Beam Reaction Calculator
Calculate support reactions for a simply supported beam with a point load. Find reactions at both supports, maximum bending moment, and verify equilibrium.
Enter Values
Distance from support A to the applied load
Result
Enter values above and click Calculate to see your result.
AI Assistant
Ask about this calculator
I can help you understand the beam reaction calculator formula, interpret your results, and answer follow-up questions.
Try asking
Formula
How it works: For a simply supported beam of length L with a point load P at distance a from support A: take moments about A to find Rb, then use vertical equilibrium (Ra + Rb = P) to find Ra. The maximum bending moment occurs at the load point.
Worked Example
What Are Beam Reactions?
Beam reactions are the foundational forces exerted by a structure's supports to counteract the applied external loads, ensuring the entire structure remains in a state of static equilibrium. For any stable engineering structure, the sum of all upward forces must precisely balance the sum of all downward forces, and the sum of all rotational moments about any arbitrary point must be zero. These fundamental principles of statics are indispensable for accurately determining beam reactions. In the context of a simply supported beam, which typically rests freely on two supports, often a pin at one end and a roller at the other, these reactions are exclusively vertical forces. When a concentrated point load is applied, the magnitude of the reaction at each support is directly influenced by the load's position along the beam. Engineers and designers calculate these reactions as the crucial initial step in analyzing a beam's internal forces, such as shear force and bending moment, which are vital for selecting appropriate materials and dimensions to guarantee the beam's structural integrity and prevent failure.
- Beam reactions are the essential upward forces provided by supports to maintain structural equilibrium.
- They are calculated using the fundamental principles of static equilibrium: sum of forces equals zero, sum of moments equals zero.
- Accurate determination of support reactions is the first step in analyzing a beam's internal shear forces and bending moments.
- These calculations are critical for ensuring structural safety, preventing collapse, and guiding material selection.
Understanding beam reactions is paramount for any structural analysis. Use this calculator to quickly find support reactions and the maximum bending moment, making your structural design tasks more efficient and precise.
You can also calculate changes using our Torque and Moment Calculator.
Frequently Asked Questions
What is a simply supported beam?
A beam resting on two supports (pin and roller) with no fixed ends. It can rotate at the supports and is the most common beam type in engineering statics problems.
How do you find beam reactions?
Use two equilibrium equations: sum of moments about one support equals zero (to find the other reaction), and sum of vertical forces equals zero (to find the remaining reaction).
Where does maximum bending moment occur?
For a single point load on a simply supported beam, the maximum bending moment occurs at the point of load application. It equals Ra × a (or Rb × b).
Can I use this Beam Reaction Calculator on my own web page?
You can. Look for the "Embed" button near the top of this calculator. It lets you pick a size, border style, and color palette, then gives you an iframe tag to paste into any webpage. The widget is responsive, loads fast, and costs nothing. More details at calculory.com/services/embed-calculators.
AI Assistant
Ask about this calculator
I can help you understand the beam reaction calculator formula, interpret your results, and answer follow-up questions.
Try asking
Related Calculators
More Engineering Calculators
View allTorque and Moment Calculator
Calculate torque from force, distance, and angle.
DSP Calculator
Calculate Nyquist frequency, sampling rate, SNR, and frequency resolution for DSP.
Superheat and Subcooling Calculator
Superheat and subcooling for HVAC charging.
Air Changes Per Hour Calculator
ACH from room volume and CFM.
Related Articles
All articles
Seattle Sales Tax vs NYC, Chicago, LA, and SF: 2026 Guide
Seattle's sales tax is 10.25% in 2026, tied with Chicago and LA for the highest of any major US city. See how it stacks up against NYC, SF, Houston, and Portland.
Read article
Agentic ROI Blueprint: Replacing Roles in 2026
In 2026, teams are measuring total capability, not just headcount. Learn how to model the cost of replacing or augmenting full-time roles with an AI agent stack.
Read article
Best Math Training Apps in 2026: 12 Picks for Students, Adults, and Speed Enthusiasts
We tested 12 math training apps across four categories: academic support, logical reasoning, mental math speed, and gamified learning. See which apps actually improve your skills in 2026.
Read article
Biological Age vs Chronological Age: Real Health in 2026
Biological age tracks how fast your body is aging, not just how many birthdays you have had. Learn how it is calculated in 2026 and how to lower it with measurable habits.
Read articleModern Tools for Every Need
Accurate and Reliable
All calculations run locally. Engineering-grade precision for every calculation.
Verified Precision
Precise Engineering Calculations Powered by Calculory AI