Deflection Limit Calculator

Q: What are standard deflection limits for beams?

The International Building Code (IBC) and AISC specify deflection limits as a fraction of the span length L. For floor beams supporting live load only, the limit is L/360. For roof beams with live load, the limit is L/240. For total load deflection (dead plus live), L/240 is typical. Members supporting plaster ceilings use L/360 for the live load portion to prevent cracking. These limits ensure serviceability by controlling visible sag, preventing damage to finishes, and maintaining occupant comfort.

Q: How is beam deflection calculated for a uniform load?

For a simply supported beam with a uniformly distributed load, the maximum deflection at midspan is delta = 5wL4 / (384EI), where w is the load per unit length, L is the span, E is the elastic modulus, and I is the moment of inertia about the bending axis. For a point load P at midspan, the formula is delta = PL3 / (48EI). Both formulas assume linear elastic behavior and prismatic (constant cross-section) members. For other load patterns and support conditions, different coefficients apply.

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Reviewed by Abdullah, Technical Content Specialist

Formula

delta = 5wL4/(384EI) (uniform) | delta = PL3/(48EI) (point at midspan)

Maximum midspan deflection for a simply supported beam with uniform load w is 5wL4/(384EI). For a concentrated load P at midspan, it is PL3/(48EI). The calculated deflection is compared against the allowable deflection limit, which is the span L divided by a code-specified ratio such as 360 for floor live load or 240 for roof live load.

Worked Examples

Example 1: Steel Floor Beam

Problem:A 20-foot simply supported steel beam (E = 29,000 ksi, I = 500 in4) carries a uniform live load of 2 kips/ft. Check against L/360.

Solution:L = 20 * 12 = 240 in\nw = 2/12 = 0.1667 kip/in\ndelta = 5 * 0.1667 * 240^4 / (384 * 29000 * 500)\ndelta = 0.4643 in\nAllowable = 240/360 = 0.667 in\n0.4643 < 0.667 = PASS

Result:Actual = 0.4643 in, Allowable = 0.667 in, PASS

Example 2: Roof Beam with Point Load

Problem:A 16-foot roof beam (E = 29,000 ksi, I = 200 in4) has a 10-kip point load at midspan. Check L/240.

Solution:L = 192 in\ndelta = 10 * 192^3 / (48 * 29000 * 200)\ndelta = 0.2546 in\nAllowable = 192/240 = 0.800 in\nPASS

Result:Actual = 0.2546 in, Allowable = 0.800 in, PASS

Frequently Asked Questions

What are standard deflection limits for beams?

The International Building Code (IBC) and AISC specify deflection limits as a fraction of the span length L. For floor beams supporting live load only, the limit is L/360. For roof beams with live load, the limit is L/240. For total load deflection (dead plus live), L/240 is typical. Members supporting plaster ceilings use L/360 for the live load portion to prevent cracking. These limits ensure serviceability by controlling visible sag, preventing damage to finishes, and maintaining occupant comfort.

How is beam deflection calculated for a uniform load?

For a simply supported beam with a uniformly distributed load, the maximum deflection at midspan is delta = 5wL4 / (384EI), where w is the load per unit length, L is the span, E is the elastic modulus, and I is the moment of inertia about the bending axis. For a point load P at midspan, the formula is delta = PL3 / (48EI). Both formulas assume linear elastic behavior and prismatic (constant cross-section) members. For other load patterns and support conditions, different coefficients apply.

References

Reviewed by Abdullah, Technical Content Specialist · Editorial policy