Calculating Force R: Distributed Load Homework

[princejan7]

Homework Statement

http://postimg.org/image/7vpxry28t/


Can someone explain how they calculated the force R representing the distributed load?
Did they even make use of the value "800N/m" from the question?

 

[SteamKing]

The calculation for R is included in the solution section. You don't need to use the 800 N/m unless you calculated the value of R using the formula for the area of a trapezoid:

R = (0.6/2)*(400 + 800) = 360 N

I think they are trying to show how to break up a trapezoidal load into a constant distributed load and a triangular load.

 

[Chestermiller]

Homework Statement

http://postimg.org/image/7vpxry28t/



Can someone explain how they calculated the force R representing the distributed load?
Did they even make use of the value "800N/m" from the question?

Yes, they used the 800, but they obtained the force R result a stupid (IMHO) way. The way I would have done it would have been to note that the average distributed load over the length of the member is 600 N/m. If we multiply that by the length of the member (0.6), we get 360 N. They did something like the following: the minimum distributed load over the length of the member is 400 N/m, so this contributes 400 (0.6) = 240N. Over and above that, the remainder of the load varies from 0 at the left end to 400 at the right end (400 to 800, minus the 400 already accounted for). The average of this excess is (0+400)/2 = 200. The load contribution of this excess is (400/2)(0.6)=120N. The total load R is again 360 N. As I said, their method is kinda stupid.

Chet

 

[princejan7]

thanks

 

[Nickie]

To calculate the force R representing the distributed load, we need to use the formula for distributed load, which is the product of the load per unit length (800N/m) and the length of the beam (5m). This gives us a total load of 4000N acting on the beam.

However, we also need to take into account the fact that the load is distributed over the entire length of the beam, not just at a single point. This means that the force R will also be distributed, and we need to calculate the average force per unit length. This can be done by dividing the total load (4000N) by the length of the beam (5m), giving us an average force of 800N/m.

Therefore, the value of "800N/m" from the question was indeed used in the calculation of the force R. This represents the average force per unit length acting on the beam due to the distributed load.