Beam Formula

62 We now have the ingredients in place to derive one of the most important equations in structures, the beam formula. This formula will be extensively used for design of structural components.

63 We merely substitute Eq. 12.24 into 12.23,

kE y2dA

which shows that the curvature of the longitudinal axis of a beam is proportional to the bending moment M and inversely proportional to EI which we call flexural rigidity.

64 Finally, inserting Eq. 12.18 above, we obtain

Hence, for a positive y (above neutral axis), and a positive moment, we will have compressive stresses above the neutral axis.

65 Alternatively, the maximum fiber stresses can be obtained by combining the preceding equation with Equation 12.25

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