A tie bar is to be chosen for the bottom chord of a roof truss
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids
Fluids and Continuum Physics, Ch Mechanical properties of materials: the Young modulus, plasticity and fracture
Problem
A tie bar is to be chosen for the bottom chord of a roof truss. A tensile test on a specimen of the candidate steel gives the following measured engineering strain ϵ and engineering stress σ, the last point being the point of fracture. Data as pairs (ϵ, σ in MPa): (0, 0), (0.0005, 100), (0.0010, 200), (0.00125, 250), (0.005, 252), (0.02, 320), (0.06, 400), (0.12, 430), (0.18, 405), (0.22, 360). The tie must carry a steady tensile force of 45 kN, and the design rule for this steel is that the working stress must not exceed half the yield stress. The bar is a solid circular rod, 3.00 m long between its end connections, and the weight of the bar itself is ignored.
((a)) Read the Young modulus and the yield stress of this steel from the data.
((b)) Give the ultimate tensile strength and the strain to failure, and say whether the steel is ductile or brittle and how the data show it.
((c)) Find the smallest rod diameter that satisfies the design rule.
((d)) For a rod of exactly that diameter, find the extension of the 3.00 m tie at the working load of 45 kN.