 ## Deflection

Here is a chart you can use to calculate the deflection of a beam under specified loading conditions. The information you will need to use this chart is the Linear Load on the beam, the span of the beam, the size of the beam, and the Modulus of Elasticity for the specified material. Typically, in code references you will see deflection limits of L/360 or L/480. Knowing this information, you can solve for an equation to see how much a beam will deflect under different loading conditions.

How do you calculate this?

First, here is the equation

D = 5wL4 / 384EI
where
D = Deflection
w = weight per linear foot (or metre)
L= Span
E = Modulus of Elasticity
I = Moment of Inertia

Consider a deflection limit of L/360. The L refers to the span. For instance, a beam spanning 10 feet having a deflection limit of L/360 would equate to 10 ft / 360 which is is 0.0277 ft or convert the feet value to inches to get a more meaningful answer. (10 feet x 12 inches = 120 inches) so 120 / 360 = 0.33 inches or about 3/8". This means that a beam spanning 10 feet with a deflection limit of L/360 can sag a maximum amount of 3/8". When people study this, they sometimes size the beam up in order to decrease the deflection amount.

Knowing the maximum deflection allowed you then have to calculate how much a specific beam will deflect under various loading conditions. Typically, deflection calculations are made with specified loads only, not factored loads.

The chart below is an embedded exce sheet that you can use to calculate different deflection amounts. The chart begins with a linear load value on the beam so you may have to do a few calculations beforehand to come up with this value. Red numbers in the chart are the ones you can change.

Here are some Modulus of Elasticity values for reference

 SPF wood No. 2` 1.4 ksi SPF Select Structural 1.5 ksi Douglas Fir 1.6 ksi LVL (Laminated Veneer Lumber) 1.9 ksi LVL (Laminated Veneer Lumber) 2.0 ksi Steel 29.0 ksi