How do you calculate the support reaction of a simply supported beam?

Author

Christopher Ramos

Published Feb 27, 2026

How do you calculate the support reaction of a simply supported beam?

To determine the reactions at supports, follow these simple steps:

Let the sum of moments about a reaction point equal to ZERO (ΣM = 0)
Let the sum of vertical forces equal to 0 (ΣF_y = 0)

Also, how many reactions does a simply supported beam have?

3 support reactions

One may also ask, how do you calculate beams? How to Calculate Load Bearing Beams

Calculate the weight the beam must support.
Calculate the maximum bending moment for the wooden beams.
Calculate the beam's section modulus by dividing the maximum bending moment by the allowable fiber stress for wooden beams.
Calculate the section modulus for the different beams which you could use.

Likewise, people ask, how do you calculate bending moment for simply supported beam?

In case of simply supported beam, bending moment will be zero at supports. And it will be maximum where shear force is zero. Bending moment at point B = M(B) = R1 x Distance of R1 from point B.

What are the types of beams?

The four different types of beams are:

Simply Supported Beam.
Fixed Beam.
Cantilever Beam.
Continuously Supported Beam.

What is beam reaction?

Reaction is a response to action that is acting on the beam in the form of vertical forces. In order to calculate reactions R1 and R2, one should must be familiar about taking moment and law of equillibrium. Take moment about point D, for calculation of reaction R1.

What is moment reaction?

A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. Beams can also have one end fixed and one end simply supported.

What is a load diagram?

The loading diagram is a visual representation of the loading on the beam being designed. Below the loading diagram there is also a summary of the various loads on the beam.

What is fixed beam?

A fixed beam is one with ends restrained from rotation. In reality a beams ends are never completely fixed, as they are often modeled for simplicity. However, they can easily be restrained enough relative to the stiffness of the beam and column to be considered fixed.

How do you solve a beam problem?

Solving for beam reactions

Draw the beam free body diagram.
Replace the uniform distributed load (if any) with the equivalent point load.
Solve ΣM_A = 0 (sum of moments about support A).
Solve ΣM_B = 0.
Using R_A and R_B found at steps 3 and 4 check if ΣV = 0 (sum of all vertical forces) is satisfied.

What is the use of simply supported beam?

Simply supported beams

A simply supported beam is one that rests on two supports and is free to move horizontally. Typical practical applications of simply supported beams with point loadings include bridges, beams in buildings, and beds of machine tools.

What do you mean by simply supported beam?

A simply supported beam is a type of beam that has pinned support at one end and roller support at the other end. Depending on the load applied, it undergoes shearing and bending. It is the one of the simplest structural elements in existence. The following image illustrates a simply supported beam.

What happens when a load is applied to the beam?

When a beam structure is placed under load the behaviour is the action or actions that can be observed as the beam responds to that load. Cracking is the breakdown or alteration of the molecular structure of the material as it compresses or experiences tension due to a load being applied.

How do you calculate beam load?

Calculating Shear Force and Bending Moment

The load acting over the section RS of the beam will be equal to W. δx (moment of Force). Now assuming the Shear Force at point R to be = F, Then at point S it will be F + δF.

How do you calculate dead load?

Dead load = volume of member x unit weight of materials

By calculating the volume of each member and multiplying by the unit weight of the materials from which it is composed, an accurate dead load can be determined for each component.

What is I in beam deflection formula?

There is a range of beam deflection equations that can be used to calculate a basic value for deflection in different types of beams. Generally, deflection can be calculated by taking the double integral of the Bending Moment Equation, M(x) divided by EI (Young's Modulus x Moment of Inertia).

What is the slope of a beam?

Deflection of a beam: The deflection at any point on the axis of the beam is the distance between its position before and after loading. Slope of a beam: slope at any section in a deflected beam is defined as the angle in radians which the tangent at the section makes with the original axis of the beam.

What is deflection formula?

There is a range of beam deflection equations that can be used to calculate a basic value for deflection in different types of beams. Generally, deflection can be calculated by taking the double integral of the Bending Moment Equation, M(x) divided by EI (Young's Modulus x Moment of Inertia).

How do you find the maximum stress of a beam?

where I_c = b·h³/12 is the centroidal moment of inertia of the cross section. The maximum shear stress occurs at the neutral axis of the beam and is calculated by: where A = b·h is the area of the cross section.

What is unit load method?

In truth, displacements lie at the heart of how structures sustain loads. The unit-load method is a technique that will help us to quantify displacements and rotations of the equilibrium configuration, that is, the shape of the structure after it has managed to equilibrate the applied loads.

What is elastic beam theory?

Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams.

What is the bending moment at end supports of a simply supported beam?

The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported at both ends. Simply supported means that each end of the beam can rotate; therefore each end support has no bending moment. The ends can only react to the shear loads.

What is SFD and BMD?

BMD(Bending moment diagram ) is a diagram representing the variation of bending moment along the length of member . SFD(shear force diagram ) is diagram representing variation of shear force along the length of structural member .

What is bending moment in beam?

A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. Beams can also have one end fixed and one end simply supported.

What is bending moment diagram?

The bending moment diagram shows where and how the moments will act on the structure, i.e. how a structure will bend, on application of a load or a combination of various types of loads and hence steel reinforcement can be provided respectively in the areas subjected to tension to strengthen them and the member sizes

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