Compute the vertical displacement of the hinge at \(C\) for the funicular loading shown in Figure P8.16.

The funicular loading produces direct stress on all sections of the arch. Columns transmit only axial load from the roadway beams to the arch. Also assume that the roadway beams and the columns do not restrain the arch. All reactions are given. For all segments of the \(\operatorname{arch} A=70 \mathrm{in}^{2}\), \(I=7800\) in. \(^{4}\), and \(E=30,000\) kips/in. \({ }^{2}\).

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39 kips 40 kips J A 90 kips 35 kips B 30 kips 38.46' H 35 kips 50' -4@30= 120- G D 40 kips F E 90 kips 39 kips