Cantilever Beam

ENGINEERING – TRUCTURAL ENGINEERING β€” BEAM & FRAME CALCULATOR Cantilever Beam A precise tool.
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What is the Cantilever Beam & How does it work?
A cantilever beam is fixed at one end and free at the other, making it a common structural element for over‑hangs, balconies, and sign supports. Because the fixed support restrains translation and rotation, the beam develops internal shear forces and bending moments that vary along its length. When a vertical point load P is applied at the free tip, the shear diagram is constant (V = P) and the bending moment diagram is linear, reaching a maximum moment M_max = PΒ·L at the fixed end. The tip deflection Ξ΄ can be derived from the Euler‑Bernoulli beam theory, giving the classic closed‑form expression. The governing formulas are summarized below. They allow engineers to size the section (through the moment of inertia I) and select material stiffness (modulus E) to keep deflection within serviceability limits while ensuring the beam can resist the induced moment and shear.
M_{max}=P,Lquad;V_{max}=Pquad;delta=frac{P,L^{3}}{3,E,I}
M = maximum bending moment, V = shear force, Ξ΄ = tip deflection
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Frequently Asked Questions
What is a cantilever beam?
A cantilever beam is fixed at one end and free at the other, commonly used for overhangs and balconies.
How do shear forces vary along a cantilever beam?
Shear forces are constant along the length of a cantilever beam when a point load is applied at the free end.
What is the maximum bending moment in a cantilever beam?
The maximum bending moment occurs at the fixed end and is equal to PΒ·L, where P is the point load and L is the length of the beam.
How does the deflection of a cantilever beam change with load?
Deflection increases linearly with the applied load at the free end of the cantilever beam.
What are the key factors affecting the bending moment in a cantilever beam?
The key factors include the point load P, the length L of the beam, and the material properties.

Results are for informational purposes only and do not constitute professional advice.