________________________________________________________________________ PROBLEM (12.50) A truss ABC of three steel members supports a vertical load P at C as shown in Fig. P12.50. The cross-sectional areas of members are AAB , ABC , and AAC . What is the vertical displacement δ v of joint C? Apply Castigliano’s theorem. Given: AAB = 0.002 m, ABC = 0.003 m, AAC = 0.0026 m, P = 25 kN, E = 210 GPa SOLUTION F ∂F F ∂F F ∂F ∂U 1 = ∑ ( AB AB + BC BC + AC AC ) ∂P E AAB ∂P ABC ∂P AAC ∂P Joint C δv = P 5.4 2.25 FAC (1) We have C LAC = 5.42 + 2.252 = 5.85 m 2.25 LBC = 32 + 2.252 = 3.75 m LAB = 2.4 m 3 FBC 5.4 3 FAC + FBC = 0 5.85 3.75 2.25 2.25 ∑ Fy = 0 : − 5.85 FAC + 3.75 FBC = 0 Solving, FAC = 3.25 P FAC = 3.75 P ∑F x = 0: − Joint B FBC 2.25 B 3 FAB ∑F x 3 FBC = 0 3.75 = 3P = 0 : FAB + FAB RB Equation (1) is therefore P 3 3.75 3.25 P [( )(3) + ( )(3.75) + ( )(3.25)] = 13.25(103 ) δv = −3 3 2.6 E (10 ) 2 E The value of displacement at C is 25(103 ) δ v = 13.25(103 ) = 1.577 mm ↓ 210(109 ) 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.