Cantilever beam: tip deflection under a point load

A steel cantilever 2.5 m long carries a 5 kN load at its free end. Its second moment of area is 8.5 × 10⁶ mm⁴ and E = 200 GPa. Find the tip deflection and the moment at the fixed end.

Given

Solution

1. 1.Tip deflection of a cantilever with an end load
   $$\delta =\frac{P{L}^3}{3EI}$$
   $$\delta =15.32\mathrm{mm}$$
2. 2.Moment at the fixed end
   $$M_{max}=PL$$
   $$M_{max}=12.5\mathrm{kN}\cdot \mathrm{m}$$

Worked in ProveCalc

Mixing kN, m, GPa and mm⁴ is where hand calculations go wrong by a factor of a thousand. The engine converts every unit itself and reports the deflection in the unit you ask for.

The results above were evaluated by ProveCalc's compute engine (SymPy and Pint), the same engine the desktop app runs on your machine.

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