hw02 statics - STATICS AND MECHANICS OF MATERIALS, 2nd...

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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 59 Chapter 4 4-1 An aluminum tube with an outside diameter of 1.000 in. will be used to support a 10-kip load. If the axial stress in the member must be limited to 30 ksi T or C, determine the wall thickness required for the tube. SOLUTION 10,000 30,000 psi P AA V ± ² 22 2 10,000 1 i n . 4 30,000 i Ad S ³ 0.75867 in. 1 2 i dt ³ 0.1207 in. t .......................................................................................................................... Ans. 4-2 Three steel bars with 25 u 15-mm cross sections are welded to a gusset plate as shown in Fig. P4-2. Determine the normal stresses in the bars when the forces shown are being applied to the plate. SOLUTION 62 40,000 106.7 10 N/m 106.7 MPa 0.025 0.015 A P A V u u ........................................ Ans. 50,000 133.3 10 N/m 133.3 MPa 0.025 0.015 B P A V u u ......................................... Ans. 20,000 53.3 10 N/m 53.3 MPa 0.025 0.015 C P A V u u ............................................. Ans. 4-3 Two ¼-in. diameter steel cables A and B are used to support a 220-lb traffic light as shown in Fig. P4-3. Determine the normal stress in each of the cables. SOLUTION From a free-body diagram of the ring, the equations of equilibrium 0: x F o6 cos25 cos20 0 BA TT q y F n6 sin 20 sin 25 220 0 AB are solved to get 1.03684 281.977 lb A T 292.365 lb B T ± ² 2 281.977 5740 psi 0.25 4 A A A T A V S ...................................................................................... Ans. ± ² 2 292.365 5960 psi 0.25 4 B B B T A V S ...................................................................................... Ans. 4-4 A system of steel pipes is loaded and supported as shown in Fig. P4-4. If the normal stress in each pipe must not exceed 150 MPa, determine the cross-sectional areas required for each of the sections. SOLUTION From free-body diagrams of the pipes, the equations of equilibrium give y F 650 0 A P ³ 650 kN A P y F 650 850 0 B P ³³ 1500 kN B P
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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 60 0: y F n6 650 850 1500 0 C P ±±± 3000 kN C P 3 62 2 6 650 10 4333 10 m 4330 mm 150 10 A A A P A V ± u u # u ....................................................... Ans. 3 2 6 1500 10 10,000 10 m 10,000 mm 150 10 B B B P A V ± u u # u .............................................. Ans. 3 2 6 3000 10 20,000 10 m 20,000 mm 150 10 C C C P A V ± u u # u ............................................ Ans. 4-5 Two 1-in. diameter steel bars are welded to a gusset plate as shown in Fig. P4-5. Determine the normal stresses in the bars when forces F 1 = 550 lb and F 2 = 750 lb are applied to the plate. SOLUTION ² ³ 1 2 550 700 psi 14 A A F A V S ............................................................................................... Ans. ² ³ 2 2 750 955 psi B B F A V S ............................................................................................... Ans. 4-6 Two strips of a plastic material are bonded together as shown in Fig. P4-6. The average shearing stress in the glue must be limited to 950 kPa. What length L of splice plate is needed if the axial load carried by the joint is 50 kN? SOLUTION From a free-body diagram of the middle plate, the equations of equilibrium x F o6 3 25 0 1 00 V ±u gives ² ³² ³ ² ³ 3 3 25 10 N 950 10 0.3 2 VA L W u u 0.1754 m 175.4 mm L ..................................................................................................... Ans. 4-7 A coupling is used to connect a 2-in. diameter plastic rod to a 1.5-in. diameter rod, as shown in Fig. P4-7. If the average shearing stress in the adhesive must be limited to 500 psi, determine the minimum lengths L 1 and L 2 required for the joint if the applied axial load P is 8000 lb. SOLUTION From a free-body diagram of the rod, the equation of equilibrium x F 8000 0 V ± gives ² ³² ³² ³ 1 2 8000 lb 500 2 500 1.5 L L W S S 1 2.55 in. L ................................................................ Ans.
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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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hw02 statics - STATICS AND MECHANICS OF MATERIALS, 2nd...

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