________________________________________________________________________ PROBLEM (11.48) A pin-ended rod AB of diameter d carries an eccentrically applied load of P as shown in Fig. P11.48. If the maximum deflection at the midlength is v max , calculate: (a) The eccentricity e. (b) The maximum stress in the rod. Given: d = 40 mm, P = 60 kN, v max = 0.6 mm, E = 200 GPa SOLUTION P A = π (20) 2 = 1256.64 mm 2 A I= 40 mm vmax π 4 Pcr = 0.7 m B e Figure (a) (20) 4 = 125.66 ×103 mm 4 π 2 EI L2 π 2 (200 × 109 )(125.66 ×10−9 ) = (0.7) 2 = 506.2 kN P (a) Using Eq. (11.18): ⎡ ⎛π 60 ⎞ ⎤ o 0.6 ×10−3 = e ⎢sec ⎜⎜ ⎟⎟ − 1⎥ = e ⎡⎣sec(31 ) − 1⎤⎦ , ⎣⎢ ⎝ 2 506.2 ⎠ ⎦⎥ e = 3.6 mm (b) Referring to Fig. (a): M = P (vmax + e) = 60(0.6 + 3.6) = 252 N ⋅ m P Mc Hence, σ max = + A I 60 ×103 252(20)10−3 = 87.9 MPa = + 1256.64 ×10−6 125.66 ×10−9 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.