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1038 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. Equilibrium: The disturbing force F can be determined by summing moments about point A. a Spring Formula: The restoring spring force F 1 can be determine using spring formula . Critical Buckling Load: For the mechanism to be on the verge of buckling, the disturbing force F must be equal to the restoring spring force F 1 . Ans. P cr = kL 4 2 P cr u = kL u 2 F s = k a L 2 u b = kL u 2 F s = kx F = 2 P u + M A = 0; P ( L u )-F a L 2 b = 131. Determine the critical buckling load for the column. The material can be assumed rigid. P k A L 2 L 2 1039 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. Equilibrium: The disturbing forces F 1 and F 2 can be related to P by writing the moment equation of equlibrium about point A . Using small angle ananlysis, where and , 1 (1) Spring Force. The restoring spring force and can be determined using the spring formula, , where and , Fig. b .Thus, x 2 = 1 3 L u x 1 = 2 3 L u F sp = kx A F sp B 2 A F sp B 1 F 2 + 2 F 1 = 3 P u + M A = 0; F 2 a L 3 b + F 1 a 2 3 L b-PL u = sin u = u cos u > 1 132. Determine the critical load for the rigid bar and spring system. Each spring has a stiffness k . P cr k k P L 3 L 3 L 3 A A F sp B 1 = kx 1 = k a 2 3 L u b = 2 3 kL u A F sp B 2 = kx 2 = k a 1 3 L u b = 1 3 kL u Critical Buckling Load. When the mechanism is on the verge of buckling the disturbing force F must be equal to the restoring force of the spring F sp .Thus, Substituting this result into Eq. (1), Ans. P cr = 5 9 kL 1 3 kL u + 2 a 2 3 kL u b = 3 P cr u F 1 = A F sp B 1 = 2 3 kL u F 2 = A F sp B 2 = 1 3 kL u 13 Solutions 46060 6/11/10 11:56 AM Page 1039 1040 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. a Require: Ans. P cr = 4 k L + M A = 0;-P ( u ) a L 2 b + 2 k u = 133. The leg in (a) acts as a column and can be modeled (b) by the two pin-connected members that are attached to a torsional spring having a stiffness k (torque y rad).Determine the critical buckling load.Assume the bone material is rigid.... View Full Document

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