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Beam Bending

Equations from classical (Euler-Bernoulli) beam theory.

Symbols used:
is Young's Modulus for the material (Pa);
is the second moment of area (m4);
is the bending moment (Nm);
is the length of the beam (m);
is the force applied (N);
is the shear force in the beam (N);
is the deflection of the beam (m);
is the distance from the central axis of the beam (m);

Simply supported beam

P
Maximum bending moment:
Shear force:
Maximum deflection:

Cantilever beam

P
Maximum bending moment:
Shear force:
Maximum deflection:

Stresses

Bending stress:
Shear stress: