Cantilever Beam Calculator

Enter value and click on calculate. Result will be displayed.

Cantilever Beam with Load at End


E = Youngs Modulus
I = Area Moment of Inertia
k = Stiffness
l = Length

Youngs Modulus (E):
Nm-2
Area Moment of Inertia (I):
m4
Length (l):
m
Stiffness (k):
Nm-1

A Cantilever Beam Calculator helps determine the deflection, bending moment, shear force, and stress distribution along a cantilever beam under load. Cantilever beams are beams that are fixed at one end and free at the other, commonly used in structures like balconies, bridges, and overhangs.

Key Parameters for Cantilever Beams:

  1. Length (L) – The length of the beam from the fixed support to the free end.
  2. Load (P) – The applied load on the beam, either concentrated at the free end or distributed along the length of the beam.
  3. Beam Material (E) – The modulus of elasticity of the beam's material.
  4. Beam Moment of Inertia (I) – The second moment of area, which depends on the beam’s cross-section shape (rectangular, circular, etc.).

Common Calculations for Cantilever Beams:

1. Bending Moment (at the Fixed End):

For a point load at the free end:

M=P×L

Where:

  • M is the bending moment at the fixed support,
  • P is the applied load,
  • L is the length of the beam.

For a uniformly distributed load (w) along the length of the beam:

2. Deflection (at the Free End):

For a point load at the free end:

Where:

  • δ is the deflection at the free end,
  • P is the applied load,
  • L is the length of the beam,
  • E is the modulus of elasticity of the material,
  • I is the moment of inertia of the beam's cross-section.

3. Shear Force (at the Fixed End):

For a point load at the free end:

V=P

Where V is the shear force at the fixed end (equal to the applied load).

For a uniformly distributed load along the beam:

Example Calculation:

1. Bending Moment at the Fixed End:

M=P×L=1000 N×4 m=4000 Nm

2. Deflection at the Free End: