The stepped bar shown in the figure is made up of two different materials. Material 1 has Young’s modulus = 2 × 10⁵ N/mm², while that of Material 2 is 1 × 10⁵ N/mm². What is the extension of the bar under a pull of 30 kN if both the portions are 20 mm in thickness ? (The dimensions shown below are in mm)
- A0·5125 mmCorrect
- B0·4000 mm
- C0·1125 mm
- D0·2875 mm
Solution
Concept
Total extension of a composite stepped bar
Formula
δ = Σ P L / (A E)
Step-by-step solution
1. Material 1: b = 40, L = 600 → A = 40 × 20 = 800 mm²; δ₁ = 30 000 × 600 / (800 × 2×10⁵) = 0.1125 mm. 2. Material 2: b = 30, L = 800 → A = 600 mm²; δ₂ = 30 000 × 800 / (600 × 1×10⁵) = 0.4 mm. 3. Total δ = 0.1125 + 0.4 = 0.5125 mm.
Explanation
The same axial force acts in both portions, so the extensions are added. Each portion has its own length, area and modulus.
Why the other options are wrong
0.4 mm and 0.1125 mm are the extensions of Material 2 and Material 1 alone. 0.2875 mm is not the sum.
Shortcut
Same P in both; add P L /(A E) for each portion.
Common mistake
Using one area or one modulus for the whole bar.
Correct answer: A) 0·5125 mm