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Beam Deflection Calculator

Beam Deflection Calculator

This beam deflection calculator will help you determine the maximum beam deflection of simply-supported and cantilever beams carrying simple load configurations.

You can choose from a selection of load types that can act on any length of beam you want. The magnitude and location of these loads affect how much the beam bends.

In this beam deflection calculator, you’ll learn about the different beam deflection formulas used to calculate simply-supported beam deflections and cantilever beam deflections. You will also learn how the beam’s modulus of elasticity and its cross-sectional moment of inertia affect the calculated maximum beam deflection.

What is beam deflection and beam bending?

Image of a structural frame of a house in the middle of construction

In building construction, we usually use framing structures that are held in place by the foundations in the ground. These framing structures are like the skeletons of buildings, houses, and even bridges. In a frame, we call the vertical framing columns and the horizontal ones beams. Beams are the extended members of a structure that carry the loads brought by the horizontal slabs of the structures like solid concrete floors, wooden floor joist systems, and roofs.

When beams carry loads too heavy for them, they start to bend. We call the amount of beam bending beam deflection. Beam deflection is the vertical displacement of a point along the centroid of a beam. We can also consider the beam’s surface as our reference point as long as there are no changes in the beam’s height or depth during the bending.

How to calculate the maximum beam deflection

We equipped our beam deflection calculator with the formulas that engineers and engineering students use to quickly determine the maximum deflection a specific beam will experience due to the load it carries. However, these formulas can only solve simple loads and a combination of these loads. We have tabulated these formulas for you, as shown below:

Simply-supported beam deflection formulas

Table of maximum deflection for simply-supported beam subjected to simple load configurations.

Cantilever beam deflection formulas

Table of maximum deflection for cantilever beam subjected to simple load configurations.

Method of superposition

To calculate the maximum deflection of a beam with a combination of loads, we can use the method of superposition. The superposition method states that we can approximate a beam’s total deflection by adding together all the deflections brought about by each load configuration. However, this method only gives us an approximate value for the actual maximum deflection. Calculating complicated loads would require us to use what is known as the double integration method.

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