Mechanics of Materials Lecture 3: Shear Stress and Strain, Study notes of Acting

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ME 323 – Mechanics of Materials

Lecture 3: Shear stress and

strain

Lecture Book: Chapter 3

Joshua Pribe

Fall 2019

Review of last class

• Average normal stress:
• Extensional strain:
• Mechanical properties (for linear elastic materials under uniaxial loading)
  • Young’s modulus E : relates axial stress and strain,
  • Poisson’s ratio ν : relates axial strain to transverse strain,
• Follow-up on Example 2.7: ave

 = P A

0

 =  L L

x x  = E  y z x

Course website reminder 4 Homework assignments Gradescope (homework submission) instructions Syllabus, slides for class, and links to pre-week videos and quizzes Solution videos for almost all examples in Lecture Book and “Additional Examples”

Objectives

• Define shear stress and shear strain
  • When does a state of direct shear exist in a material?
  • Single shear vs. double shear for pinned/bolted connections
• Relate shear stress and shear strain
• Calculate normal and shear components of stress

Direct shear 7 What happens to the shear force and bending moment between the pairs of applied forces as d → 0? V (shear force) M (bending moment)

Single and double shear connections 8 Single shear: Double shear: FBD of pin shear stress FBD of pin shear stress

Example: Stress on an inclined plane Motivation: Metals typically fail due to shear stress Motivation: Axial member with a weld line For the axially loaded rectangular bar, what are the normal and tangential components of the stress acting on the plane given by the angle θ?

Example: Stress on an inclined plane For the axially loaded rectangular bar, what are the normal and tangential components of the stress acting on the plane given by the angle θ?