The power is transmitted through a spur gear with 20° pressure angle mounted at the mid span of shaft supported on bearings at the ends. The nature of stress induced in the shaft is

Correct option is B

​$$\begin{aligned}&\textbf{1. Bending Stress (Primary Stress)} \\[0.5em]&\bullet\ \text{Cause: The gear transmits a \textit{tangential force} (due to torque) and a \textit{radial force} (due to the } 20^\circ \text{ pressure angle),} \\&\quad \text{both of which act as transverse loads on the shaft.} \\[0.5em]&\bullet\ \text{Nature:} \\&\quad \circ\ \text{Cyclic (Reversing) Stress: Alternates between tension and compression at any point on the shaft.} \\&\quad \circ\ \text{Maximum at mid-span: Highest bending moment at the gear location (mid-span).} \\[1em]&\textbf{Bending Moment Calculation:} \\&\text{For a simply supported shaft with a central load (gear force } F\text{):} \\&M_{\text{bending}} = \frac{F \cdot L}{4} \\&\text{where } L \text{ is the distance between bearings.} \\[2em]&\textbf{2. Torsional Shear Stress (Secondary Stress)} \\[0.5em]&\bullet\ \text{Cause: The gear transmits \textit{torque} (}T\text{) to the shaft, inducing shear stress.} \\[0.5em]&\bullet\ \text{Nature:} \\&\quad \circ\ \text{Pure Shear Stress: Constant in magnitude but \textit{rotates} with the shaft.} \\[0.5em]&\quad \circ\ \text{Governed by:} \\&\tau = \frac{T \cdot r}{J} \\&\text{where } r = \text{shaft radius, } J = \text{polar moment of inertia.}\end{aligned}$$​​