Question

The stresses at a point on the circumference of a circular rod in tension and shear are 120 MPa and 60 MPa respectively. If the yield strength of the rod material is 340 MPa, the factor of safety in the rod material using maximum shear stress theory is nearly equal to

• A. Factor of safety = 2.0
• B. Factor of safety = 4.0
• C. Factor of safety = 2.5
• D. Factor of safety = 3.0

Answer 1

Answer:

A. Factor of safety = 2.0

Given:$\sigma_{x} = 120 MPa$, $\tau_{xy} =60 MPa$, $S_{yt} =340 MPa$; $S_{ys} =\frac{S_{yt}}{ 2}$=$\frac{ 340}{ 2} =170 MPa$

$\sigma{ 1, 2} =(\frac{\sigma_x + \sigma_y}{2}) \pm \frac 12 \sqrt{(\sigma_x - \sigma_y )^ 2 +4 \tau_{xy} ^ 2}$ $\Rightarrow$

$\sigma_{1, 2} =\frac{120}{2} \pm \frac 12 \sqrt{ (120)^ 2 +4\times 60^ 2}$ =144.85,-24.85$</p><p style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px" data-pxy="true">and$\tau_{max} = \frac{\sigma_1 - \sigma_2}{2} =\frac {144.85-(-24.85)}{ 2} =84.85 MPa$; </p><p style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px" data-pxy="true">For the factor of safety,$\tau_{max} \le \frac{S_{ys}}{N} 84.85 \le \frac{170}{N} N \le2 \Rightarrow N=2$