9.Influence

# 9.Influence - Influence Lines Theory and Design of...

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P = 1 i j z(j) j ) ( j z P Q i = i P Single concentrated moving load Influence line due to unit load System of concentrated moving loads P = 1 i j = j j j i z P Q i P 3 P 1 P 2 z 1 z 2 z 3 Uniformly distributed moving load P = 1 i j = = A p pzdx Q i i p z A d Influence Lines for Beams Consider a simply supported beam with overhang as shown A B D C 4m 4m 16m Moving unit load R B 1.25 A B D C 4m 4m 16m x P = 1 I.L. for reaction at B, R B Imagine a unit load P starts at C and moves towards B and A so that distance x of the load from C is varying. Taking moment about C for the whole beam, Px L R B = 16 x R B = 20 0 x I.L. for R B R B
R B 1.25 A B D C 4m 4m 16m x P = 1 I.L. for reaction at B, R B When P is at C, When P is at B, When P is at A, 0 , 0 = = B R x 1 , 16 = = B R x 25 . 1 , 20 = = B R x I.L. for R B R B I.L. for reaction at B, R B I.L. for reaction at C, R C Imagine a unit load P moves from A to C so that x is the distance of P to the right of B. Taking moment about B for the whole beam, R C (16) = P x R C = x /16 for -4 x 16 1.0 R C -0.25 A B D C 4m 4m 16m x P = 1 I.L. for R C R C I.L. for reaction at C, R C To draw I.L. for shear at section immediately to the

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• Spring '10
• profchai
• Force, MD D B RB SD MD, I.L.

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