Estimate the bending strength of the shaft shown in Fig. 10.50 for two materials

(a) Normalised 0.4% C steel with an unnotched endurance limit of $206 MN/m^{2}$

(b) Heat-treated $3 \frac{1}{2}$ % Nickel steel with an unnotched endurance limit of $480 MN/m^{2}$ .

Question

Estimate the bending strength of the shaft shown in Fig. 10.50 for two materials

(a) Normalised 0.4% C steel with an unnotched endurance limit of [latex]206 MN/m^{2}[/latex]

(b) Heat-treated [latex]3 \frac{1}{2}[/latex]% Nickel steel with an unnotched endurance limit of [latex]480 MN/m^{2}[/latex].

Accepted Answer

From the dimension of the figure

[latex]\frac{D}{d}=\frac{25}{19} =1.316[/latex] and [latex] \frac{r}{d} =\frac{3}{19}=0.158[/latex]
From Fig. 10.24 [latex] K_{t}=1.75[/latex]

From Fig. 10.37 for notch radius of 3 mm

q = 0.93 for normalised steel

q = 0.97 for nickel steel (heat-treated)

:. From eqn. (10.32) for the normalised steel

[latex]K_{f}=1+q(K_{t}-1)[/latex] (10.32)
[latex]=1+0.93(1.75-1)=1.698[/latex]

and the fatigue strength

[latex]\sigma _{f}=\frac{206}{1.698} =12.3 MN/m^{2}[/latex]

and for the nickel steel

[latex]K_{f}=1+0.97(1.75-1)=1.728[/latex]

and the fatigue strength

[latex]\sigma _{f}=\frac{480}{1.728} =277.8 MN/m^{2}[/latex]

N.B. Safety factors should then be applied to these figures to allow for service loading conditions, etc.

Question 10.5: Estimate the bending strength of the shaft shown in Fig. 10....