mee342_hw3_2026.md

layout	default
title	MEE342 Homework 3 2026

Disclaimer

Images for Problems are taken from Shigley's (9th edition).

Problem 1

A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-energy and maximum-shear-stress theories determine the factors of safety for the following principal stresses:

• $\sigma_A = 100 MPa$, $\sigma_B = 100 MPa$
• $\sigma_A = 100 MPa$, $\sigma_B = -100 MPa$
• $\sigma_A = -50 MPa$, $\sigma_B = -100 MPa$

Problem 2

A ductile material has the properties $S_{yt}=60ksi$, $S_{yc}=75ksi$ Using the ductile Coulomb-Mohr theory, determine the factor of safety for the states of stress given below:

• $\sigma_x = 25 kpsi$, $\sigma_y = 15 kpsi$
• $\sigma_x = -12 kpsi$, $\sigma_y = 15 kpsi$, $\tau_{xy} = -9 kpsi$

Problem 3

A brittle material has the properties $S_{ut} = 30 kpsi$, $S_{uc} = 90 kpsi$. Using the brittle Coulomb-Mohr and modified-Mohr theories, determine the factor of safety for the following states of plane stress.

• $\sigma_x = -15 kpsi$, $\sigma_y = 10 kpsi$, $\tau_{xy} = -15 kpsi$
• $\sigma_x = 15 kpsi$, $\sigma_y = -15 kpsi$

Problem 4

Determine the actual factor of safety for yielding for problem 2 from HW1. Use the distortion-energy theory. The material is 1018 CD steel.

Problem 5

The figure shows a shaft mounted in bearings at A and D and having pulleys at B and C. The forces shown acting on the pulley surfaces represent the belt tensions. The shaft is to be made of AISI 1035 CD steel. Using distortion-energy theory with a design factor of 2, determine the minimum shaft diameter to avoid yielding.

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