influenca lines for statically indeterminante beams

influenca lines for statically indeterminante beams -...

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1 ! Comparison Between Indeterminate and Determinate ! Influence line for Statically Indeterminate Beams ! Qualitative Influence Lines for Frames INFLUENCE LINES FOR STATICALLY INDETERMINATE BEAMS
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2 A B C E D R A A B C E D R A Indeterminate Determinate Comparison between Indeterminate and Determinate 1 1
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3 A B C E D R A A B C E D R A A B C E D M E A B C E D M E A B C E D V D A B C E D V D 1 1 1 Indeterminate Determinate 1 1 1
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4 f 1j f jj · 1 = + 1 1 2 3 j 4 Redundant R 1 applied 1 1 = f 11 f j1 & R 1 Influence Lines for Reaction Compatibility equation: 0 1 1 11 1 = = + R f f j ) 1 ( 11 1 1 f f R j = ) ( 11 1 1 f f R j =
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5 1 1 2 3 j 4 1 = + & R 2 Redundant R 2 applied f jj f 2j 1 f j2 f 22 Compatibility equation. 0 2 2 22 2 = = + R f 0 2 2 22 2 = = + R f f j ) 1 ( 22 2 2 f f R j = ) ( 22 2 2 f f R j =
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6 1 2 3 j 4 f j 4 1 1 Influence Lines for Shear 4 44 ) 1 ( j E f f V = f 44 1 1
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7 4 44 ) 1 ( j E f M α = 1 2 3 j 4 Influence Lines for Bending Moment 11 44 f j 4
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8 R 3 ) ( 33 3 3 f f R j = R 2 ) ( 22 2 2 f f R j = R 1 ) ( 11 1 1 f f R j = 1 2 3 j 4 1 1 & Influence line of Reaction 1 Using Equilibrium Condition for Shear and Bending Moment 1 11 11 = f f 11 41 f f 11 1 f f j 1 22 22 = f f 22 2 f f j 22 42 f f 1 33 33 = f f 33 3 f f j 33 43 f f
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9 1 2 3 j 4 4 V 4 V 4 = R 1 R 1 V 4 M 4 1 & Unit load to the right of 4 & Influence line of Shear V 4 = R 1 V 4 = R 1 - 1 1 R 2 R 3 R 1 1 1 1 R 1 1 x V 4 M 4 1 & Unit load to the left of 4 V 4 = R 1 - 1 0 1 ; 0 4 1 = = Σ + V R F y 1 R 1 0 ; 0 4 1 = = Σ + V R F y
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