An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in figure. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminum of 90 MPa, or in bronze of 100 MPa.
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- A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?A single steel strut AB with a diameter (a) Find the strut force Fs and average normal stress ds= 8 mm supports the vehicle engine hood of a in the strut. mass 20 kg that pivots about hinges at C and D (see (b) Find the average shear stress t aver in the bolt at A,figure parts a and b). The strut is bent into a loop at (C) Find the average bearing stress bon the bolt at A. its end and then attached to a bolt at A with a diameter db= 10 mm. Strut AB lies in a vertical plane.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.
- A slightly tapered bar AB of solid circular crass section and length L is supported at end B and subjected to a tensile load P at the free end A. The diameters of the bar at ends A and B are dAand dB. respectively. Determine the length of the bar if the elongation of the bar due to the load P = 45 kips is 0.02 in. Assume that E = 10,400 ksi.A bar of monel metal with a length L = 9 in. and a diameter d = 0225 in. is loaded axially by a tensile force P (see figure). If the bar elongates by 0.0)95 in., what is the decrease in diameterA plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.
- Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.A horizontal rigid bar of weight If' = 72001b is supported by three slender circular rods that are equally spaced (see Figure)'. The two outer rods are made of aluminum (£-, = 10 X 10 psi) with diameter f/j = 0.4 in. and length Ly= 40 in. The inner rod is magnesium {F-, = 6.5 X 10* psi) with diameter rf, and length L-,. The allowable stresses in the aluminum and magnesium are 24,000 psi and 13,000 psi, respectively. IF it is desired to have all three rods loaded to their maximum allowable values, what should be the diameter d2and length LzoF the middle rod?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.
- Solve the preceding problem for a plate of dimensions 100 mm × 250 mm subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction (see figure).A circle of a diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions of 400 x 400 x 20 mm. Forces are applied to the plate, producing uniformly distributed normal stressescr^ =59 MPaander^ = —17 MPa. Calculate the following quantities: (a) the change in length Aac of diameter at: (b) the change in length Abd of diameter bd; (c) the change At in the thickness of the plate; (d) the change AV in the volume of the plate; (e) the strain energy U stored in the plate; (f) the maximum permissible thickness of the plate when strain energy £/must be at least 784 J; and (g) the maximum permissible value of normal stress axwhen the change in volume of the plate cannot exceed 0.015% of the original volume. (Assume E = 100 GPa and v = 0.34A flat bar of width b and thickness t has a hole of diameter d drilled through it (see figure). The hole may have any diameter that will fit within the bar. What is the maximum permissible tensile load Pmaxif the allowable tensile stress in the material is st?