Statics Problem istributed Loads

[Chandasouk]

Statics Problem:Distributed Loads

http://imageshack.us/a/img845/5825/112639502.jpg

When measuring from the left side of the beam Xa,Xb ,Xc ,Xd ,Xe ,and Xf are the locations where the resultant force is applied in each of the six cases. Rank these six locations.

Rank the items from smallest to largest. To rank items as equivalent, overlap them.

For this problem, I just made the assumption the L was equal to 1 so I could work with real numbers.

Xa and Xb I found to be the same locations as in 1/2 because they are rectangles.

The centroid of a triangle is 1/3L from its peak, so Xc I said it was 1/3.

Xd = 2/3 since the peak is on the right hand side this time.

I don't know how to find the centroid of the last trapezoids. I just know that Xf > Xe and that they are somewhere in between L/3 and L/2 from a hint in my HW.

The current ranking I have from SMALLEST to LARGEST is

Xc, Xe, Xf, Xa, Xb (they are equal), and Xd but that is wrong. How do I solve this?

 

[SteamKing]

When the problem statement said rank the locations of the resultant, it appears it did not specify if they should be ranked from smallest to largest or vice versa.

 

[Chandasouk]

Sorry about that

Rank the items from smallest to largest. To rank items as equivalent, overlap them.

I shall also edit my post

 

[laurenwilliams]

This probably doesn't help the person who originally answered the question but the answer is Xc, Xe, Xa, Xb (they are equal), Xf, and then Xd.