Second moment area - formula validation

[RPM7]

Hi Everyone,

I'm trying to calculate the deflection of a beam but I'm not 100% sure about my calculation of the second moment area.
I've compared it to the section properties in a cad model and they don't seem to add up.

I'd be grateful if someone could have a quick look over my formula and correct me on where I've gone wrong.

Thanks

 

[hokie66]

It looks as if you are using the right approach, which is called the parallel-axis theorem. But your arithmetic is all over the shop, and your number is too large.

Hints: 1) Keep all your calculations in mm, makes it all much simpler. 2) Don't use the same symbol to mean two different things. You have used d2, etc. to mean both the depth and the distance to neutral axis, and have used the wrong one to find the area. 3) After you revise your calculations, go back and check it another way by using the moment of inertia of the whole rectangle, then subtracting the voids, again using the parallel-axis theorem. This will be good practice for you, and will prove your answer if the two match.

 

[RPM7]

Thanks hokie66.

I've got it working now.
I was doing this late last night and completely overlooked the basic stuff .
I thought it was the formula itself that I had wrong.

 

[Engdoitbetter]

My result is 6.35*10^6 mm^4 for the second moment of area

 

[rb1957]

I1 and I2 look wrong ... I2 should be much bigger than I1, and I3 should be about 4x I1

other than that i think it looks ok, nicely laid out.

Quando Omni Flunkus Moritati

 

[RPM7]

I have it all working ok now.

It might not look elegant, but I'm confident that they're right as they match the cad section properties.
I thought I'd upload the results in case someone else may be looking for something similar. I've also included the results based on the Y-axis.

Thanks for all the input.

 

[rb1957]

looks plenty elegant, to me at least.

how'd you mess up the Ii calcs ? (since they're changed a lot)

Quando Omni Flunkus Moritati

 

[RPM7]

The formula was correct but I had duplicated d1, d2, & d3.
The wrong input was then being referenced for the main formula.

So basically, instead of using the height of each rectangle, the centroid was used.