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Engineering ToolBox > Stresses and Deflections in Beams
The calculator below can be used to calculate maximum stress and deflection of beams with one or uniform loads.
Maximum stress in a beam with uniform load supported at both ends can be calculated as
σ = y q L2 / 8 I (1)
where
σ = maximum stress (Pa (N/m2), psi)
y = Perpendicular distance from to neutral axis (m, in)
q = uniform load (N/m, lb/in)
L = length of beam (m, in)
I = moment of Inertia (m4, in4)
Maximum deflection can be expressed as
δ = 5 q L4 / E I 384 (2)
where
δ = maximum deflection (m, in)
E = modulus of elasticity (Pa (N/m2), psi)
The maximum stress in a "W 12 x 35" Steel Wide Flange beam, 100 inches long, moment of inertia 285 in4, modulus of elasticity 29000000 psi, with uniform load 100 lb/in can be calculated like
σ = y q L2 / 8 I
= 6.25 (in) 100 (lb/in) 1002 (in2) / 8 285 (in4)
= 2741 (lb/in2 (psi))
The maximum deflection can be calculated as
δ = 5 q L4 / E I 384
= 5 100 (lb/in) 1004 (in4) / 29000000 (lb/in2) 285 (in4) 384
= 0.016 in
Maximum stress in a beam with uniform load supported at both ends can be calculated as
σ = y F L / 4 I (1)
where
σ = maximum stress (Pa (N/m2), psi)
y = Perpendicular distance from to neutral axis (m, in)
F = load (N, lb)
L = length of beam (m, in)
I = moment of Inertia (m4, in4)
Maximum deflection can be expressed as
δ = F L3 / E I 48 (2)
where
δ = maximum deflection (m, in)
E = modulus of elasticity (Pa (N/m2), psi)
The maximum stress in a "W 12 x 35" Steel Wide Flange beam, 100 inches long, moment of inertia 285 in4, modulus of elasticity 29000000 psi, with a center load 10000 lb can be calculated like
σ = y F L / 4 I
= 6.25 (in) 10000 (lb) 100 (in) / 4 285 (in4)
= 5482 (lb/in2 (psi))
The maximum deflection can be calculated as
δ = F L3 / E I 48
= 10000 (lb/in) 1003 (in3) / 29000000 (lb/in2) 285 (in4) 48
= 0.025 in