## Circular shaft with fillet subjected to bending moment

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Stress concentration factor (SCF) for a circular shaft with fillet subjected to bending moment $$M$$, diameters $$D$$ and $$d$$, fillet radius $$r$$.
$$K_t$$ is calculated so that the max. von Mises stress can be calculated as $$\sigma^\prime = K_t 32 M / (\pi d^3)$$.

 Enter $$D/d$$ : Enter $$r/d$$ : $$K_t$$ = 2.65

In this site, $$K_t$$ is calculated by a response surface that has been adjusted to 32 data points spanning the domain $$D/d=[1.02,3.0]$$, $$r/d=[0.025,0.3]$$, as shown below.

The 32 data points have been calculated automatically by 96+ Abaqus simulations using a parameterized (Python) script. The number of simulations is 3X the number of data points because computing $$K_t$$ for each pair $$[D/d,r/d]$$ requires 3+ simulations to achive a solution with less than 1% error, by invoking automatic adaptive mesh refinement for each data point within the script. Red dots are data points. A few may be hidden right below the blue surface.

You can learn how to produce similar simulations here [link to be provided].