Question 4.9: At a given point in a machine element, the following stresse...
At a given point in a machine element, the following stresses were evaluated: 100 MPa (tensile) and a zero shear on a horizontal plane and 50 MPa (compressive) on a plane perpendicular to this plane (refer Figure 4.19). Determine the stresses at this point on a plane having a slope of 3 vertical to 4 horizontal.
Let us draw the Mohr’s circle (Figure 4.20) and determine the stress as follows
Radius of the circle is (100 – 25) = 75 MPa. The stress state on the inclined plane B–B corresponds to point C having normal stress (tensile) and shear stress (negative). Thus,
\begin{aligned} \sigma_n & =\text { normal stress on } B – B \\ & =\left(25-75 \cos 73.7^{\circ}\right) MPa =3.95 MPa \end{aligned}
and |τ | = magnitude of shear stress, then
\tau=-75 \sin 73.7^{\circ}=-72 MPa
Thus, the stress state on the inclined plane B–B is shown in Figure 4.21.
