Why Is There an Extra Term in the Distributed Load Calculation?

In summary, the question is asking why there is an extra term (60-30y+3.75y^2)-(30y-7.5y^2) in the solution for the net vertical force at point A. The author has divided the triangle into three parts and is trying to find the net force left of point A, which is y to the left of support B. The term in question is the contribution from the load per unit length q, which is 7.5y at point A. The author introduces another variable w for a variable distance left of B and integrates to arrive at the above expression, but it is unclear how the author arrived at it.
  • #1
foo9008
678
4

Homework Statement


For region 8<x<12 , why there's an extra (60-30y +3.75y^2 ) - (30y-7.5y^2) ?
How to get that? I have no idea at all...
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Homework Equations

The Attempt at a Solution


here's my working, i have divided the triangle into three parts, i gt 129-80 -75- (60-30y=3.75y^2) - (30y-7.5y^2)-(3.75y^2) instead of 129-80 -75- (60-30y=3.75y^2) - (30y-7.5y^2)
Is the author wrong?
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  • #2
foo9008 said:
why there's an extra (60-30y +3.75y^2 ) - (30y-7.5y^2)
The aim is to find the net vertical force left of point a, which is y to the left of support B.
The term in question is the contribution from q. The load per unit length from q is 7.5y at a. To avoid confusion, I'll introduce another variable w for a variable distance left of B, ranging from y to 4. The total force over that range from q is therefore ##\int _y^47.5w.dw##. If you evaluate that you should arrive at the above expression, though by what logic the author arrived at it I am not sure.
 

1. What is a moment at distributed load?

A moment at distributed load, also known as a bending moment, is a measure of the internal force that causes a structure to bend. It is typically caused by a distributed load, which is a force that is applied over a large area rather than at a single point.

2. How is a moment at distributed load calculated?

A moment at distributed load can be calculated by multiplying the magnitude of the load by the distance from the point of interest to the center of the load. This distance is known as the moment arm and is typically represented by the variable "d" in equations.

3. What is the relationship between a moment at distributed load and stress?

A moment at distributed load can cause stress in a structure, as it creates a bending force that can result in tension or compression in the material. The amount of stress is directly proportional to the magnitude of the moment and the distance from the point of interest to the location where the stress is being measured.

4. How does a moment at distributed load affect the stability of a structure?

A moment at distributed load can decrease the stability of a structure, as it introduces a bending force that can cause the structure to deform or even fail. The magnitude of the moment and the location at which it is applied are important factors in determining the stability of a structure.

5. Can a moment at distributed load be counteracted?

Yes, a moment at distributed load can be counteracted by applying an equal and opposite moment at another location. This is commonly achieved through the use of structural supports or reinforcements, such as beams or columns, to redistribute the load and balance out the bending forces.

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