A shaft is subjected to a bending moment of 30 Nmm and a twisting moment of 40 Nmm. The equivalent twisting moment on this shaft is

Concept:

Equivalent Twisting TM:

It is the twisting moment T_eq that alone produces maximum shear stress equal to the maximum shear stress produce due to combined bending and torsion.

Let Teq be equivalent TM.

\(\tau = \frac{{16{T_{eq}}}}{{\pi {d^3}}}\)

As per the definition of T_eq τ = τmax

\(\frac{{16{T_{eq}}}}{{\pi {d^3}}}= \frac{{16}}{{\pi {d^3}}}\left\{ {\sqrt {{M^2} + {T^2}} } \right\}\)

\({T_{eq}} = \sqrt {{M^2} + {T^2}} \)

Calculation:

Given:

M = 30 Nmm, T = 40 Nmm

Equivalent Twisting TM:

\({T_{eq}} = \sqrt {{M^2} + {T^2}} \)

\({T_{eq}} = \sqrt {{30^2} + {40^2}} \)

\({T_{eq}} = \sqrt {{900} + {1600}} =\sqrt{2500}=50\;Nmm\)