Learn To Engineer

Learn To Engineer

Uniform Distributed Loads

What is a UDL

A uniform distrubuted load (UDL) is a distributed load which has a constant value such as 1kN/m. Simple point forces do not always provide an accurate enough way to determine the stresses in an object such as a beam so more complex theoretical loads must be used in our analysis. This will be made clear in the following example.

we want to examine the force due to the self weight of a simply supported beam, if the beam is made out of Iron and weighs 35 kg per metre of its span, then what is the force on it?

[math]F = 35{\color{red}kg/m} \times 9.81{\color{red}m/s^2}[/math] = [math]343.35 \color{red}N/m[/math]

Take special note of the units in this equation, we are left with a force of 343.35N/m. this is different to forces that you would previously have seen, because it is a force per metre.

Drawing the UDL

Its quite simple really, it's a lot more arrows than a single point force, you draw vectors along where the load acts and connect the tails of them with a line, the line is representative of the force at that point, because we are talking about UDL's only, the line will always be horizontal in this case. If the load was changing along the length of the beam then the line would represent the magnitude of the force at that point.
Uniform Distributed load
<br>On a Simply Supported Beam
Uniform Distributed load
On a Simply Supported Beam

Working Out Forces (Simplification Method)

if you are not required to draw load, shear force, bending moment, angle of rotation or deflection diagrams you may be able to simplify the distributed load to a point force, for example if the reaction forces of the simply supported beam above were being determined, the whole UDL would be transformed into a point force for the purpose of the calculation.

To change a UDL to a point force you need to know two things:
1: The Total Force, and
2: The location it acts through

To find the total force, you must find the area enclosed by the object being analysed, the left of the UDL, the right side of the UDL and the top of the UDL. for a simple shape such as a rectangle, you multiply the force applied per metre (such as 10kN/m) by the length it acts over (such as 0.5m) to determine the entire force. For more complex loading shapes (non-uniform distributed loads) you may need to integrate the area enclosed by the load to determine this.

To find the point it acts through you must find the centroid of the shape of the load, for any UDL, the centroid is in the direct centre of the load, for more complex shapes such as a right angled triangle (centroid is located 1/3 length from big end) you may need to lookup a table to find the centroid or use integration to find it.

When Simplifying the UDL Doesn't Work (eg: Beam Diagrams)

Sometimes, you cannot transform the UDL into a point force, a point force and a UDL are never equivalent when drawing bending moment diagrams for example. when this is the case, the equation for the distributed load must be determined, for a UDL it is simple the equation is F = A N/m, where A is any number. To work out the shear force diagram for a UDL, the force must be integrated so that it becomes S = Ax N/m, the shear force diagram will vary linearly with a gradient based on the magnitude of the distributed load. Once you have the shear force diagram from a distributed load, you work out the remaining diagrams like you normally would.

If you want, you can use the Learn To Engineer beam calculator to examine the effects of distributed loads on the shear force, bending moment and deflection diagrams:
Examine the effects of distributed loads on a beam