The cross section of a narrow-gage railway bridge is shown in part (a) of the figure. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines. The spacing of the girders is s1 = 55 in. and the spacing of the rails is s2 = 30 in. The load transmitted by each rail to a single tie is P = 1,600 lb. The cross section of a tie, shown in part (b) of the figure, has width b = 5.0 in. and depth d. Steel rail Wood tie Steel girder (b) (a) Determine the minimum value of d based upon an allowable bending stress of 1,525 psi in the wood tie. (Disregard the weight of the tie itself.). Round your answer to one decimal place. dmin in.

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System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.