Reference no: EM131135656
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, Φτ = 21°,
The average stress, σavg = 25 MPa.
Knowing that
tan (2Φτ) = [-(σx - σy ) / 2 τxy],
i) Calculate the normal stresses, σx and σy and state if they are tensile or compressive
ii) Calculate shear stress, τxy 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, τmax,
v) The principal direction, Φσ
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.
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