# Hw03 statics - STATICS AND MECHANICS OF MATERIALS 2nd Edition RILEY STURGES AND MORRIS 4-57 Determine the movement of the pointer of Fig P4-57 with

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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 83 4-57 Determine the movement of the pointer of Fig. P4-57 with respect to the scale zero when the temperature increases 80 q F. The coefficients of thermal expansion are 6.6(10 ± 6 )/ q F for the steel and 12.5(10 ± 6 )/ q F for the aluminum. SOLUTION The steel post and the steel scale each stretch the same amount ² ³² ³² ³ 6 6.6 10 80 20 0.01056 in. so GG ± u The aluminum post stretches 6 12.5 10 80 20 0.02000 in. a G ± u Therefore, the motion of the pointer relative to the zero on the steel scale is 51 p as ± 0.0472 in. p n ..................................................................................................................... Ans. 4-58 A bronze [ D B = 16.9(10 ± 6 )/ q C] sleeve with an inside diameter of 99.8 mm is to be placed over a solid steel [ D S = 11.9(10 ± 6 )/ q C] cylinder, which has an outside diameter of 100 mm. If the temperatures of the cylinder and sleeve remain equal, how much must the temperature be increased in order for the bronze sleeve to slip over the steel cylinder? SOLUTION 6 6 100 11.9 10 100 99.8 16.9 10 99.8 dT T ± ± ´ u ' ´ u ' 403 C T ' q ................................................................................................................................ Ans. 4-59 A steel [ E = 30,000 ksi and D = 6.5(10 ± 6 )/ q F] surveyor’s tape ½-in. wide u 1/32-in. thick is exactly 100 ft long at 72 q F and under a pull of 10 lb. What correction should be introduced if the tape is used to make a 100-ft measurement at a temperature of 100 q F and under a pull of 25 lb. SOLUTION 1 LLL T EL L L VG HD cc ± ´ ' ± where L is the length at 72 q F and zero force. When 10 lb P , ² ³ ² ³ 10 640 psi 12 132 V , 100 ft L c , and 6 100 640 10 30 10 L ± ´ u 99.99787 ft L Then, when 25 lb P , ² ³ ² ³ 25 1600 psi , and 28 F T ' q ² ³² ³ 6 6 1600 1 6.5 10 28 30 10 L L ± c ´ u u 100.02140 ft L 0.02140 ft 0.257 in. L correction 0.257 in. ± ............................................................................................................ Ans.

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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 84 4-60 A 25-mm diameter aluminum [ D = 22.5(10 ± 6 )/ q C, E = 73 GPa, and Q = 0.33] rod hangs vertically while suspended from one end. A 2500-kg mass is attached at the other end. After the load is applied, the temperature decreases 50 q C. Determine (a) The axial stress in the rod. (b) The axial strain in the rod. (c) The change in diameter of the rod. SOLUTION (a) ² ³² ³ ² ³ 62 2 2500 9.81 49.962 10 N/m 50.0 MPa 0.025 4 V S u # ...................................................... Ans. (b) ² ³² ³ 6 66 9 49.962 10 22.5 10 50 441 10 m/m 73 10 a T E HD ±± u ´ ' ´ u ± ± u u ...................... Ans. (c) ² ³ ² ³² ³ 6 9 49.962 10 0.33 22.5 10 50 1350.86 10 m/m 73 10 t T E HQD §· u ± ´ ' ± ´ u ± ± u ¨¸ u ©¹ ² ³² ³ 6 1350.86 10 25 0.0338 mm dt d GH ± ± u ± ........................................................... Ans. 4-61 The rigid yokes B and C of Fig. P4-61 are securely fastened to the 2-in. square steel ( E 30,000 ksi) bar AD . Determine (a) The maximum normal stress in the bar. (b) The change in length of segment AB . (c) The change in length of segment BC . (d) The change in length of the complete bar. SOLUTION (a) 3 max max 82 10 20,500 psi 20.5 ksi 22 P A u u ................................................................. Ans. (b) ² ³² ³ ² ³² ³ 3 6 82 10 8 12 0.0656 in. 30 10 2 2 AB PL EA G uu ........... Ans. (c) ² ³² ³ ² ³² ³ 3 6 12 10 5 12 0.00600 in. 30 10 2 2 BC ±u u ± .............. Ans. ² ³² ³ ² ³² ³ 3 6 45 10 4 12 0.01800 in.
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## This note was uploaded on 02/11/2009 for the course CIVIL ENGI 560 taught by Professor Brody during the Fall '08 term at University of Maryland Baltimore.

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Hw03 statics - STATICS AND MECHANICS OF MATERIALS 2nd Edition RILEY STURGES AND MORRIS 4-57 Determine the movement of the pointer of Fig P4-57 with

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