▪ Support reaction at A is

**Rᴀ = 3.3333 lbf**

**Rʙ = 1.6667 lbf**

# Beam Load Calculator

This **beam load calculator** will help you determine the reactions at the supports of a simply-supported beam due to vertical point loads or forces. In this calculator, you will learn what **support reaction** is and learn the basics of how to calculate beam load capacity.

Knowing how to find support reactions is a great place to start when analyzing beams, such as when determining beam deflection. Keep on reading to learn more.

## What is a support reaction?

According to **Newton's third law of motion**, every force on an object has an equal and opposite reaction. If you try to push on to something, let's say a wall, it feels like the wall is also pushing back at you. That is exactly the phenomena Newton's third law of motion describes.

In engineering, structural members such as beams and columns interact with each other at the points where they meet. Imagine a beam that is being **supported** in place by two columns. The beam's weight pushes down on the columns, and, because of Newton's third law of motion, we can then also say that the columns exert an equivalent opposite reacting force back on the beam. We call these reacting forces **support reactions**.

On a simply-supported beam, the support reactions at each end of the beam can either be equal to each other or of different values. Their values depend on the beam's applied loads. If more loads are found at a closer distance to one support, that support experiences more force and therefore experiences a greater reaction.

## How to calculate support reactions in the beam?

Since support reactions act in the opposite direction as the force, we can say that the whole system is in equilibrium. That means the beam is not moving and the summation of forces and moments result in zero. By equating the **moments due to load** to the **moments due to support reactions**, we can then determine the reactions at the supports.

Just like when calculating torque, we can also perform a summation of moments at each supports to solve for the reactions. Below, we express a summation, `Σ`

, of the moments at support A to find the reaction at support B, denoted as `R`

, as shown below:_{B}

`Σ(F * x) - (R`

_{B} * span) = 0

`(F`

_{1} * x_{1}) + (F_{2} * x_{2}) + (F_{3} * x_{3}) + ... + (F_{n} * x_{n}) - (R_{B} * span) = 0

where:

`F`

,`F`

,_{1}`F`

,_{2}`F`

and_{3}`F`

are point loads on the beam at distances_{n}`x`

,`x`

,_{1}`x`

;_{2}`x`

and_{3}`x`

from support A; respectively,_{n}`R`

is the reaction at support B, and_{B}`span`

is the length of beam between support A and support B.

By rearranging the equation, we can isolate `R`

as follows:_{B}

`R`

_{B} * span = (F_{1} * x_{1}) + (F_{2} * x_{2}) + (F_{3} * x_{3}) + ... + (F_{n} * x_{n})

✔**R _{B}** = ((F

_{1}* x

_{1}) + (F

_{2}* x

_{2}) + (F

_{3}* x

_{3}) + ... + (F

_{n}* x

_{n})) / span

Now that we have an expression to find `R`

, and since we know that the total applied forces are equal to the reactions' total, we can now also find the reaction at support A _{B}`R`

, using the following equations:_{A}

` Σ(F) = Rᴀ + Rʙ`

✔**R _{A}** = Σ(F) - Rʙ

## Sample calculation of support reaction

Suppose we have a **4.0-meter** long simply-supported beam with an applied **10.0 kilonewtons (kN) point load 2.0 meters from support A** and another applied **3.5 kN point load 1.5 meters from support B**, as shown below:

To calculate for R_{B}, we formulate the equation of moment equilibrium as follows:

`R`

_{B} = (F_{1} * x_{1} + F_{2} * x_{2}) / span

`R`

_{B} = (10 kN * 2.0 m + 3.5 kN * (4.0 m - 1.5 m)) / 4.0 m

`R`

_{B} = (20 kN-m + 3.5 kN * 2.5 m) / 4.0 m

`R`

_{B} = (20 kN-m + 8.75 kN-m) / 4.0 m

**R _{B} = 7.1875 kN**

By performing a summation of forces, we obtain:

` Σ(F`

_{n}) = 0

` F`

_{1} + F_{2} + (-Rᴀ) + (-Rʙ) = 0

` 10 kN + 3.5 kN + (-Rᴀ) + (-7.1875 kN) = 0`

`R`

_{A} = 10 kN + 3.5 kN - 7.1875 kN

**R _{A} = 6.3125 kN**

Please note that **for this summation**, we have considered all **downward forces as positive** and all **upward forces as negative**. Based on our calculations above, we have now obtained the reactions at supports A and B to be **6.3125 kN** and **7.1875 kN**, respectively.

Also, please take note that in this example and in the beam load calculator, we assumed that the beam is weightless. However, if the beam's weight is indicated, you can consider the beam's weight as another downward point load at the center, or centroid, of the beam.

## Using our beam load calculator

Our calculator is easy and simple to use. All you have to do is **input the span of the beam**, **the magnitude of the point loads**, and their **distances from support A**. At first, you will only see fields for two loads (Load 1 and Load 2), but once you enter a value for x_{2}, the fields for Load 3 will show up, and so on.

If you want to enter an upward load, simply enter a negative value for the load magnitude. In total, you can input up to 11 point loads in our beam load calculator.

## Want to learn more?

Now that you have learned how to calculate beam load capacity by determining the reactions at the supports, perhaps you might also want to learn more about what beam deflection and beam bending is.