Enter the unreduced design live load per square foot, the live load element factor, and the tributary area into the calculator to determine the reduced live load.
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Live Load Formula
The following formula is used to calculate the reduced design live load per ft² of the area supported by a member.
L = L_0\left(0.25 + \frac{15}{\sqrt{K_{LL}A_t}}\right)- Where L is the reduced design live load per ft²
- L0 is the unreduced design live load per ft²
- KLL is the live load element factor
- At is the tributary area (ft²)
- L is typically limited so it does not exceed L0; for KLL × At ≤ 400 ft², no reduction is taken (L = L0).
To calculate the reduced live load, multiply the unreduced design live load by the result of 0.25 plus 15 over the square root of the product of the live load element factor and the tributary area.
If At is entered in m², use 4.57 instead of 15 (since 15 ft = 4.57 m), with L and L0 in consistent pressure units (e.g., kPa).
L = L_0\left(0.25 + \frac{4.57}{\sqrt{K_{LL}A_t}}\right)Live Load Definition
A live load is defined as the load or force per unit area that a structure is subjected to in addition to its own weight.
Example Problem
How to calculate live load?
First, determine the unreduced live load the structural member is designed for. For this example, the unreduced design live load is 40 lb/ft².
Next, determine the live load element factor. For this example, the element is an interior column that has a KLL of 4.
Next, determine the tributary area. For this problem, the area is found to be 400 square feet (ft²).
Finally, using the formula above, calculate the reduced live load:
L = L0 * (0.25 + 15 / SQRT (KLL * At ) )
= 40 * (0.25 + (15/SQRT(4*400)))
= 40 * (0.25 + 0.375)
= 25 lb/ft²
