3 A three hinged parabolic arch is used to construct the bri

3- A three hinged parabolic arch is used to construct the bridge shown in Figure 1. In Figure 2, you can see a sketch of the bridge. This bridge is supposed to carry the uniform horizontally distributed vertical load of w that is applied to its deck. If the maximum allowable moment that maximum w that the bridge can carry. Based on the W that you have calculated, determine the shear and axial forces at point D. (25 points) Figure i 10 ft Figure 2 10 ft lo ft 20 f

Solution

Solution:-

Maximum bending moment in arch = WL/8

1000 = W L/8

W = 8000/40

W = 200 kips      Answer

Hoizontal thrust(H) = WL/(8r)

H = 200* 40/(8*10)

= 100 kips   Answer

Axial shear (F) = Vcos – Hsin

Equation of parabola

Y = 4 r x (L – x ) /L²

Y = 4 * 10 * x(40 – x) /40²

dY/dx = (40 – 2x)/40 = (40 – 2 *10)/40

tan = dy/dx = 0.5

= 26.56 degree

Axial shear (F) = W/2 * cos(26.56) – 100 sin(26.56)

           Axial force (F) = 44.73 kips      Answer