Simplified Design Criteria for Bernoulli–Euler Beams: Deflection versus Flexural Strength

With computer solutions becoming more commonplace for structural designs, designers may lose some of the insight that comes from hand calculations. A typical Bernoulli–Euler beam design requires checking strength (bending/flexural and shear stress) and stiffness (deflections). For most design scenarios, shear does not govern, leaving the designer to check flexural strength and deflections. A new method is presented for beams commonly designed in practice and provides a simple check to determine which of these two criteria govern. This method is valid for (1) any cross section where the neutral axis is located at its mid-height, and (2) where closed-form solutions are known for the beam’s maximum bending moment and deflection. These include a large class of beam designs (e.g., steel and wood beams, where the equations for maximum bending moments and deflections are known). For this method, one only needs the beam’s elastic modulus (E); allowable bending strength (${\mathit{F}}_{\mathit{b}}$); length (L); and desired deflection limitation (e.g., $\mathrm{\Delta }=L/240$). Based on these parameters, a value of a transition beam depth, $d^{*}$, can be calculated. Then, if the actual beam depth, $d$ is $<d^{*}$, then deflection of the beam will govern (not flexure). If $d>d^{*}$, then flexure governs (not deflection). A simple check is also presented to see whether live load deflections govern a design, for the case in which the live load and total loads have different deflection criteria. Also, if factored loads, or the plastic section modulus, are used in design, simple adjustment factors are given for these situations.