Calculating Stress and Strain in a Steel Rod Under Load
School
The University of Hong Kong**We aren't endorsed by this school
Course
MECH 1420
Subject
Mechanical Engineering
Date
Dec 12, 2024
Pages
1
Uploaded by DoctorHippopotamus8827
Topic 2: Strength of Materials2.Question:A steel rod of diameter 20 mm and length 2 m is subjected to a tensile load of 50 kN. Calculate:a) The stress in the rod.b) The strain in the rod if the Young's modulus of the material is 200 GPa200GPa.Solution:a) Stress (σσ) is calculated using:σ=FAσ=AFWhere:F=50,000 NF=50,000N, A=πd24=π(0.02)24=3.1416⋅10−4 m2A=4πd2=4π(0.02)2=3.1416⋅10−4m2σ=50,0003.1416⋅10−4≈159.15 MPaσ=3.1416⋅10−450,000≈159.15MPab) Strain (ϵϵ) is given by Hooke's Law:ϵ=σEϵ=EσWhere:E=200 GPa=200⋅109 PaE=200GPa=200⋅109Paϵ=159.15⋅106200⋅109=7.9575⋅10−4ϵ=200⋅109159.15⋅106=7.9575⋅10−4Answers:a) Stress = 159.15 MPa159.15MPab) Strain = 7.96⋅10−47.96⋅10−41.
