Deflection
The information you will need to calculate the deflection of a beam under
specified loading conditions 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. Knowing this information, you
can solve for an equation to see how much a beam will deflect under different
loading conditions.
Here is the equation to use
D = 5wL4 / 384EI
where
D = Deflection
w = weight per linear foot (or metre)
L= Span
E = Modulus of Elasticity
I = Moment of Inertia
Typically, you will see deflection limits of L/360 or L/480
when referring to Beam span limits. 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 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" under specified loading
conditions. When deflection limits are close it is
sometimes better to size the beam up by increasing its depth.
Deflection calculations are made with specified loads,
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 |
|
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