# Structural analysis of a wooden board and dowel

Suppose you have a wooden board lying horizontal, with grain along the long axis as is the case with normal boards.

There is a wooden dowel embedded into the board, as is the case with common dowel joints.

The other end of the dowel is fixed, to simplify let's say it's slotted into some steel housing or something.

We then begin to apply downward loads on the board. Disregarding rotation - let's say it's set up so as to make that not a factor - what forces determine the breaking point of the system?

It seems to me like you have two:

- The dowel might shear, so that it breaks into two halves - one half in the steel and the other in the wood - and the board is now free
- The dowel might rip through the wood above it, freeing the board
- The board might break over the fulcrum of the dowel (this seems a bit of a stretch)

Is this a complete list, and if so, how do you calculate the forces to determine which will happen first? I know that it depends on some constant representing the strength of the wood; let's assume that dowel and board have the same constant.

## 2 answers

Your list of potential failure modes seems pretty comprehensive. The dowel could shear, rip through the wood, or the board itself might break. To determine which will happen first, you need to consider the shear strength of the dowel and the tensile strength of the wood. Calculate the forces acting on the dowel and the board, then compare them to these strength values. If the applied force exceeds the shear strength of the dowel, it will shear. If it exceeds the tensile strength of the wood, the wood will rip or the board will break. This way, you can predict the failure mode based on the material properties and the applied forces.

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