Class 31 - Statically Indeterminate Beams

Structural Analysis (6th Edition)

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Unformatted text preview: . : Q .5.“ ' ”gfigmggfié €$fi Fxfigbfigfi 5 ’W gfif’éfiéfig mm m 252% . $23M”? 0 3x; \ 5 WE “Mg? £2 3% «x saga} a: / ‘3 55m; 3&3: Efiwfizffiw \“fl bgfiéC-F $35§§fi¥flfig :2 iéwgfif gig; Mgflmb WW 5?} fig“; 17:, mg , .- E Method of Superposition The problems for Section 10.4 are 20 be solved by the method of superposition. All beams have constant flexural rigidity El unless otherwise stated. When drawing shear-force and bending—moment diagrams, be sure to label all critical ordinates, including maximum and minimum values. Problem 10.4.1 A propped cantilever beam AB of length L carries a concentrated load P acting at the position shown in the figure. Determine the reactions R A, R B, and M A for this beam. Also, draw the shear-force and bending-moment diagrams, labeling all critical ordinates. 642 CHAPTER 10 Smtically Indeterminate Beams Method of Superposition The problems for Section 10.4 are to be solved by the method of superposition. All beams have constantflexural rigidity E1 unless otherwise stated. When drawing shear-force and bending-moment diagrams, be sure to label all critical ordinates, including maximum and minimum values. Problem 10.44 A propped cantilever beam AB of length L carries A a a concentrated load P acting at the position shown in the figure. Determine the reactions R A, R B, and M A for this beam. Also, draw the shear-force and bending-moment diagrams, labeling all critical ordinates. Solution 10.44 Propped cantilever beam Select R 3 as redundant. COMPATIBILITY 53 z (63): " (53)2 = 0 EQUILIBRIUM 5 Pa; (3L ) B 3 0 z —— «- Q ~—- = RA=P~RB MA=Pa—RBL 1’ 6E1 351 Pa2 R 2 —— 3L — +- RELEASED STRUCTURE AND FORCE~DISPLACEMENT 5 2L3 ( a) RELATIONS P OTHER REACTIONS (FROM EQUILIBRIUM) Pb P b :A a i b B i Paz RA=~—3(3L2-—b2) MA=—12—(L+b) 4—— \ ”(3191 =33 (3L ~ a) 2L 2" T J. SHEAR~F0RCE AND BENDmG-MOMENT DIAGRAMS RBL3 (fish 3‘33} L 3T T RB M1: Rgb ...
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