SlopeDefl MomentDi - For a typical span AB Problem 1.1(a...

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For a typical span AB: MAB=2EIL2 A+ B-3 L±MAB θ θ δ Problem 1.1 (a) Objective: Use the slope deflection method in order to analyze the span frame. Draw the shear and moment diagrams. Solution Summary: 1) Unknown/known deflections: , , , = ƟA ƟB ƟC ƟD ? ; , , , = δA δB δC δD 0 2) Fixed End Moments: = - =- . =- MAB wl212 q 75l212 3ql243 = MBA 3ql264 = = = = MBC MCB MCD MDC 0 Slope Deflection Equations:
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= . + - MAB 2EI 75l2θA θB 3ql243 = . + + MBA 2EI 75l2θB θA 3ql243 = + MBC 2EIl2θB θC = + MCB 2EIl2θC θB = . + MCD 2EI 75l2θC θD = . + MDC 2EI 75l2θD θC 3) Theta Determination: = * = . θA 69ql328 20EI 0 013476563 ql3EI = - * =- . θB 32ql329EI 69ql327 20EI 0 009375 ql3EI =- + * = . θC 27ql328EI 69ql325 20EI 0 00234275 ql3EI = - * =- . θD 27ql329EI 69ql326 20EI 0 001171875 ql3EI 4) Final Moments: = MAB 0 = . = . - MBA 0 032812501ql2 157 5 k ft =- . =- . - MBC 0 032812501ql2 157 5 k ft =- . =- - MCB 0 009375ql2 45 k ft = . = - MCD 0 009375ql2 45 k ft = MDC 0
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Problem 1.1 (a) Objective: Use the moment distribution method in order to analyze the span frame. Draw the shear and moment diagrams. Solution Summary: Note that because A and B are free to rotate, we apply the principle that when one end of a beam fixed in position rotates Ɵ , and other end remains fixed in position but not in direction, the moment required at first end is ¾ stiffness of that required if the second end were fixed in
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