Beam Reaction Calculator
Estimate beam reaction for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Reviewed by Abdullah, Technical Content Specialist
Formula
Ra + Rb = Total Load; Sum of Moments about A = 0 to find Rb
Apply static equilibrium: the sum of all vertical forces equals zero (Ra + Rb = total applied load), and the sum of moments about any point equals zero. Taking moments about the left support eliminates Ra and allows solving for Rb directly. For uniform load: Ra = Rb = wL/2. For point load at distance a: Ra = P(L-a)/L, Rb = Pa/L.
Worked Examples
Example 1: Uniform Load on Simply Supported Beam
Problem:Find reactions for a 20-ft beam with 500 plf uniform load.
Solution:Total load = 500 x 20 = 10,000 lbs\nRa = Rb = 10,000 / 2 = 5,000 lbs each\nMax moment = 500 x 20^2 / 8 = 25,000 lb-ft\nMax shear = 5,000 lbs at supports
Result:Ra = 5,000 lbs, Rb = 5,000 lbs, M_max = 25.00 kip-ft
Example 2: Off-Center Point Load
Problem:Find reactions for a 16-ft beam with 8,000 lb point load at 6 ft from left support.
Solution:a = 6 ft, b = 10 ft, P = 8,000 lbs\nRa = P x b/L = 8,000 x 10/16 = 5,000 lbs\nRb = P x a/L = 8,000 x 6/16 = 3,000 lbs\nMoment at load = 5,000 x 6 = 30,000 lb-ft
Result:Ra = 5,000 lbs, Rb = 3,000 lbs, M = 30.00 kip-ft
Frequently Asked Questions
How do I calculate beam reactions for a simply supported beam?
For a simply supported beam, use static equilibrium equations. Sum of vertical forces equals zero: Ra + Rb = total load. Sum of moments about one support equals zero to solve for the other reaction. For a uniform load w over span L, both reactions equal wL/2. For a point load P at distance a from the left support, Ra = P(L-a)/L and Rb = Pa/L. These principles apply to any combination of loads using superposition for linear elastic analysis.
What is the difference between a reaction force and an internal force?
Reaction forces are the external forces that the supports exert on the beam to maintain equilibrium. They act at the support points and represent the load transferred to the supporting structure below. Internal forces (shear and moment) exist within the beam at every cross section and represent the forces the beam material must resist. A reaction force at a wall column or footing determines the required capacity of that supporting element. Internal forces determine the required size and strength of the beam itself.
How do I calculate the load-bearing capacity of a beam?
Beam capacity depends on material, cross-section dimensions, span length, and support conditions. For a simple rectangular wood beam, bending strength = (F_b x b x d^2) / 6, where F_b is allowable stress, b is width, and d is depth. Always consult a structural engineer for critical applications.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy