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# ch01-03 stress &amp; strain &amp; properties

## 01 Solutions 46060

01 Solutions 46060 5/6/10 2:43 PM Page 67 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *1–100. The hanger is supported using the rectangular pin. Determine the required thickness t of the hanger, and dimensions a and b if the suspended load is P = 60 kN. The allowable tensile stress is (s t ) allow = 150 MPa, the allowable bearing stress is (s b ) allow = 290 MPa, and the allowable shear stress is t allow = 125 MPa. 75 mm a a 20 mm b 10 mm t P 37.5 mm 37.5 mm Allowable Normal Stress: For the hanger (s t ) allow = P A ; 150A106 B = 60(103 ) (0.075)t t = 0.005333 m = 5.33 mm Ans. Allowable Shear Stress: For the pin t allow = V A ; 125A106 B = 30(103 ) (0.01)b b = 0.0240 m = 24.0 mm Ans. Allowable Bearing Stress: For the bearing area (s b ) allow = P A ; 290A106 B = 30(103 ) (0.0240) a a = 0.00431 m = 4.31 mm Ans. 67

01 Solutions 46060 5/6/10 2:43 PM Page 68 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. •1–101. The 200-mm-diameter aluminum cylinder supports a compressive load of 300 kN. Determine the average normal and shear stress acting on section a–a. Show the results on a differential element located on the section. Referring to the FBD of the upper segment of the cylinder sectional through a–a shown in Fig. a, +Q©F x¿ = 0; N a - a - 300 cos 30° = 0 N a - a = 259.81 kN +a©F y¿ = 0; V a - a - 300 sin 30° = 0 V a - a = 150 kN Section a–a of the cylinder is an ellipse with a = 0.1 m 0.1 and b = . Thus, cos 30° m 0.1 A a - a = p ab = p(0.1)a . cos 30° b = 0.03628 m2 As a - a B avg = N a - a = 259.81(103 ) = 7.162(10 6 ) Pa = 7.16 MPa A a - a 0.03628 At a - a B avg = V a - a A a - a = 150(103 ) 0.03628 = 4.135(106 ) Pa = 4.13 MPa Ans. Ans. The differential element representing the state of stress of a point on section a–a is shown in Fig. b a 300 kN d a 30 1–102. The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8 kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of the plate defined by the section lines a–a, and the average shear stress in the bolt head along the cylindrical area defined by the section lines b–b. s s = P A = 8 (103 ) p 4 (0.007)2 = 208 MPa (t avg ) a = V A = 8 (10 3 ) = 4.72 MPa p (0.018)(0.030) (t avg ) b = V A = 8 (10 3 ) = 45.5 MPa p (0.007)(0.008) Ans. Ans. Ans. 8 mm a 7 mm b 18 mm b a 30 mm 8 kN 68

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