Lecture 3 – Shear stress and strain

Instructor: Prof. Marcial Gonzalez

Fall, 2020ME 323 – Mechanics of Materials

Reading assignment: 2.7

Last modified: 8/22/20 11:19:25 PM

3

Normal stress:- Force per (undeformed) unit area, acting perpendicular to a given

plane and at a given point.(e.g., normal stress at point (x,y,z) on cross section with normal x)

Resultant normal force:

Average normal stress:

Stress and strain

4

Shear stress:- Force per (undeformed) unit area, acting tangential to a given plane

and at a given point.(e.g., shear stress at point (x,y,z) on cross section with normal x)

Resultant shear force:

Shear stress and strain

Average shear stress:

5

Direct shear.- Direct shear is caused by forces that act parallel to a particular surface,

with the direct result of shearing the material at that surface.Example: sheet-metal punch

Shear stress and strain

Note: the body is in equilibriumO

Average shear stress:

Free Body Diagram

6

Direct shear.- Direct shear is caused by forces that act parallel to a particular surface,

with the direct result of shearing the material at that surface.Example: lap splice

Shear stress and strain

Average shear stress:

Note: the body is in equilibriumFBD

7

Direct shear.- Direct shear is caused by forces that act parallel to a particular surface,

with the direct result of shearing the material at that surface.Example: bolted joint

Shear stress and strain

Average shear stress:

Note: the body is in equilibriumFBD

8

Direct shear.- Direct shear is caused by forces that act parallel to a particular surface,

with the direct result of shearing the material at that surface.Example: pinned joint

Shear stress and strain

Average shear stress:

FBDNote: the body is in equilibrium

9

Direct shear. Heavy duty CNC punching machine.

Shear stress and strain

10

Mechanical properties – Next time …

Linear elastic deformations (in homogeneous and isotropic materials)- Hooke’s law:

+ elongation+ shear

- Young’s modulus

- Poisson’s ratio

- Shear modulus

- Note: only two material constants are needed for the description of linear elastic materials.You will learn other elastic material properties in future lectures (however, all these properties are related)

S.D. Poisson

Any questions?

11

Stress and strain