# area in circle segment.

• May 8th 2009, 06:59 PM
slasherz
area in circle segment.
Hey guys,

hopefully a fairly straightforward question in the right subforum! First, some background. (If you can't be bothered reading, go straight to the blue text)

Currently completing a design project for a civil engineering subject, steel structures.

Basically what i've gotta do is come up with a structure able to support a 1.5t water tank 15 or so meters in the air.

As the diagram below illustrates, it will be supported by 5 secondary beams, which in turn are supported by 2 primary beams.

http://img10.imageshack.us/img10/1272/planview.jpg

In order to design the secondary and primary beams, I have to come up with a weight (kN) that acts upon each secondary beams. This weight comes directly from the effective area from the water tank acting upon each beam. This is indicated by this poorly drawn diagram below: (circle radius is 3m)

http://img15.imageshack.us/img15/3425/47620664.jpg

So i'm after the area of each segment, inside the circle!

Basically, I've got an answer out of my ti-83 calculator, but i was hoping for an answer by hand using calculus, so I can double check my calculator answer as well as submit the calculus calcs with my report.
• May 8th 2009, 10:15 PM
CaptainBlack
Quote:

Originally Posted by slasherz
Hey guys,

hopefully a fairly straightforward question in the right subforum! First, some background. (If you can't be bothered reading, go straight to the blue text)

Currently completing a design project for a civil engineering subject, steel structures.

Basically what i've gotta do is come up with a structure able to support a 1.5t water tank 15 or so meters in the air.

As the diagram below illustrates, it will be supported by 5 secondary beams, which in turn are supported by 2 primary beams.

http://img10.imageshack.us/img10/1272/planview.jpg

In order to design the secondary and primary beams, I have to come up with a weight (kN) that acts upon each secondary beams. This weight comes directly from the effective area from the water tank acting upon each beam. This is indicated by this poorly drawn diagram below: (circle radius is 3m)

http://img15.imageshack.us/img15/3425/47620664.jpg

So i'm after the area of each segment, inside the circle!

Basically, I've got an answer out of my ti-83 calculator, but i was hoping for an answer by hand using calculus, so I can double check my calculator answer as well as submit the calculus calcs with my report.

Use the information on the MathWorld page.

CB