Section Moments of Area

Draw it on squared paper. Count the squares where more than 50% of the area of the square is inside the object. Exclude the squares where less than 50% of the area of the square is inside the object. Multiply the number by the area of the square and the scale of the drawing. Hey presto.

That compleatly skiped my mind, once i work out the area how can i go on to find the second moment of area (the x-x) of the shape. Working it out on rectangular shapes is easy enought but this one has got me ripping my hair out.

(Comment withdrawn.)

First you need to decide what axis the 2nd moment of area is about. Is this the x-----x on your sketch? Does this line go through the centroid?

Yes the x---x is the axis i am working on and no it doesn't go through the centroid.

currently i am doing a HNC Mechanical Engineering course and we have done bending moments on flat bar and I beams but they don't teach us anymore than that, i want to learn how to work this out so in the future if i have any more 'funny' shapes i have some where to start from.

If you want to understand what is done, go to my #7. When you don't understand the process, the computer becomes a black box and you have no basis for judging its correctness.You could get a reasonable, and quicker, estimate by squaring off the rounded portions.

You need to know the position of x---x. It's probably best to calculate the centroid position first, and work out the 2nd moment about that. If you divide your thingy up into shapes that approximate shapes with tabulated (or calculable) 2nd moments, you can build up the total 2nd moment. But note these individual pieces won't usually be about their own centroid, so you need to use the parallel axis theorem to work out the 2nd moment for each about the main centroid, then add them.

Then if you want the answer about some other line, use the parallel axis theorem again.

I would guess the value about the centroid would be something like that of a pipe 80 OD, 16 thick = 4.75*10⁶ = pi*(D⁴ - d⁴).

Sorry, dropped a cod in the calculation. Should be pi/64*(D⁴ - d⁴) = 1.19*10⁶.

I've worked out the area it is 1574.454mm^2

Is there anyway now to get the second moment of area?

7 significant digits? Wow! Not bad for a starting drawing with no more than two in any of them....

I found out how to work out the area on the 3D software, i was hoping it would show me the second moment of area aswell but sadly no.

I agree with too many significant digits. Many people just don't seem to be aware of significant digits. If the calculator or computer can spit it out it is OK! But it's not; you can't improve the precision by running it thru a calculation.

Having read (I think) all the previous posts, and realizing that some of your dimensions are radii and some are diameters, I had to check for myself.

According to my CAD program (VectorWorks), and assuming all of your dimensions are defined and therefore have as many significant figures as needed, I get an area of 1559.8 units^2 (you didn't say what units). I could have given more significant figures, but there is no point, since we disagree at the third significant figure. Some folks don't count an initial one as a significant figure, so it might only be two...

Obviously, either my drawing does not agree completely with yours, or at least one of our CAD programs has an error in the area calculation. Here's mine above yours:

This could be done by hand, remembering that every segment is either an arc or a straight line, so it would be a matter of adding and subtracting sections of circles.

Sorry - I didn't have my precision set high enough to see that I had the r50 arc very slightly undersized. Once I corrected that error, Vectorworks agrees with all the others at 1574.45 units^2.

If you can draw this in Auto Cad it has an area feature command.

However that won't show you the math.

Inventor says:-

sorry its not the radius which is 100 its the Diameter which is 100

Then it doesn't look like that, then, because the 100 diameter is now actually smaller than the 84 radius given the common centre point.

Start again?

I ment if you look at the drawing you can see there is the Dia symbol (Ø) and not the raidous symbol (r)

Quite right, my error. Inventor re-calculates the area as 1574.45mm2

Opps.. you have diameters vs radii error here I think, I did the same thing but then took a re-look, as I avoid diameter unless it is a full round feature.

It's pointless these days to try and calculate these types of problems by hand. It's time consuming. If it's only to learn the fundamentals that's one thing but to do it on a regular basis... use CAD software!....We can still navigate the seas using a sextant but...why?

I agree, I assumed it was to learn and understand, rather than to do. But then he tells us he has software although he can't get second moment from it, so....

Because a sextant doesn't need anything but the sun. A calculator &/or GPS needs a power source. I can think of several ways off hand to lose the power source for higher tech.

I was trying to illustrate a point but I think you know that and you're just being silly. Have it your way. Throw your smart phone in the garbage, take a bat to your computer, disconnect the electricity and water from house, drive your car into the river!

Now...go build an out house, by a horse, and get crackin' on that fire. Let me know how that works out for ya!

I'm not being silly. Even the Navy teaches it's deck officers STILL to navigate by sextant simply because any powered gadget CAN fail.

I understand that but I'm trying to illustrate a point in the context of this thread which is about calculating area for an irregular shape. The point being that....there is no point to calculating by hand if you have access to a CAD program. Yes the computer can fail and you'll have to resort to the hand calcs so it's good to know the fundamentals but...that's irrelevant in terms of the computer being your first choice to do the job. Similarly, there is no point to using the sextant if you have modern GPS and nav equip. I didn't say learning how to use it is pointless. I said that you'll always choose the GPS first because it's easier. That's all I was try to say earlier in just a few words.

Wow! This was kind of like having to explain a joke. I'm spent. Cheers.

You have totally missed the point that bluebelly and I are making about marine navigation which applies especially to the type of small boats that I sail. Sextants and manual course plotting are not alternatives to GPS and radar, they are complementary. When a GPS fails you cannot apply a parking brake and spend 20minutes calculating manually where you are. There are no points of reference when the horizon is flat in all directions, and your GPS screen is blank so that won't help. If you stop you drift or are carried by the tidal flow and if you do not immediately know where you are when the GPS fails, you also cannot look up the speed and direction of the current in the prevailing conditions and work out if you are moving towards rocks or into a busy shipping lane. I can quote you lots of examples where over reliance on automatic navigation has led to disaster and loss of life. MV Torrey Cannion and VLCC Metula are just two. I used CAD to calculate the answers I offered for the area. It was appropriate as you say. I use GPS to enter way points and sound an alarm when I need to change course. But I always know where I am and that knowledge is methodically logged so that in the event of GPS failure I can carry on using manual methods. I rarely use my sextant to shot the sun or stars, but I use it all the time to triangulate between my position and two known points on the coast. Partly I do it to keep in practice so I can use it correctly and quickly in and emergency.

Fine to use technology where it is appropriate. The example you quoted is one where reliance on GPS in wholly inappropriate and down right dangerous.

"You have totally missed the point that bluebelly and I are making about marine navigation which applies especially to the type of small boats that I sail"

"The example you quoted is one where reliance on GPS in wholly inappropriate and down right dangerous"

It's completely irrellevant to this thread and I'm dismissing the point not missing it! You're way too fixated on the GPS thing / navigating the seas and going...overboard with this whole thing. It was just an example and it has clearly upset you.

As I said, subsitute the sextant / GPS example with the lighter vs rubbing to sticks together. Forget I even mentioned sextant. This way nobody gets lost at sea.

Others reading these post are probably rolling their eyes right now.

You'd think that Aeroscraft would have this all worked out already......

"You'd think that Aeroscraft would have this all worked out already......"

Yup. Probably using CAD!!

This one diverges a finit no of arcs(sectors) and triangles - just a quick check - and there're not too few of'em

(you must be more tired than i am v-.-V)

Ive done some cals to work out the centroid and the area

this now proves the center of gravity,

now i need help on where to go from here to get the second moment of area.

anyone got any ideas?