# Beam Deflection Formula

## Beam Deflection Formula

In Structural Engineering, deflection means the movement of a beam or node from its original position. This occurs due to the forces and stresses acting on the body. Deflection, also called displacement, can be caused by an externally applied load or the weight of the body structure itself, and it can occur in beams, trusses, frames and basically any other body structure. This article explains the Beam Deflection Formula using an example. Students can also take the help of the Extramarks website, which provides accurate answers to every question for the Beam Deflection Formula.

Deflection is the extent to which a particular structural member can be displaced using a large load. Also called an angle or distance. The deflection distance of a component under load is directly related to the slope of the deflection shape of the body under that load. This can be calculated by integrating the functions used to describe the slope of the bar under this load. A beam is a long body that can hold loads by resisting bending. The deflection of a beam in a specific direction when force is applied to the beam is called Beam Deflection Formula.

Beams can be bent or moved from their original position. This distance at any point along the bar represents the deflection. There are four main variables that can determine the magnitude of the Beam Deflection Formula which students can easily find on the website of Extramarks.

There are various Beam Deflection Formula that can be used to calculate the baseline value of deflection for different types of beams. In general, students calculate the deflection by dividing the double integral of the bending moment equation M(x) by the product of E and I (that is, Young’s modulus and moment of inertia). Units of deflection or displacement are units of length and are usually measured in millimetres, and this number defines how far the beam can be deflected from its original position. A cantilever beam is a special type of beam that is constrained only by specific supports. These types of objects are naturally distracting because they are only supported on one end.

### Beam Deflection Formula

What is deflection? Deflection refers to the movement of a beam or node from its original position due to forces and loads applied to members. Also called displacement, it can be caused by externally applied loads or by the weight of the structure itself and the gravity force to which it is applied. Deflection can occur in beams, trusses, frames, and almost any other structure.

The force of a person standing on the edge causes the beam to bend and move out of its original position. In the figure below, the blue bar is the original position and the dotted line simulates the deflection of the cantilever beam.

What is deflection or displacement? Simple cantilever example, Beam Deflection Formula.

As students can see, the beams are bending and moving away from their original positions, and this distance at any point along the bar is the meaning or definition of deflection.

In general, there are four main variables that determine the amount of Beam Deflection Formula.

Beam Deflection Formula (Beam Deflection) is calculated based on various factors such as material, cross-sectional moment of inertia, applied force, and distance from supports.

There are a number of Beam Deflection Formula and equations that can be used to calculate basic values ​​of deflection for various types of beams. In general, deflection can be calculated by dividing the double integral of the bending moment formula M(x) by EI (Young’s Modulus x Moment of Inertia).

What will be the unit of deflection? Units of deflection or displacement are units of length, commonly used as mm (metric) and in (imperial) and this number defines the distance the beam is deflected from its original position.

• Cantilever Deflection

A cantilever beam is a special type of beam that is constrained only by supports, as seen in the example above. Since these elements are only supported at one end, they naturally flex more.

To calculate the cantilever deflection, students can use the following formula: where W is the force at the endpoint, L is the cantilever length, E = Young’s modulus, and I = moment of inertia.

### What Is Beam Deflection?

Deflection is the extent to which a particular structural member can be displaced by a large load. You can call it an angle or a distance. The deflection distance of a component under load is directly related to the slope of the component’s deflection shape under that load. This can be calculated by integrating the function representing the slope of the bar under this load.

A beam is a long body that can hold loads by resisting bending. The deflection of a beam in a specific direction when force is applied to the beam is called Beam Deflection Formula.

Based on the type of deflection, there are many Beam Deflection Formula below.

w = uniform load (in units of force/length)

V = shear

I = moment of inertia

E = modulus of elasticity

d = deflection

M = moment

### The Formula For Beam Deflection:

All the formulas and other related formulas can be checked on the website of Extramarks which has proved to be a reliable source of information for students and teachers for years.

### Solved Examples

Example 1: A 50 cm long pin-pin beam is uniformly loaded with 60 g at x = 5 cm. Determine shear.

Solution:

The given parameters are

Length L = 50 cm

Displacement x = 5 cm

V = w(L/2 – x).

= 0.06 kg (0.5/2 m – 0.05 m)

= 0.06 kg (0.25-0.05) m

= 0.012 kilograms.

Example 2: A uniform load of 200 g is applied to n fixed beams of length 30 cm. where x is 20 cm.

Solution:

The given parameters are

Length L = 30 cm,

uniform load w = 200 g,

Displacement x = 20 cm

that moment

V = −wx2/2

= -0.2 kg x 0.22/2

= 0.004 kgm2.