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

A portion of lecture notes from ME 323 – Mechanics of Materials, Lecture 3. The notes cover the topics of shear stress and strain, shear modulus, single and double shear connections, and calculating normal and shear components of stress. The document also includes examples and objectives for the class.

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ME 323 Mechanics of Materials
Lecture 3: Shear stress and
strain
Lecture Book: Chapter 3
Joshua Pribe
Fall 2019
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Download Mechanics of Materials Lecture 3: Shear Stress and Strain and more Study notes Acting in PDF only on Docsity!

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  = Ey 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?