Assumptions
- The angle between the wall and the strut is $\theta$
- $a$ is the depth of the table top
- $P$ is the weight on the table top, applied at the edge furthest from the wall
- The strut will fail when it buckles, which implies $F_{\text{max}}=\frac{\pi^2EI}{L^2}$ where $L$, $E$ and $I$ are the length, the elastic modulus, and the moment of area, respectively, of the strut
Analysis
The axial force on the strut will be $F=\frac{P}{\cos\theta}$.
The length of the strut will be $L=\frac{a}{\sin\theta}$.
Combining both equations with the equation for buckling we have: $(EI)_{\text{required}}=\frac{Pa^2}{\pi^2\sin^2\theta \cos\theta}$.
$EI$ is the stiffness of the strut.
The most efficient strut will be one for which $(EI)_{\text{required}}$ is minimized.
The lowest $(EI)_{\text{required}}$ occurs when $\sin^2\theta \cos\theta$ is maximized and that is when $\theta=\sin^{-1}\sqrt{\frac{2}{3}}$ so the most efficient angle is $\theta\approx54.7^{\circ}$
![strut](https://cdn.statically.io/img/i.sstatic.net/K74XZ.jpg)