Q1. For the figure shown below, the rigid platform has negligible mass and rests on two steel bars, each 250.00 mm long. The center bar is aluminum and 249.90 mm long. Compute the stress in the aluminum bar after the center load P = 400 kN. has been applied. For each steel bar, the area is 1200 mm2 and E = 200 GPa. For the aluminum bar, the area is 2400 mm² and E = 70 GPa. Steel Aluminum Steel
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- A spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.Solve the preceding problem if the internal pressure is 3,85 MPa, the diameter is 20 m, the yield stress is 590 MPa, and the factor of safety is 3.0. (a) Determine the required thickness to the nearest millimeter. (b) If the tank wall thickness is 85 mm, what is the maximum permissible internal pressure?A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut? (b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.
- A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)A pressurized circular cylinder has a sealed cover plate fastened with steel bolts (see figure). The pressure P of the gas in the cylinder is290psi, the inside diameter D of the cylinder is 10.0 in., and the diameter dBof the bolts is 0.50 in. I f the allowable tensile stress in the bolts is 10,000 psi, find the number n of bolts needed to fasten the cover.An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.
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- Truss members supporting a roof are connected to a 26-mm-thick gusset plate by a 22-mm diameter pin, as shown in the figure and photo. The two end plates on the truss members are each 14 mm thick. (a) If the load P = 80 kN, what is the largest bearing stress acting on the pin? (b) If the ultimate shear stress for the pin is 190 MPa, what force Pult is required to cause the pin to fail in shear? Disregard friction between the plates.Two bars AC and BC of the same material support a vertical load P (see figure). The length L of the horizontal bar is fixed, but the angle fl can be varied by moving support A vertically and changing the length of bar AC to correspond with the new position of support A. The allowable stresses in the bars are the same in tension and compression. When the angle ft is reduced, bar AC becomes shorter, but the cross-sectional areas of both bars increase because the axial forces are larger. The opposite effects occur if the angle 0 is increased. Thus, the weight of the structure (which is proportional to the volume) depends upon the angle ft. Determine the angle ft so that the structure has minimum weight without exceeding the allowable stresses in the bars. Note: The weights of the bars are very small compared to the force P and may be disregarded.A long re Lai nine: wall is braced by wood shores set at an angle of 30° and supported by concrete thrust blocks, as shown in the first part of the figure. The shores are evenly spaced at 3 m apart. For analysis purposes, the wall and shores are idealized as shown in the second part of the figure. Note that the base of the wall and both ends of the shores are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force acting on a 3-meter length of the walls is F = 190 kN. If each shore has a 150 mm X 150 mm square cross section, what is the compressive stress