(Solved): The three-hinged parabolic arch shown in Figure 5 has a span of 12m and central rise of 3m. The eq ...

The three-hinged parabolic arch shown in Figure 5 has a span of 12m and central rise of 3m. The equation of the centreline of the arch is given as: 4r y = x - x2) where L is the span and r is the rise of the arch. a) Determine the location for the maximum sagging bending moment and calculate the values of the corresponding bending moment, axial force and shear force at that location (10 Marks) b) If the central hinge (i.e. the hinge at C) is removed the arch then becomes two-hinged. Calculate the values of bending moment, axial force and shear force at the crown (i.e. point C). You may assume that the second moment of area of the arch at any section I varies round the profile of the arch such that I = 1 sec a where I is the second moment of area at the crown and a is the angle which the tangent at the section makes with the horizontal (8 Marks) c) If the point load 12kN is replaced by a uniformly distributed load of 12kN (total) across the right half span, how would the reaction forces change and what would the values calculated in b) become? (7 Marks) The relevant data sheet for a two pinned parabolic arch is attached at the end of the paper 2kN/m 12EN y = (Lx-x) X D 4m L-12m Figure 5