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When a bridge is built as a straight line. The force exerted by a vehicle or body on the bridge is equal to the weight ( M g ) of that object.

When the bridge is constructed in a convex shape, then the objects (vehicles) moving on the bridge go in a circular path. Hence, the equation for balancing forces will be:

M g - M V² / R = N, V = velocity of the vehicle.

R = radius of curvature of the bridge

N = normal force exerted by bridge on the vehicle

When the bridge is constructed in a convex shape, then the objects (vehicles) moving on the bridge go in a circular path. Hence, the equation for balancing forces will be:

M g - M V² / R = N, V = velocity of the vehicle.

R = radius of curvature of the bridge

N = normal force exerted by bridge on the vehicle

*Thus the stress on the bridge reduces. Hence the stability of the bridge is better. Also, the bending of the bridge is lessened as compared to the straight line bridges.***Hence the force exerted by vehicles (called the load) is less by the centripetal force.**