...Ch. 4.6 - Draw the free-body diagram of each object.Ch. 4.6 - In each case, write the moment equations about the...Ch. 4.6 - Prob. 7FPCh. 4.6 - Prob. 8FPCh. 4.6 - The rod is supported by smooth journal bearings at...Ch. 4.6 - Determine the support reactions at the smooth...Ch. 4.6 - Determine the force developed in the short link...Ch. 4.6 - Determine the components of reaction that the...Ch. 4.6 - The uniform load has a mass of 600 kg and is...Ch. 4.6 - Due to an unequal distribution of fuel in the wing...Ch. 4.6 - Determine the components of reaction at the fixed...Ch. 4.6 - The 50-lb mulching machine has a center of gravity...Ch. 4.6 - Prob. 30PCh. 4.6 - The uniform concrete slab has a mass of 2400 kg....Ch. 4.6 - Prob. 32PCh. 4.6 - Determine the tension in each cable and the...Ch. 4.6 - The bent rod is supported at A, B, and C by smooth...Ch. 4.6 - Prob. 35PCh. 4.6 - The bar AB is supported by two smooth collars. At...Ch. 4.6 - The rod has a weight of 6 lb/ft. If it is...Ch. 4.6 - The sign has a mass of 100 kg with center of mass...Ch. 4.6 - Both pulleys cite fixed to the shaft and as the...Ch. 4.6 - Both pulleys are fixed to the shaft and as the...Ch. 4.6 - Prob. 41PCh. 4.8 - Determine the friction force at the surface of...Ch. 4.8 - Determine the couple moment M needed to cause...Ch. 4.8 - Prob. 6PPCh. 4.8 - Prob. 7PPCh. 4.8 - Prob. 13FPCh. 4.8 - Determine the minimum force P to prevent the 30-kg...Ch. 4.8 - Determine the maximum force P that can be applied...Ch. 4.8 - Prob. 16FPCh. 4.8 - Prob. 17FPCh. 4.8 - Prob. 18FPCh. 4.8 - Prob. 19FPCh. 4.8 - If the coefficient of static friction at all...Ch. 4.8 - Prob. 21FPCh. 4.8 - Prob. 42PCh. 4.8 - The tractor exerts a towing force T = 400 lb....Ch. 4.8 - The mine car and its contents have a total mass of...Ch. 4.8 - The winch on the truck is used to hoist the...Ch. 4.8 - Prob. 46PCh. 4.8 - The automobile has a mass of 2 Mg and center of...Ch. 4.8 - Prob. 48PCh. 4.8 - Prob. 49PCh. 4.8 - Prob. 50PCh. 4.8 - Determine the angle at which the applied force P...Ch. 4.8 - Prob. 52PCh. 4.8 - The 180-lb man climbs up the ladder and stops at...Ch. 4.8 - The 180-lb man climbs up the ladder and stops at...Ch. 4.8 - The spool of wire having a weight of 300 lb rests...Ch. 4.8 - The spool of wire having a weight of 300 lb rests...Ch. 4.8 - The ring has a mass of 0.5 kg and is resting on...Ch. 4.8 - Determine the smallest force P that must be...Ch. 4.8 - The man having a weight of 200 lb pushes...Ch. 4.8 - The uniform hoop of weight W is subjected to the...Ch. 4.8 - Prob. 61PCh. 4.8 - Prob. 62PCh. 4.8 - Prob. 63PCh. 4.8 - The coefficient of static Friction between the...Ch. 4 - If the roller at B can sustain a maximum load of 3...Ch. 4 - Determine the reactions at the supports A and B...Ch. 4 - Determine the normal reaction at the roller A and...Ch. 4 - Determine the horizontal and vertical components...Ch. 4 - Determine the x, y, z components of reaction at...Ch. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - The uniform 60-kg crate C rests uniformly on a...
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- Problem 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_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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