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Beams &amp; Frames Deflections Formulas FALL 2009 P

# Beams &amp; Frames Deflections Formulas FALL 2009 P -...

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DISPLACEMENTS OF PRISMATIC BEAMS 1- P A B CW is - C L/2 L/2 θ A = -PL 2 /16EI, θ B = PL 2 /16EI, Δ C = -PL 3 /48EI 2- A M B C L/2 L/2 θ A = - ML/24EI, θ B = - ML/24EI, Δ C = 0 3- A B C M L/2 L/2 θ A = ML /6EI, θ B = -ML /3EI, Δ C = ML 2 /16EI 4- P P A B C L/3 L/3 L/3 θ A = -PL 2 /9EI, θ B = PL 2 /9EI, Δ C = -23PL 3 /648EI Beams & Frames Deflections formulas FALL 2009 1

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5- C A B L/2 L/2 θ A = -WL 3 /24EI, θ B = WL 3 /24EI, Δ C = -5WL 4 /384EI 6- P A B L θ A = 0, θ B = -PL 2 /2EI, Δ B = -PL 3 /3EI 7- A B L θ A = 0, θ B = -ML/EI, Δ B = -ML 2 /2EI 8- A B L θ A = 0, θ B = -WL 3 /6EI, Δ B = - WL 4 /8EI Beams & Frames Deflections formulas FALL 2009 2
Beams & Frames Deflections formulas FALL 2009 3

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Beams & Frames Deflections formulas FALL 2009 4
m j m i 1 1/2 1/2 1/2 2/3 1/3 1/3 2/3 2/3 1/2 1/3 1/6 1/4 1/3 1/4 1/12 5/12 1/4 1/2 1/6 1/3 1/4 1/3 1/12 1/4 1/4 5/12 1/2 1/4 1/4 1/3 5/12 7/48 7/48 17/48 17/48 2/3 1/3 1/3 5/12 8/15 1/5 1/5 7/15 7/15 1/3 1/4 1/12 7/48 1/5 1/5 1/30 3/10 2/15 1/3 1/12 1/4 7/48 1/5 1/30 1/5 2/15 3/10 2/3 5/12 1/4 17/48 7/15 3/10 2/15 8/15 11/30 2/3 1/4 5/12 17/48 7/15 2/15 3/10 11/30 8/15 Table 1. Values of the alpha α

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Beams &amp; Frames Deflections Formulas FALL 2009 P -...

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