while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly, there therefore exists a point on the linear path between them where there is no bending stress. The locus of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams (-beams) and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region. The classic formula for determining the bending stress in a beam under simple bending is: where is the bending stress – the moment about the neutral axis – the perpendicular distance to the neutral axis – the second moment of area about the neutral axis z. - the Resistance Moment about the neutral axis z. Extensions of Euler-Bernoulli beam bending theory Plastic bending The equation is valid only when the stress at the extreme fiber (i.e., the portion of the beam farthest from the neutral axis) is below the yield stress of the material from which it is constructed. At higher loadings the stress distribution becomes non-linear, and ductile materials will eventually enter a plastic hinge state where the magnitude of the stress is equal to the yield stress everywhere in the beam, with a discontinuity at the neutral axis where the stress changes from tensile to compressive. This plastic hinge state is typically used as a limit state in the design of steel structures. Complex or asymmetrical bending The equation above is only valid if the cross-section is symmetrical. For homogeneous beams with asymmetrical sections, the maximum bending stress in the beam is given by where are the coordinates of a point on the cross section at which the stress is to be determined as shown to the right, and are the bending moments about the y and z centroid axes, and are the second moments of area (distinct from moments of inertia) about the y and z axes, and is the product of moments of area. Using this equation it is possible to calculate the bending stress at any point on the beam cross section regardless of