Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

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Mechanical Engineering : Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

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Distributed Loads

Wind and water loads, cars on a bridge, and people on a crowded walkway often generate loads that are approximated as a pressure (force per unit area) or a distributed load (force per unit length). In order to utilize our equilibrium equations, however, we need forces and moments. Consequently, it is often necessary to replace a pressure or distributed load with a single force. First, consider a simple example. We will apply a uniform load to a beam that is 3 m long and the space, a between the wall and the beginning of the applied load is 0.5 m. It should be easy to see that, if we want to replace this with a single force, it must be a 250 N load placed in the middle of the loaded region (i.e. Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev 1:75 m).

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

Next, take the system shown below, a cantilevered beam with an increasing, triangular distributed load which peaks at w0.

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

The distributed load has units of force per unit length (N/m or lbs./ft.) and, in this case, can be written as,

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev          (11.1)

In order to ensure that the forces in the two systems are equivalent, we require

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev      (11.2)

which yields,

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

We also want it to have the same moment about the origin. In order to do this we require that,

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev  (11.3)

which yields,

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev

and the position of the force,  Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev must be 2/3 L

Example Here is another distributed load acting on a beam. Replace the distributed load with a single force.

Reduction of a Simple Distributed Loading Mechanical Engineering Notes | EduRev 

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