Rectangular bar with symmetric fillet, in-plane bending moment

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Stress concentration factor (SCF) for a rectangular bar with a symmetric fillet, subjected to in-plane bending moment \(M\), thickness \(h\), widths \(w\) and \(d\), fillet radius \(r\).
\(K_t\) is calculated so that the max. von Mises stress can be calculated as \( \sigma^\prime = K_t 6 M / (h d^2) \).

Enter \(D/d\) :    Rectangular bar with symmetric fillet, bending
Enter \(r/d\) :    
\(K_t\) = 3.02    

In this site, \(K_t\) is calculated by a response surface that has been adjusted to 35 data points spanning the domain \(D/d=[1.02,1.5]\), \(r/d=[0.025,0.3]\), as shown below.

SCF in a rectangular bar with symmetric fillet, bending

The 35 data points have been calculated automatically by 105+ 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].

Here is a plot of \(K_t\) vs. \(r/d\).

SCF in a rectangular bar with symmetric fillet, bending