Overview: Deflection in Beams

While the elongation or contraction of axially loaded members along their longitudinal axes is usually of little consequence, beams may experience excessive deflection perpendicular to their longitudinal axes, making them unserviceable. Limits on deflection are based on several considerations, including minimizing vibrations, thereby improving occupant comfort; preventing cracking of ceiling materials, partitions, or cladding supported by the beams; and promoting positive drainage (for roof beams) in order to avoid ponding of water at midspan. These limits are generally expressed as a fraction of the span, L (Table 1).

Formulas for the calculation of maximum deflection are shown in Table 2, along with additional values for the recommended minimum depth of reinforced concrete spanning elements.

The maximum (mid span) deflection, Δ, of a uniformly loaded simple span can also be found from the equation:

where w distributed load (lb/in. or kips/in.), L span (in.), E modulus of elasticity (psi or ksi), and I moment of inertia (in 4 ). When using Equation 8.1 with L in feet, w in lb/ft or kips/ft, E in psi or ksi (compatible with load, w ), and I in in⁴, as is most commonly done, multiply the expression by 12³ to make the units consistent.