The maximum permissible deflection of a timber beam supporting a roof, is A. $$\frac{{\text{L}}}{{100}}$$ B. $$\frac{{\text{L}}}{{150}}$$ C. $$\frac{{\text{L}}}{{260}}$$ D. $$\frac{{\text{L}}}{{360}}$$

The correct answer is $\frac{{\text{L}}}{{360}}$.

The maximum permissible deflection of a timber beam supporting a roof is $\frac{{\text{L}}}{{360}}$, where L is the span of the beam. This means that the beam can deflect no more than $\frac{1}{360}$ of its span under load.

The deflection of a beam is the amount that it bends under load. The amount of deflection that a beam can withstand depends on a number of factors, including the type of wood used, the size and shape of the beam, and the load that it is carrying.

The maximum permissible deflection of a beam is usually specified by the building code. In the United States, the International Residential Code (IRC) specifies that the maximum permissible deflection of a timber beam supporting a roof is $\frac{{\text{L}}}{{360}}$.

If a beam deflects more than the maximum permissible amount, it may be considered to be structurally unsafe. In this case, the beam may need to be replaced or reinforced.