Topic: Strength of Materials
A 0.75 meter aluminium bar 25*10^-4 m² in cross-sectional area is attached to a 0.50 meter steel bar 15*10^-4 m² in cross-sectional area, as shown in the figure. Take E (Young's modulus) value of 200 GPa for steel & 70 GPa for aluminium. Total shortening due to an axial compressive force of 175 kN is
- A. 157/168 mm
- B. 175/168 mm
- C. 175/186 mm
- D. 157/186 mm
Answer: B. 175/168 mm
Explanation: The total shortening delta is the sum of the shortenings of the individual bars: delta = delta_st + delta_Al. For the steel bar, delta_st = (P * L_st) / (A_st * E_st) = (175 * 10^3 * 0.5) / (15 * 10^-4 * 200 * 10^9) = 2.9167 * 10^-4 m. For the aluminium bar, delta_Al = (P * L_Al) / (A_Al * E_Al) = (175 * 10^3 * 0.75) / (25 * 10^-4 * 70 * 10^9) = 7.5 * 10^-4 m. Total shortening delta = (2.9167 + 7.5) * 10^-4 = 10.4167 * 10^-4 m, which is 1.04167 mm. As a fraction, this equals 175/168 mm.