________________________________________________________________________ PROBLEM (10.38) A structural steel shaft of specific weight γ , diameter d, and elastic modulus E, is supported by roller bearings at its ends A and B (Fig. P10.38). Determine the maximum permissible length L for this shaft. Requirement: The deflection of the shaft due to its own weight per unit length w at the midspan is limited to vmax . Assumption: Bearings act as simple supports. Given: vmax =5 mm, d=75 mm, g=9.81 kg/s2, 4 vmax =5wL /384EI γ = 7860 kg/m3 E=200 GPa (from Table B.4) (from Table B.14) SOLUTION vmax 5wL4 = 384 EI (by Table B.14) or L=( 384 EIvmax 1 4 ) 5w Where I= πd4 64 = π (75)4 64 = 1.55(106 ) mm 4 w = (γ g ) A = (7,860 × 9.81)( = 340.65 N m π × 0.0752 4 ) Thus 384(200 × 109 )(1.55 × 10−6 )(0.005) 1 4 L =[ ] = 4.32 m 5(340.65) Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.