BEAM DEFLECTION FORMULAE BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x 1. Cantilever Beam – Concentrated load P at the free end
Pl 2 2 EI
θ=
y=
MAXIMUM DEFLECTION
Px 2 ( 3l − x ) 6 EI
δ max =
Pl 3 3EI
2. Cantilever Beam – Concentrated load P at any point
Px 2 ( 3a − x ) for 0 < x < a 6 EI Pa 2 y= ( 3x − a ) for a < x < l 6 EI
y=
Pa 2 θ= 2 EI
δ max
Pa 2 = ( 3l − a ) 6 EI
3. Cantilever Beam – Uniformly distributed load ω (N/m)
ωl 3 6 EI
θ=
δ max =
ωl 4 8 EI
ωo x 2 (10l 3 − 10l 2 x + 5lx2 − x3 ) 120lEI
δ max =
ωo l 4 30 EI
Mx 2 2 EI
δ max =
Ml 2 2 EI
y=
ωx 2 x 2 + 6l 2 − 4lx ) ( 24 EI
4. Cantilever Beam – Uniformly varying load: Maximum intensity ωo (N/m)
θ=
ωol 3 24 EI
y=
5. Cantilever Beam – Couple moment M at the free end
θ=
Ml EI
y=