Beam_Deflection_Formulae

# Beam_Deflection_Formulae - BEAM DEFLECTION FORMULAE BEAM...

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BEAM DEFLECTION FORMULAE BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION 1. Cantilever Beam – Concentrated load P at the free end 2 2 Pl EI θ= () 2 3 6 Px yl x EI = 3 max 3 Pl EI δ= 2. Cantilever Beam – Concentrated load P at any point 2 2 Pa EI 2 3f o r 0 6 Px ya x x a EI = −< < 2 o r 6 Pa yx a a x l EI = < 2 max 3 6 Pa la EI δ =− 3. Cantilever Beam – Uniformly distributed load ω (N/m) 3 6 l EI ω 2 22 64 24 x l l x EI ω =+ 4 max 8 l EI ω 4. Cantilever Beam – Uniformly varying load: Maximum intensity ω o (N/m) 3 o 24 l EI ω 2 32 2 3 o 10 10 5 120 x l x l x x lEI ω + 4 o max 30 l EI ω 5. Cantilever Beam – Couple moment M at the free end Ml EI 2 2 Mx y EI = 2 max 2 Ml EI

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BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. Beam Simply Supported at Ends – Concentrated load P at the center 2 12 16 Pl EI θ=θ= 2 2 3 for 0 12 4 2 Px l l yx x EI ⎛⎞ = −< < ⎜⎟ ⎝⎠ 3 max 48 Pl EI δ= 7. Beam Simply Supported at Ends – Concentrated load P at any point 22 1 () 6 Pb l b lEI θ= 2 (2 ) 6 Pab l b lEI 222 for 0 6 Pbx yl x b x a lEI = −− << 3 3 6 for Pb l a l b x x lEI b axl =− +
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Beam_Deflection_Formulae - BEAM DEFLECTION FORMULAE BEAM...

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