Analyzing calculus to find section modulus for a beam

by William Noble

Submitted : Spring 2016

While the performance of calculus is rarely used by engineers in the modern era, the use of formulas based on these theorems is ubiquitous in the industry.  One such example is in the design of structural building members.  Structural engineers determine required section properties of components in buildings based on parameters including material strength, span, tributary loading area and code requirements for superimposed loading and allowable deflection.  Upon determining the required section properties, members are then chosen with actual section properties that exceed the values required by calculation.  One of the critical section properties in structural engineering is the moment of inertia, also called the second moment of mass with respect to distance from an axis. These values, while commonly published for use by engineers, are calculated with a double integral over the object in question and relate the object's mass to it's center of gravity.

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