Tip Deflection of a Cantilever Beam
Mediumdeflectioncantilever
A steel cantilever 3 m long (E = 200 GPa, I = 80 × 10⁶ mm⁴) carries a 10 kN point load at its free end. The tip deflection is most nearly:
- A1.1 mm
- B2.1 mm
- C5.6 mm
- D16.9 mm
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Answer: C. 5.6 mm
Equation: tip deflection of a cantilever with an end load, δ = PL³/(3EI). Values: P = 10,000 N, L = 3 m, E = 200 × 10⁹ Pa, I = 80 × 10⁶ mm⁴ = 80 × 10⁻⁶ m⁴. Step 1: PL³ = 10,000 × 27 = 270,000 N·m³. Step 2: 3EI = 3 × 200×10⁹ × 80×10⁻⁶ = 48 × 10⁶ N·m². Step 3: δ = 270,000/48×10⁶ = 0.00563 m = 5.6 mm. 16.9 mm uses PL³/EI; 2.1 mm uses PL³/8EI; 1.1 mm uses the simply supported formula.
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