Solving Beams with Triangular Loads - Why the Third Point?”

In summary, the conversation discusses a question about mechanics regarding the point of application of a triangular load's net force and the division of a right triangle into three equal fields. The expert summarizer explains that the location of the resultant force at 1/3 the distance from the fat end is the center of gravity of the load, and encourages the speaker to calculate it as an exercise.
  • #1
remi_c
3
0
Hi. I can't understand one thing in mechanics.

I am trying to learn how to solve beams in mchanics.

I have a triangular load (a load which changes constantly). Why is the point of application of the net force in the one third of the triangle's base?

While dividing a right triangle into 3 parts, we don't get two equal fields...

Thanx
 
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  • #2
remi_c said:
Hi. I can't understand one thing in mechanics.

I am trying to learn how to solve beams in mchanics.

I have a triangular load (a load which changes constantly). Why is the point of application of the net force in the one third of the triangle's base?

While dividing a right triangle into 3 parts, we don't get two equal fields...

Thanx
You are dividing the triangle into two parts equal in area, or equal in weight. This location of the resultant at 1/3 the distance from the fat end is the center of gravity of the triangular load, which you can calculate as a good exercise.
 

1. What is a triangular load and how does it affect a beam?

A triangular load refers to a load that is distributed along a beam in a triangular shape. This type of load can be either a concentrated load or a distributed load. A triangular load can cause a beam to experience shear and bending moments, which can result in deflection and stress.

2. Why is the third point important in solving beams with triangular loads?

The third point is important because it helps determine the shape and magnitude of the triangular load. This point is used to calculate the area under the load curve, which is essential in determining the shear and bending moment diagrams for the beam. Without the third point, it is not possible to accurately solve for the beam's reactions and internal forces.

3. How do you determine the location of the third point for a triangular load?

The location of the third point can be determined by using the principle of moments. This involves setting up an equation for the sum of moments about a point and solving for the unknown location of the third point. The location can also be determined graphically by plotting the load curve and finding the point at which the area under the curve is equal to the total load.

4. Can the third point be located anywhere along the beam?

No, the third point must be located between the two points of support for the beam. This is because the load must be distributed over the entire length of the beam. If the third point is located outside of the beam's supports, the load distribution will be incorrect and the solution will be inaccurate.

5. Are there any other factors to consider when solving beams with triangular loads?

Yes, in addition to the third point, it is important to consider the type of support at each end of the beam and any other loads or constraints present. The beam's material properties, such as its cross-sectional area and moment of inertia, also play a role in the solution. It is important to carefully consider all of these factors in order to accurately solve for the beam's reactions and internal forces.

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