Calculate the minimum principal stress sigma2 and state if

Question

Design of Machine Elements

1. The figure shows the typical state of stress on an element. At this stage it is not known if the normal stresses are tensile or compressive and the shear stresses are positive or negative. You are given the following information:

The maximum principal stress, σ₁ = 165 MPa

Direction of the maximum shear stress plane, Φ_τ = 21°,

The average stress, σ_avg = 25 MPa.

Knowing that

tan (2Φ_τ) = [-(σ_x - σ_y ) / 2 τ_xy],

i) Calculate the normal stresses, σ_x and σ_y and state if they are tensile or compressive

ii) Calculate shear stress, τ_xy and state if it is positive or negative.

iii) Calculate the minimum principal stress, σ₂ and state if it is tensile or compressive.

iv) Maximum shear stress, τ_max,

v) The principal direction, Φ_σ

vi) Draw the three stress elements as discussed in the class or as seen in the textbook and show the stresses and angles as applicable to each element.

vii) Sketch the approximate Mohr's circle showing the principal stresses and shear stresses as explained in the classroom.