Worked Example: Cantilever Beam Shear and Bending Moment

This worked example demonstrates how to find the maximum internal shear force and bending moment in a cantilever beam subjected to a point load at its free end.

1. Problem Statement

A cantilever beam of length $L = 4 \text{ m}$ is fixed at one end (at $x=L$ ) and carries a downward point load $P = 10 \text{ kN}$ at its free end (at $x=0$ ). What is the maximum shear and maximum bending moment in the beam?

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2. Given Data

Point Load (P)

Beam Length (L)

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3. Formula and Calculation

Shear Force: Starting from the free end, the downward point load forces the shear to instantly become $V = -10 \text{ kN}$ . Since there are no other loads along the beam, the shear remains constant. $V_{max} = -P = -10 \text{ kN}$

Bending Moment: At the fixed support ( $x=L$ ):

Error: Formula cantilever-point-load-moment not found in the Formula Registry.

The absolute maximum internal shear is $10 \text{ kN}$ (magnitude) and maximum moment is $-40 \text{ kN·m}$ , both critical at the fixed support.

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