Reducing section modulus of beams by adding cross-sectional area

This technical note shows that the injudicious addition of area to the cross section of a beam in bending may reduce the minimum elastic section modulus. Simple expressions are derived, which give the locations within a section where this occurs. For initially symmetrical standard beam sections these locations extend from the neutral axis for distances of between 12% of the section depth for round bars, to 35% for I-beams. An expression is derived for the location at which any added area will give the maximum reduction in minimum section modulus and another expression from which the magnitude of this maximum reduction may be calculated. The theoretical worst case is an idealized I-beam with a negligible web area for which any added area except at the neutral axis or flanges will reduce the section modulus; and the theoretically possible maximum reduction is 16.7%, corresponding with a 20% increase in stress. The results obtained in this paper should be particularly useful in the design of built-up sections such as box-girder bridges, aircrafts, and ship hulls in which fatigue and/or fracture may be a limiting constraint.