P8.5 A beam is subjected to equal bending moments of M₂ = 45 kip. ft, as shown in Figure P8.54. The cross-sectional dimensions (Figure P8.5b) are b₁ = 7.5 in., d₂ = 1.5 in., b₂ = 0.75 in., d₂ = 6.0 in., b3 = 3.0 in., and d3 = 2.0 in. Determine FIGURE P8.5a b₁ b₂ by d₁ d₂ dy M. FIGURE P8.5b (a) the centroid location, the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. State whether the normal stress at H is tension or compression. (c) the bending stress at point K. State whether the normal stress at Kis tension or compression. (d) the maximum bending stress produced in the cross section. State whether the stress is tension or compression.

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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.