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ch01-03 stress & strain & properties

01 Solutions 46060

01 Solutions 46060 5/6/10 2:43 PM Page 59 © 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. *1–88. The frame is subjected to the load of 4 kN which acts on member ABD at D. Determine the required diameter of the pins at D and C if the allowable shear stress for the material is t allow = 40 MPa. Pin C is subjected to double shear, whereas pin D is subjected to single shear. E 1 m C 1.5 m D 4 kN 45 Referring to the FBD of member DCE,Fig.a, 1.5 m a +©M E = 0; D y (2.5) - F BC sin 45° (1) = 0 (1) : + ©F x = 0 F BC cos 45° - D x = 0 (2) B Referring to the FBD of member ABD,Fig.b, 1.5 m a +©M A = 0; 4 cos 45° (3) + F BC sin 45° (1.5) - D x (3) = 0 (3) A Solving Eqs (2) and (3), F BC = 8.00 kN D x = 5.657 kN F BC Substitute the result of into (1) D y = 2.263 kN Thus, the force acting on pin D is F D = 2 D x 2 + D y 2 = 2 5.657 2 + 2.263 2 = 6.093 kN Pin C is subjected to double shear white pin D is subjected to single shear. Referring to the FBDs of pins C, and D in Fig c and d, respectively, V C = F BC 2 = 8.00 2 = 4.00 kN V D = F D = 6.093 kN For pin C, t allow = V C ; 40(10 6 ) = 4.00(103 ) p A C 4 d C 2 d C = 0.01128 m = 11.28 mm Use d C = 12 mm Ans. For pin D, t allow = V D ; 40(10 6 ) = 6.093(103 ) p A D d D = 0.01393 m = 13.93 mm 4 d D 2 Use d D = 14 mm Ans. 59

01 Solutions 46060 5/6/10 2:43 PM Page 60 © 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. •1–89. The eye bolt is used to support the load of 5 kip. 1 in. 1 Determine its diameter d to the nearest and the required 1 thickness h to the nearest 8 in. 8 in. of the support so that the washer will not penetrate or shear through it. The allowable normal stress for the bolt is s allow = 21 ksi and the allowable shear stress for the supporting material is t allow = 5 ksi. d h 5 kip Allowable Normal Stress: Design of bolt size s allow = P ; 21.0(10 3 ) = 5(103 ) p A b 4 d2 d = 0.5506 in. Use d = 5 8 in. Ans. Allowable Shear Stress: Design of support thickness t allow = V A ; 5(103 ) = 5(103 ) p(1)(h) Use h = 3 8 in. Ans. 60

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