Finding Kip/Ft: Homework Solutions & Explanations

[1question]

Homework Statement

Number 1-5 from here http://www.slideshare.net/hotman1991/met-302-chapter-01

How do I deal with the 1.5 kip/ft? Am I right to think that the smaller arrows to the left mean that the kip/ft there is less than 1.5kip/ft? How can I find kip/ft at a given point along the horizontal axis?
* I know that the answers are given, however I do not understand it.

Homework Equations

Possibly A = 1/2(b*h) = 1/2(12)(1.5) = 9 kips

EDIT: I also found the same 9kip/ft through ∫(1.5x/12)dx from 0 to 12.

The Attempt at a Solution

The answers use area to get total (?) kips. I sort of understand why they would do that, something like integrating from 0-12 ft. However, I do not understand how they found 9kips at 4ft from B, or why they put the 9 kips there at 4ft.

 

[SteamKing]

The triangularly distributed load is 0 kip/ft on the left side and 1.5 kip/ft on the right side.

The total load is not 9 kip/ft, it's 9 kips, period.

What is the location of the center of gravity of a right triangle?

 

[1question]

The triangularly distributed load is 0 kip/ft on the left side and 1.5 kip/ft on the right side.

The total load is not 9 kip/ft, it's 9 kips, period.

What is the location of the center of gravity of a right triangle?

Yes, sorry about the units mix up.

Ah, I see what you mean. So we take it as if the 9 kips is at the center of gravity... Do we ignore the vertical part of the center of gravity? The answer seems to do so (both equations and equations don't take it into account).

 

[SteamKing]

The load is along the length of the beam. You are confusing the graphical representation of a distributed load with how the load is actually distributed. In other words, the vertical component doesn't exist.

 

[1question]

The load is along the length of the beam. You are confusing the graphical representation of a distributed load with how the load is actually distributed. In other words, the vertical component doesn't exist.

Whoops. Thanks for reminding me. I appreciate all of your help.