Rectangular bar with a hole, out-of-plane-bending

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Stress concentration factor (SCF) for a rectangular bar with a hole, out-of-plane-bending moment \(M\), thickness \(h\), width \(w\), hole diameter \(d\).
\(K_t\) is calculated so that the max. von Mises stress can be calculated as \( \sigma^\prime = K_t 6 M / [(w-d) h^3] \).

Enter \(d/h\) :    Stress concentration factor (SCF) for a rectangular bar with a hole, out-of-plane-bending moment M
Enter \(d/w\) :    
\(K_t\) = 3    

In this site, \(K_t\) is calculated by a response surface that has been adjusted to 35 simulation points spanning the domain \(d/h=[0,10]\), \(d/w=[0,0.5]\), as shown below.

SCF in a rectangular bar with a hole, out-of-plane bending, 3D plot

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 \([d/h,d/w]\) 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.

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

Here is a 2D plot of \(K_t\) vs. \(d/w\).

SCF in a rectangular bar with a hole, out-of-plane bending

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

SCF in a rectangular bar with a hole, out-of-plane bending