A three-hinged arch bridge carries an unsymmetrical distributed load. How does the horizontal reaction at the abutments specifically relate to the internal shear and bending moment at the arch crown?

A three-hinged arch bridge is a specific type of arch structure that has three pin hinges: one at each abutment and one at the crown. Abutments are the supports at the ends of the arch that resist both vertical and horizontal forces from the bridge. This three-hinged configuration makes the structure statically determinate, meaning all reaction forces and internal forces can be calculated using only the equations of static equilibrium. The horizontal reaction, denoted as H, is the horizontal thrust exerted by the arch onto its abutments, which the abutments resist. Due to the arch action, this horizontal thrust is a primary characteristic of arches, significantly reducing bending moments throughout the structure compared to a simply supported beam. The arch crown refers to the highest point of the arch, where the third hinge is located. Internal shear force (V) is the force acting perpendicular to the cross-section of the arch, tending to cause sliding. Internal bending moment (M) is the rotational ....