________________________________________________________________________ PROBLEM (10.154) A propped cantilever beam AB is subjected to loads as shown in Fig. P10.154. Calculate the reactions at each support. SOLUTION 5 kN/m 10 kN MB A B C RA M/EI A1 A2 M/EI A3 Parabolic Spandrel Select RA as redundant. Draw M EI diagrams (see Table A.4). 10 RA 50 RA 1 10 RA A1 = ( )(10) = 2 EI EI 1 80 320 A2 = − ( )(8) = − x 2 EI EI 1 90 180 A3 = − ( )(6) = − -80 3 EI EI Place reference tangent at B: x θ B = 0. Also 2 2 t A B = A1[ (10)] + A2 [ (8) + 2] -90 3 3 1 + A3 [10 − (6)] = 0 4 RB Then tA B = 50 RA 20 320 28 180 ( )− ( )− (8.5) = 0 EI 3 EI 3 EI or RA = 13.55 kN ↑ Equilibrium: RB = 10 + 30 − 13.55 = 26.45 kN ↑ M B = 34.5 kN ⋅ m 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.