Tensile test of an aluminium alloy

Problem statement

A tensile test has been carried out on a cylindrical bar of an aluminium alloy, $[[d]]$ mm in diameter, using an extensometer with gauge length $L_0 = [[L0]]$ mm. In the resulting $F$-$\Delta L$ graph, the force at the yield strength was $F = [[Fy]]$ N. Given that the initial length between gauge marks was $L_i = [[Li]]$ mm, the final length between the marks after fracture was $L_f = [[Lf]]$ mm and the calculated Young's modulus was $[[E_GPa]]$ GPa, determine:

a) (0.5 marks) The stress at the yield strength (in MPa).

b) (0.5 marks) The elongation at break (in %).

c) (0.5 marks) The increase in length that a bar of the same diameter as in the statement, $[[Lbarra_cm]]$ cm long, would undergo when a stress of $[[sigma_c]]$ MPa is applied to it.

d) (0.5 marks) The minimum diameter that a beam under tension made of the same alloy should have so that it does not deform plastically under a force of $[[F_d_kN]]$ kN.

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Technology and Engineering · Question 2.2. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.