1170026001 - 1 Tension, Compression, and Shear Normal...

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Normal Stress and Strain Problem 1.2-1 A solid circular post ABC (see figure) supports a load P 1 5 2500 lb acting at the top. A second load P 2 is uniformly distributed around the shelf at B . The diameters of the upper and lower parts of the post are d AB 5 1.25 in. and d BC 5 2.25 in., respectively. (a) Calculate the normal stress s AB in the upper part of the post. (b) If it is desired that the lower part of the post have the same compressive stress as the upper part, what should be the magnitude of the load P 2 ? Solution 1.2-1 Circular post in compression 1 Tension, Compression, and Shear 1 A B C P 1 d AB d BC P 2 P 1 5 2500 lb d AB 5 1.25 in. d BC 5 2.25 in. (a) N ORMAL STRESS IN PART AB (b) L OAD P 2 FOR EQUAL STRESSES 5 s AB 5 2040 psi Solve for P 2 : P 2 5 5600 lb s BC 5 P 1 1 P 2 A BC 5 2500 lb 1 P 2 p 4 (2.25 in.) 2 s AB 5 P 1 A AB 5 2500 lb p 4 (1.25 in.) 2 5 2040 psi A LTERNATE S OLUTION FOR P ART (b) P 2 5 2.24 P 1 5 5600 lb d BC d AB 5 1.8 P 1 1 P 2 d BC 2 5 P 1 d AB 2 or P 2 5 P 1 d BC d AB 2 2 1 R s AB 5 P 1 A AB 5 P 1 p 4 d AB 2 Ê s BC 5 s AB s BC 5 P 1 1 P 2 A BC 5 P 1 1 P 2 p d BC 2 A B C P 1 P 2
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Piston rod 5 mm 50 mm 225 mm P = 40 N Problem 1.2-2 Calculate the compressive stress s c in the circular piston rod (see figure) when a force P 5 40 N is applied to the brake pedal. Assume that the line of action of the force P is parallel to the piston rod, which has diameter 5 mm. Also, the other dimensions shown in the figure (50 mm and 225 mm) are measured perpen- dicular to the line of action of the force P . Solution 1.2-2 Free-body diagram of brake pedal Problem 1.2-3 A steel rod 110 ft long hangs inside a tall tower and holds a 200-pound weight at its lower end (see figure). If the diameter of the circular rod is 1 / 4 inch, calcu- late the maximum normal stress s max in the rod, taking into account the weight of the rod itself. (Obtain the weight density of steel from Table H-1, Appendix H.) 2 CHAPTER 1 Tension, Compression, and Shear F 5 compressive force in piston rod d 5 diameter of piston rod 5 5mm E QUILIBRIUM OF BRAKE PEDAL F (50 mm) 2 P (275 mm) 5 0 C OMPRESSIVE STRESS IN PISTON ROD ( d 5 5 mm) s c 5 F A 5 220 N p 4 (5 mm) 2 5 11.2 MPa F 5 P ¢ 275 mm 50 mm 5 (40 N) ¢ 275 50 5 220 N © M A 5 0 ` ~ 50 mm 225 mm P = 40 N F A in. 200 lb 110 ft 1 4
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Solution 1.2-3 Long steel rod in tension Problem 1.2-4 A circular aluminum tube of length L 5 400 mm is loaded in compression by forces P (see figure). The out- side and inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measure normal strains in the longitudinal direction. (a) If the measured strain is e 5 550 3 10 2 6 , what is the shortening d of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P ? Solution 1.2-4 Aluminum tube in compression SECTION 1.2 Normal Stress and Strain 3 5 374.3 psi s max 5 374 psi 1 4074 psi 5 4448 psi Rounding, we get s max 5 4450 psi P A 5 200 lb p 4 (0.25 in.) 2 5 4074 psi g L 5 (490 lb / ft 3 )(110 ft) ¢ 1 144 ft 2 in. 2 s max 5 W 1 P A 5 g L 1 P A d L P = 200 lb P 5 200 lb L 5 110 ft d 5 1 / 4 in.
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1170026001 - 1 Tension, Compression, and Shear Normal...

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