________________________________________________________________________ PROBLEM (12.63) Use Castigliano's theorem to determine the vertical component of the deflection at point B of the curved bar of Fig. P12.62. SOLUTION A ds = Rdθ M θ = QR(1 − cos θ ) − PR cos θ ∂M θ = R(1 − cos θ ) ∂θ R dθ θ B Q Let C=0: ∂M θ Rdθ : ∂Q EI δV = ∫ M θ EI δV = ∫ π 2 0 P (− PR sin θ R(1 − cos θ ) Rdθ = − PR 3 ∫ π 2 0 sin θ (1 − cos θ )dθ 1 = − PR − cos θ + cos 2 θ 2 π 2 3 0 PR 3 =− 2 from which δV = PR 3 ↑ 2 EI 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.