Closed Book and Notes

Problem $1$: $(25$ POINTS$)$

The arch shown on the right is made of steel, and it supports the roof of a building. The roof has a triangular shape, hence, the weight of the roof is idealized by the triangular force distribution as shown on the sketch.

The following conditions are given:

The span of the arch: $L=20m$

$$ The peak load: $w=1,200k\frac{N}{m}$

$$ The maximum force the steel arch can withstand is: $T_{\text{m}\text{a}\text{x}}={10}^{4}kN$

Determine: The optimum sag $(s)$ of the arch, which determines the curvature of the arch.