2.2. Trigonometric formula for σ and τ

Try these first

1. 1.

   Define normal stress.

   Hint

   Think about the forces acting directly onto a surface.

2. 2.

   What does shear stress represent?

   Hint

   Consider how a sliding force acts across a material.

3. 3.

   What does the term normal stress refer to?

   • Force per unit area acting perpendicular
   • Force per unit area acting parallel

   Hint

   Remember how forces distribute along different surfaces.

4. 4.

   True or False: Mohr's Circle is useful for visualizing stress transformations.

   • True
   • False

   Hint

   Think about different orientations builders consider on a construction site.

5. 5.

   A material experiences normal stress σ1 = 120 MPa and σ2 = 60 MPa. Calculate the maximum shear stress using Mohr’s Circle.

   Hint

   Visualizing might help; plot this on Mohr's Circle.

6. 6.

   Given a rectangular element under loading with σ = 80 Pa, τ = 40 Pa, draw the Mohr's Circle and find σ and τ for an angle of 30°.

   Hint

   Check your trigonometric functions to aid visualization.