Mechanics of materials | axial load | Energy Methods | Engr. Adnan Rasheed Mechanical

1-84. The frame is subjected to the load of 4 kN which acts on member ABD at D . Determine the required diameter of the pins at D and C if the allowable shear stress for the material is tallow = 40 MPa. Pin C is subjected to double shear, whereas pin D is subjected to single shear.
1-86. The two aluminum rods support the vertical force of P = 20 kN. Determine their required diameters if the allowable tensile stress for the aluminum is sallow = 150 MPa.
1-89. Determine the required minimum thickness t of member AB and edge distance b of the frame if P = 9 kip and the factor of safety against failure is 2. The wood has a normal failure stress of sfail = 6 ksi, and shear failure stress of tfail = 1.5 ksi.
3-21. The two bars are made of polystyrene, which has the stress-strain diagram shown. If the cross-sectional area of bar AB is 1.5 in 2 and BC is 4 in 2 , determine the largest force P that can be supported before any member ruptures. Assume that buckling does not occur.
*4-88. If the allowable normal stress for the bar is s allow = 120 MPa, determine the maximum axial force P that can be applied to the bar.
4-94. The resulting stress distribution along section AB for the bar is shown. From this distribution, determine the approximate resultant axial force P applied to the bar. Also, what is the stress-concentration factor for this geometry?
4-95. The 10-mm-diameter shank of the steel bolt has a bronze sleeve bonded to it. The outer diameter of this sleeve is 20 mm. If the yield stress for the steel is ( sY ) st = 640 MPa, and for the bronze ( sY ) br = 520 MPa, determine the largest possible value of P that can be applied to the bolt. Assume the materials to be elastic perfectly plastic. Est = 200 GPa, Ebr = 100 GPa.
*4-100. The rigid beam is supported by a pin at A and two steel wires, each having a diameter of 4 mm. If the yield stress for the wires is sY = 530 MPa, and Est = 200 GPa, determine (a) the intensity of the distributed load w that can be placed on the beam that will cause only one of the wires to start to yield and (b) the smallest intensity of the distributed load that will cause both wires to yield. For the calculation, assume that the steel is elastic perfectly plastic.
14-11. Determine the bending strain energy in the A-36 structural steel W10 * 12 beam. Obtain the answer using the coordinates (a) x1 and x4 , and (b) x2 and x3 .
14-22. Determine the bending strain energy in the beam and the axial strain energy in each of the two posts. All members are made of aluminum and have a square cross section 50 mm by 50 mm. Assume the posts only support an axial load. Eal = 70 GPa.
*14-32. Determine the slope at point A of the beam. EI is constant.
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