Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Question
Chapter 4.9, Problem 160P
To determine
The equivalent resultant force and couple moment acting at point O.
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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
Engineering Mechanics: Statics
Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.
Ch. 4.4 - Express the result as a Cartesian vector.Ch. 4.4 - Express the result as a Cartesian vector.Ch. 4.4 - If A, B, and D are given vectors, prove the...Ch. 4.4 - Prove the triple scalar product identity A (B C)...Ch. 4.4 - Given the three nonzero vectors A, B and C, show...Ch. 4.4 - Determine the moment about point A of each of the...Ch. 4.4 - Determine the moment about point B of each of the...Ch. 4.4 - Prob. 6PCh. 4.4 - Determine the moment of each of the three forces...Ch. 4.4 - Determine the moment of each of the three forces...Ch. 4.4 - Take FB = 40 lb, FC = 50 lb. Probs. 49/10Ch. 4.4 - If FB = 30 lb and FC = 45 lb, determine the...Ch. 4.4 - Prob. 11PCh. 4.4 - Prob. 12PCh. 4.4 - Prob. 13PCh. 4.4 - Prob. 14PCh. 4.4 - Prob. 15PCh. 4.4 - Prob. 16PCh. 4.4 - Prob. 17PCh. 4.4 - The tower crane is used to hoist the 2-Mg load...Ch. 4.4 - The tower crane is used to hoist a 2-Mg load...Ch. 4.4 - The handle of the hammer is subjected to the force...Ch. 4.4 - In order to pull out the nail at B, the force F...Ch. 4.4 - Prob. 22PCh. 4.4 - Prob. 23PCh. 4.4 - Prob. 24PCh. 4.4 - If the 1500-lb boom AB, the 200-lb cage BCD, and...Ch. 4.4 - If the 1500-lb boom AB, the 200-lb cage BCD, and...Ch. 4.4 - Prob. 27PCh. 4.4 - Prob. 28PCh. 4.4 - Prob. 29PCh. 4.4 - A force F having a magnitude of F = 100N acts...Ch. 4.4 - Prob. 31PCh. 4.4 - Prob. 32PCh. 4.4 - Prob. 33PCh. 4.4 - Prob. 34PCh. 4.4 - Using a ring collar, the 75-N force can act in the...Ch. 4.4 - Prob. 36PCh. 4.4 - Prob. 37PCh. 4.4 - Force F acts perpendicular to the inclined plane....Ch. 4.4 - Force F acts perpendicular to the inclined plane....Ch. 4.4 - The pipe assembly is subjected to the 80-N force....Ch. 4.4 - The pipe assembly is subjected to the 80-N force....Ch. 4.4 - Strut AB of the 1-m-diameter hatch door exerts a...Ch. 4.4 - Determine the smallest force F that must be...Ch. 4.4 - Determine the smallest force F that must be...Ch. 4.4 - A force F = {6i 2j + 1k}kN produces a moment of...Ch. 4.4 - The force F = {6i + 8j + 10k}N creates a moment...Ch. 4.5 - F413. Determine the magnitude of the moment of the...Ch. 4.5 - F414. Determine the magnitude of the moment of the...Ch. 4.5 - Prob. 15FPCh. 4.5 - F416. Determine the magnitude of the moment of the...Ch. 4.5 - Express the result as a Cartesian vector.Ch. 4.5 - Prob. 18FPCh. 4.5 - Prob. 47PCh. 4.5 - Prob. 48PCh. 4.5 - Prob. 49PCh. 4.5 - Prob. 50PCh. 4.5 - Determine the moment of this force about the...Ch. 4.5 - Determine the magnitude of the moments of the...Ch. 4.5 - Determine the moment of this force F about an axis...Ch. 4.5 - The board is used to hold the end of a four-way...Ch. 4.5 - The board is used to hold the end of a four-way...Ch. 4.5 - Prob. 56PCh. 4.5 - Prob. 57PCh. 4.5 - Prob. 58PCh. 4.5 - Prob. 59PCh. 4.5 - The force of F = 30 N acts on the bracket as...Ch. 4.5 - Prob. 61PCh. 4.5 - Prob. 62PCh. 4.5 - Prob. 63PCh. 4.5 - Prob. 64PCh. 4.5 - Prob. 65PCh. 4.5 - The A-frame is being hoisted into an upright...Ch. 4.6 - F419. Determine the resultant couple moment acting...Ch. 4.6 - F420. Determine the resultant couple moment acting...Ch. 4.6 - Determine the magnitude of F so that the resultant...Ch. 4.6 - Determine the couple moment acting on the beam.Ch. 4.6 - Determine the resultant couple moment acting on...Ch. 4.6 - Determine the couple moment acting on the pipe...Ch. 4.6 - A twist of 4 N m is applied to the handle of the...Ch. 4.6 - Prob. 68PCh. 4.6 - Prob. 69PCh. 4.6 - Two couples act on the beam. If F = 125 lb,...Ch. 4.6 - Two couples act on the beam. Determine the...Ch. 4.6 - Determine the magnitude of the couple forces so...Ch. 4.6 - The man tries to open the valve by applying the...Ch. 4.6 - If the valve can be opened with a couple moment of...Ch. 4.6 - Prob. 75PCh. 4.6 - Determine the magnitude of the couple forces F so...Ch. 4.6 - Two couples act on the beam as shown. If F = 150...Ch. 4.6 - Two couples act on the beam as shown. Determine...Ch. 4.6 - Prob. 79PCh. 4.6 - Prob. 80PCh. 4.6 - Prob. 81PCh. 4.6 - Prob. 82PCh. 4.6 - Prob. 83PCh. 4.6 - Prob. 84PCh. 4.6 - Prob. 85PCh. 4.6 - Prob. 86PCh. 4.6 - Prob. 87PCh. 4.6 - Prob. 88PCh. 4.6 - Prob. 89PCh. 4.6 - Prob. 90PCh. 4.6 - If F = 80 N, determine the magnitude and...Ch. 4.6 - If the magnitude of the couple moment acting on...Ch. 4.6 - Prob. 93PCh. 4.6 - Prob. 94PCh. 4.6 - If F1 = 100 N, F2 = 120 N, and F3 = 80 N,...Ch. 4.6 - Prob. 96PCh. 4.7 - Replace the leading system by an equivalent...Ch. 4.7 - Prob. 26FPCh. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Prob. 97PCh. 4.7 - Prob. 98PCh. 4.7 - Replace the force system acting on the beam by an...Ch. 4.7 - Replace the force system acting on the beam by an...Ch. 4.7 - Replace the force system acting on the post by a...Ch. 4.7 - Prob. 102PCh. 4.7 - Prob. 103PCh. 4.7 - Prob. 104PCh. 4.7 - Prob. 105PCh. 4.7 - Prob. 106PCh. 4.7 - A biomechanical model of the lumbar region of the...Ch. 4.7 - Prob. 108PCh. 4.7 - Prob. 109PCh. 4.7 - The belt passing over the pulley is subjected to...Ch. 4.7 - The belt passing over the pulley is subjected to...Ch. 4.7 - Prob. 112PCh. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading shown by an equivalent single...Ch. 4.8 - Replace the loading shown by an equivalent single...Ch. 4.8 - The weights of the various components of the truck...Ch. 4.8 - The weights of the various components of the truck...Ch. 4.8 - Prob. 115PCh. 4.8 - Prob. 116PCh. 4.8 - Replace the loading acting on the beam by a single...Ch. 4.8 - Replace the loading acting on the beam by a single...Ch. 4.8 - R46. Replace the force system acting on the frame...Ch. 4.8 - Prob. 120PCh. 4.8 - Prob. 121PCh. 4.8 - Prob. 122PCh. 4.8 - Prob. 123PCh. 4.8 - Replace the force system acting on the post by a...Ch. 4.8 - Replace the force system acting on the post by a...Ch. 4.8 - Prob. 126PCh. 4.8 - The tube supports the four parallel forces....Ch. 4.8 - Prob. 128PCh. 4.8 - Prob. 129PCh. 4.8 - Determine the equivalent resultant force and...Ch. 4.8 - Prob. 131PCh. 4.8 - If FA= 40 kN and FB = 35 kN, determine the...Ch. 4.8 - Prob. 133PCh. 4.8 - Replace the two wrenches and the force, acting on...Ch. 4.8 - Prob. 135PCh. 4.8 - Prob. 136PCh. 4.8 - Prob. 137PCh. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Prob. 138PCh. 4.9 - Replace the distributed loading with an equivalent...Ch. 4.9 - Prob. 140PCh. 4.9 - Prob. 141PCh. 4.9 - Prob. 142PCh. 4.9 - Prob. 143PCh. 4.9 - The distribution of soil loading on the bottom of...Ch. 4.9 - R48. Replace the distributed loading by an...Ch. 4.9 - Prob. 146PCh. 4.9 - Prob. 147PCh. 4.9 - Prob. 148PCh. 4.9 - Prob. 149PCh. 4.9 - Replace the loading by an equivalent force and...Ch. 4.9 - Prob. 151PCh. 4.9 - Prob. 152PCh. 4.9 - Prob. 153PCh. 4.9 - Prob. 154PCh. 4.9 - Prob. 155PCh. 4.9 - Prob. 156PCh. 4.9 - Prob. 157PCh. 4.9 - Replace the distributed loading with an equivalent...Ch. 4.9 - Wet concrete exerts a pressure distribution along...Ch. 4.9 - Prob. 160PCh. 4.9 - Prob. 161PCh. 4.9 - Prob. 162PCh. 4.9 - Prob. 163RPCh. 4.9 - Prob. 164RPCh. 4.9 - Prob. 165RPCh. 4.9 - Prob. 166RPCh. 4.9 - R42. Replace the force F having a magnitude of F =...Ch. 4.9 - Prob. 168RPCh. 4.9 - Prob. 169RPCh. 4.9 - Prob. 170RPCh. 4.9 - Prob. 171RPCh. 4.9 - and mass center at G. If the maximum moment that...Ch. 4.9 - Prob. 173RP
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Similar questions
- 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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