Math Problem Statement

A steel wire 15 m long hanging vertically supports a tensile load of 2000 N. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 140 MPa and the total elongation is not to exceed 6 mm. Assume E 200 GPa.

15m

2000 N

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Mechanical Engineering
Stress and Strain
Hooke's Law

Formulas

Stress: σ = F / A
Cross-sectional area of a circle: A = πd^2 / 4
Elongation: ΔL = FL / AE
Diameter from stress: d = √(4F / πσ)
Diameter from elongation: A = FL / EΔL, then A = πd^2 / 4

Theorems

Hooke's Law

Suitable Grade Level

Undergraduate Engineering