Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 9.2, Problem 76P
To determine
The center of gravity at a height from the floor,
The equilibrium angle of tilt
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Chapter 9 Solutions
Engineering Mechanics: Statics
Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4P
Ch. 9.1 - Prob. 5PCh. 9.1 - Locate the centroid of the area.Ch. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Locate the centroid of the area. Prob. 9-17Ch. 9.1 - Locate the centroid x of the area. Probs. 9-11/12Ch. 9.1 - Locate the centroid of the area. Probs. 9-11/12Ch. 9.1 - Locate the centroid x of the area. Probs. 9-13/14Ch. 9.1 - Locate the centroid of the area. Probs. 9-13/14Ch. 9.1 - Prob. 15PCh. 9.1 - Prob. 16PCh. 9.1 - Prob. 17PCh. 9.1 - Locate the centroid x of the area. Probs. 9-18/19Ch. 9.1 - Locate the centroid of the area. Probs. 9-18/19Ch. 9.1 - Locate the centroid of the shaded area.Ch. 9.1 - Prob. 21PCh. 9.1 - Prob. 22PCh. 9.1 - Prob. 23PCh. 9.1 - Prob. 24PCh. 9.1 - Determine the location of its center of gravity....Ch. 9.1 - Prob. 26PCh. 9.1 - Prob. 27PCh. 9.1 - Prob. 28PCh. 9.1 - Prob. 29PCh. 9.1 - Prob. 30PCh. 9.1 - Prob. 31PCh. 9.1 - Locate the centroid x of the area. Probs. 9-32/33Ch. 9.1 - Locate the centroid of the area. Probs. 9-32/33Ch. 9.1 - Determine the location of its center of mass. Also...Ch. 9.1 - Prob. 35PCh. 9.1 - Prob. 36PCh. 9.1 - Prob. 37PCh. 9.1 - Prob. 38PCh. 9.1 - Locate the centroid of the paraboloid. Probs....Ch. 9.1 - The material is homogeneous. Prob. 9-39Ch. 9.1 - Prob. 41PCh. 9.1 - Determine the centroid of the solid. Prob. 9-42Ch. 9.1 - Locate the center of gravity z of the solid. Prob....Ch. 9.1 - Locate the centroid of the ellipsoid of...Ch. 9.1 - Prob. 45PCh. 9.1 - Determine its mass and the distance z to the...Ch. 9.1 - Locate the centroid of the quarter-cone. Prob....Ch. 9.1 - Locate the centroid z of the frustum of the...Ch. 9.1 - Prob. 49PCh. 9.1 - Suggestion: Use a triangular plate element...Ch. 9.2 - Locate the centroid (x,y,z) of the wire bent in...Ch. 9.2 - Locate the centroid of the beams cross-sectional...Ch. 9.2 - Locate the centroid of the beams cross-sectional...Ch. 9.2 - Locate the centroid (x,y) of the cross-sectional...Ch. 9.2 - Locate the center of mass (x,y,z) of the...Ch. 9.2 - Determine the center of mass (x,y,z) of the...Ch. 9.2 - If the mass of the gusset plates at the joints and...Ch. 9.2 - Prob. 52PCh. 9.2 - Prob. 53PCh. 9.2 - Neglect the thickness of the material and slight...Ch. 9.2 - Prob. 55PCh. 9.2 - Each plate has a constant width in the z direction...Ch. 9.2 - Prob. 57PCh. 9.2 - Neglect the size of the corner welds at A and B...Ch. 9.2 - Prob. 59PCh. 9.2 - Prob. 60PCh. 9.2 - Prob. 61PCh. 9.2 - Prob. 62PCh. 9.2 - Prob. 63PCh. 9.2 - Prob. 64PCh. 9.2 - Prob. 65PCh. 9.2 - Assume all corners are square and neglect the size...Ch. 9.2 - Prob. 67PCh. 9.2 - Prob. 68PCh. 9.2 - Prob. 69PCh. 9.2 - Prob. 70PCh. 9.2 - Neglect the size of the corner welds at A and B...Ch. 9.2 - Prob. 72PCh. 9.2 - If it is folded over as shown, determine the...Ch. 9.2 - Determine the location (x,y,z) of its centroid....Ch. 9.2 - It the cord is cut, the part will rotate about the...Ch. 9.2 - Prob. 76PCh. 9.2 - The location of the center of gravity of each...Ch. 9.2 - Prob. 78PCh. 9.2 - Prob. 79PCh. 9.2 - Prob. 80PCh. 9.2 - Prob. 81PCh. 9.2 - Determine the distance h to which a...Ch. 9.2 - Determine the distance z to the centroid of the...Ch. 9.2 - Prob. 84PCh. 9.2 - Prob. 85PCh. 9.2 - Prob. 86PCh. 9.2 - Determine the distance x to its center of gravity...Ch. 9.2 - Prob. 88PCh. 9.2 - The cylinder and the cone are made from materials...Ch. 9.3 - Determine the surface area and volume of the solid...Ch. 9.3 - Prob. 14FPCh. 9.3 - Determine the surface area and volume of the solid...Ch. 9.3 - Determine the surface area and volume of the solid...Ch. 9.3 - Prob. 90PCh. 9.3 - Determine the volume of the storage tank. Probs....Ch. 9.3 - Prob. 92PCh. 9.3 - Prob. 93PCh. 9.3 - Prob. 94PCh. 9.3 - Prob. 95PCh. 9.3 - Prob. 96PCh. 9.3 - Prob. 97PCh. 9.3 - Prob. 98PCh. 9.3 - Prob. 99PCh. 9.3 - Prob. 100PCh. 9.3 - Determine the surface area and the volume of the...Ch. 9.3 - Prob. 102PCh. 9.3 - Prob. 103PCh. 9.3 - Each gallon of paint can cover 250 ft2. Probs....Ch. 9.3 - Prob. 105PCh. 9.3 - Prob. 106PCh. 9.3 - Prob. 107PCh. 9.3 - Prob. 108PCh. 9.3 - Prob. 109PCh. 9.3 - Prob. 110PCh. 9.3 - Prob. 111PCh. 9.3 - Prob. 112PCh. 9.3 - Prob. 113PCh. 9.3 - Prob. 114PCh. 9.5 - Water has a density of = 1 Mg/m3. Prob. F9-17Ch. 9.5 - The specific weight of water is = 62.4 lb/ft3.Ch. 9.5 - Water has a density of = 1 Mg/m3. Prob. F9-19Ch. 9.5 - Water has a density of = 1 Mg/m3. Prob. F9-20Ch. 9.5 - The specific weight of water is = 62.4 lb/ft3....Ch. 9.5 - Prob. 115PCh. 9.5 - Prob. 116PCh. 9.5 - The load over the plate varies linearly along the...Ch. 9.5 - The load is defined by the expression p = p0 sin...Ch. 9.5 - Prob. 119PCh. 9.5 - Determine the resultant force the water exerts on...Ch. 9.5 - For the condition of high tide shown, determine...Ch. 9.5 - Prob. 122PCh. 9.5 - Prob. 123PCh. 9.5 - Determine the magnitude of the resultant...Ch. 9.5 - Prob. 125PCh. 9.5 - Prob. 126PCh. 9.5 - The tank is filled with a liquid that has a...Ch. 9.5 - Prob. 128PCh. 9.5 - Prob. 129PCh. 9.5 - Prob. 130PCh. 9.5 - Prob. 131RPCh. 9.5 - Determine the volume of material required to make...Ch. 9.5 - Prob. 133RPCh. 9.5 - Prob. 134RPCh. 9.5 - Determine the magnitude of the resultant...Ch. 9.5 - Prob. 136RPCh. 9.5 - Prob. 137RPCh. 9.5 - Locate the centroid of the rod. Prob. R9-4Ch. 9.5 - Determine the horizontal and vertical components...Ch. 9.5 - Prob. 140RP
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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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