Question

The mechanical properties of a 1040 carbon steel have been measured in the lab and are as follows:

E=200GPa;σy​ =620MPa;TS=750MPa;v=0.3
A 25 mm diameter bar of this alloy is used as a structural member in an engineering design. The length of the bar is 1 m.
a) The structural load on the bar is L0 kN in tension (the value of L0 is given to you in the email).
a1) What will be the length of the bar under this structural load? Justify the use of any equation.
a2) What will be the diameter of the bar under this structural load?
b) The design engineer is considering a structural change that will increase the tensile load on this member. What is the maximum tensile load that can be permitted without inducing plastic deformation of the bar?
c) The design engineer wants to be sure that the new design will be safe by using a safety factor S=1.8. What is the maximum load that can be applied in this case?

Answer 1

To calculate the new dimensions under load for the 1040 carbon steel bar, Hooke's law and the formula for Poisson's effect are used. The yield strength determines the maximum load without plastic deformation, and the safety factor is applied to ensure safe working conditions.

Step-by-step explanation:

The given problem involves calculating the deformation of a bar made from 1040 carbon steel under a tensile load, as well as determining the safe working loads using a specified safety factor. The key properties of 1040 carbon steel have been given, including Young's modulus (E), yield strength (σy), tensile strength (TS), and Poisson's ratio (v).

a1) Length of the bar under structural load

To calculate the new length of the 25 mm diameter, 1 m long bar under an applied load (L0 kN), we'll use Hooke's law for elastic deformation:

ΔL = (F/original cross-sectional area) * (L0/E)

Where F is the force corresponding to L0 kN, converted into Newtons (N), the original cross-sectional area is π*(d/2)^2 where d is the diameter of the bar, L0 is the original length of 1 m, and E is Young's modulus.

a2) Diameter of the bar under structural load

The diameter would change slightly due to Poisson's effect, which can be calculated by:

Δd/d0 = -v * (ΔL/L0)

Here Δd is the change in diameter, d0 is the original diameter, and v is Poisson's ratio.

b) Maximum tensile load without plastic deformation

The maximum allowable tensile load without causing plastic deformation is dictated by the yield strength (σy). To calculate this, we use:

Maximum Load (N) = σy * original cross-sectional area

c) Maximum load with safety factor

When accounting for a safety factor S=1.8, the maximum permissible load can be computed as:

Maximum Load (N) with Safety Factor = (σy * original cross-sectional area) / 1.8