Engineering Mechanics

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1. For the truss shown in the figure, calculate the normal stresses in (a) member AC; and (b) member BD. The cross-sectional area of each member is.[pic 2]

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1. For the truss shown, calculate the stresses in members CE, DE, and DF. The cross-sectional area of each member is. Indicate if tension or compression.[pic 4]

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1. The block of weight  in the figure hangs from the pin at. The bars  and  are pinned to the support at  and. The areas are  for  and  for. Neglecting the weight of the bars, determine the maximum safe value of if the stress in is limited to and that in  to.[pic 6][pic 7][pic 8][pic 9][pic 10][pic 11][pic 12][pic 13][pic 14][pic 15][pic 16][pic 17][pic 18][pic 19][pic 20]

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1. A homogeneous  bar AB is supported at either end by a cable as shown in the figure below. Calculate the smallest area of each cable if the stress is not to exceed 90 MPa in bronze and 120 MPa in steel. [pic 22]

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1. A rod made of timber is rigidly attached between a steel rod and a concrete rod as shown in the figure. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed the maximum allowable stress in each material.

1. The homogeneous bar  shown is supported by a cable that runs from  to  around the smooth peg at , a vertical cable at , and a smooth inclined surface at . Determine the mass of the heaviest bar that can be supported if the stress in each cable is limited to. The area of the cable is  and that of the cable at is .[pic 35][pic 24][pic 25][pic 26][pic 27][pic 28][pic 29][pic 30][pic 31][pic 32][pic 33][pic 34]

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1. The average shear stress in each of the 6-mm diameter bolts and along each of the four shaded shear planes is not allowed to exceed  and , respectively. Determine the maximum axial force  that can be applied to the joint.[pic 37][pic 38][pic 39]

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1. The block is subjected to a compressive force of. Determine the average normal and average shear stress developed in the wood fibers that are oriented along section  at  with the axis of the block.[pic 41][pic 42][pic 43]

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1. The inclined figure is subjected to a compressive force of 20 kN. Determine the bearing stress along the smooth areas of contact defined by AB and BD, the shear stress defined by BC, and the shear and normal stress at section a-a.

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1. A -.-diameter bolt, having a diameter at the root of the threads of., is used to fasten two timbers together as shown in the figure. The nut is tightened to cause a tensile stress of in the bolt. Compute the shearing stress in the head of the bolt and in the threads. Also, determine the outside diameter of the washers if their inside diameter is  and the bearing stress is limited to.[pic 46][pic 47][pic 48][pic 49][pic 50][pic 51]

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1. The lap joint shown in the figure is fastened by four --diameter rivets. Calculate the maximum safe load  that can be applied if the shearing stress in the rivets is limited to, the bearing stress in the plates is limited to, and the tensile stress in the plates is limited to. Assume the applied load is uniformly distributed among the four rivets.[pic 53][pic 54][pic 55][pic 56][pic 57][pic 58]

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1. Link AB is used to support the end of a horizontal beam. If link AB is subject to a 10 kips compressive force, determine the normal and bearing stress in the link and the shear stress in each of the pins. Assume [pic 60]

1. The assembly consists of three disksandthat are used to support the load of. Determine the smallest diameter of the top disk, the diameter within the support space, and the diameterof the hole in the bottom disk. The allowable bearing stress for the material is  and allowable shear stress is.[pic 69][pic 61][pic 62][pic 63][pic 64][pic 65][pic 66][pic 67][pic 68]

1. A kryptonite nanoparticle-reinforced adamantium composite tube (nPRAC) and kryptonite nanowhisker-reinforced adamantium composite tube (nWRAC) are joined at A by four 13 mm-diameter titanium pins. The outer diameters and wall thicknesses of nPRAC and nWRAC are 70 mm and 5mm, and 60 mm and 8 mm, respectively. The ultimate values of the following stresses are as follows: tensile stress in the tubes is 175 MPa, shear stress for the pins is 530 MPa and bearing stress between the pins and the tubes is 280 MPa. The factor of safety is 4. What is the controlling value of P in kN?

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1. Referring to the figure, compute the maximum force P that can be applied by the machine operator if the shearing stress in the pin at B and the axial stress in the control rod at C are limited to 4000 psi and 5000 psi, respectively. The diameters are 0.25 inch for the pin, and 0.5 inch for the control rod. Assume single shear for the pin at B.[pic 71]

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1. The lamp post is supported by two  bars pinned at A and B, and a pin at C. Determine the maximum weight of the angry bird that can be supported if the tensile stress for each bar is limited to and the allowable shear for the pins is . The diameter of pins A and B is while pin C is. Assume the weight of the bird is concentrated  to the left of point A. Assume pin C is subjected to double shear.[pic 73][pic 74][pic 75][pic 76][pic 77][pic 78]

1. A cylindrical pressure vessel has an inner diameter of  and a thickness of . Determine the maximum internal pressure it can sustain so that neither its circumferential nor its longitudinal stress component exceeds. Under the same conditions, what is the maximum internal pressure that a similar-size spherical vessel can sustain?[pic 79][pic 80][pic 81]

1. The gas storage tank is fabricated by bolting together two half cylindrical thin shells and two hemispherical shells as shown. If the tank is designed to withstand a pressure of 3 MPa, determine the required minimum thickness of the cylindrical and hemispherical shells and the minimum required number of longitudinal bolts per meter length at each side of the cylindrical shell. The tank and the 25 mm diameter bolts are made from material having an allowable normal stress of 150 MPa and 250 MPa, respectively. The tank has an inner diameter of 4 m.

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1. A wood pipe having an inner diameter of  is bound together using steel hoops each having a cross-sectional area of. If the allowable stress for the hoops is  determine their maximum spacing s along the section of pipe so that the pipe can resist an internal gauge pressure of. Assume each hoop supports the pressure loading acting along the length s of the pipe.[pic 84][pic 85][pic 86][pic 87]

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1. A boiler is constructed of - thick steel plates that are fastened together at their ends using a butt joint consisting of two - cover plates and rivets having a diameter of  and spaced  apart as shown. If the steam pressure in the boiler is , determine (a) the circumferential stress in the boiler’s plate apart from the seam,(b) the circumferential stress in the outer cover plate along the rivet line a–a, and (c) the shear stress in the rivets. [pic 89][pic 90][pic 91][pic 92][pic 93][pic 94][pic 95]

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1. The spherical gas tank is fabricated by bolting together two hemispherical thin shells. If the - inner diameter tank is to be designed to withstand a gauge pressure of, determine the minimum wall thickness of the tank and the minimum number of - diameter bolts that must be used to seal it. The tank and the bolts are made from material having an allowable normal stress of  and, respectively.[pic 97][pic 98][pic 99][pic 100][pic 101][pic 102][pic 103]

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1. The strength of longitudinal joint in the figure is 33 kips/ft, whereas for the girth is 16 kips/ft. Calculate the maximum diameter of the cylinder tank if the internal pressure is 150 psi.