Establish the shape of the funicular arch for the uniform loading acting on the three-hinged arch in Figure 6.18a. To achieve economy, the arch is tapered along its length. Determine the minimum cross sectional area at three locations (x₁ = 17.5 ft, x₂ = 35 ft, and x₃ = 52.5 ft) if the maximum allowable compressive stress is 2000 lbs/in.².

Figure 6.18a

 

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X Y2 Y X3- 70'- w = 5 kips/ft -X- + 70' h = 42'