Question

In designing structures and machines, it is important to consider the strength of material so that the material should have an adequate strength to resist applied loads or forces and retain its original shape. Strength of a material is its ability to withstand this applied load without failure or plastic deformation. Determine the minimum diameter of a steel wire, which is used to raise a load of 4000 N if the stress in the rod is not to exceed 95 N/mm2.

a) 5 mm
b) 10 mm
c) 15 mm
d) 20 mm

Answer 1

The minimum diameter of a steel wire needed to raise a load of 4000 N without exceeding a stress of 95 N/mm² is 10 mm, which is the next standard size larger than the calculated value of approximately 7.3 mm.

Step-by-step explanation:

We are tasked with calculating the minimum diameter of a steel wire that can support a load of 4000 N without the stress exceeding 95 N/mm². The formula that we use to find the diameter is based on the relationship between stress (σ), force (F), and cross-sectional area (A). Stress is defined as force per unit area, or:

σ = F / A

In terms of diameter (d), the area of a circle (which is the cross-section of the wire) is A = π * (d/2)², so we can substitute to find d, which gives us:

F = σ * A = σ * π * (d/2)²

Solving for d, we get:

d = 2 * √(F / (σ * π))

Substituting the given values:

d = 2 * √(4000 N / (95 N/mm² * π)) = 2 * √(4000 / (95 * 3.1416)) = 2 * √(13.324) ≈ 2 * 3.652 ≈ 7.3mm

Considering the standard values provided which are 5mm, 10mm, 15mm and 20mm, the minimum diameter needed to support the load without exceeding the stress limit would have to be the next standard size larger than our calculation. Therefore, the minimum diameter required is 10 mm.