Moment of Inertia of Trapezoid Beam 3

[ZeroStress]

Its been days since I have been struggling to get the right second moment of area for a composite beam.

Attached is the section in question. Concrete slab on top of a steel trapezoid girder. I just can't get the moment of inertia for the two inclined webs of the steel girder. Tried every method, even subtracting the inner empty area's inertia from the full trapezoidal inertia but still not the right answer.

Here is the right answer for the total composite section.

Elastic Neutral Axis after Concrete Transformation: 695.5mm from bottom of the girder.
Total Elastic Moment of Inertia of the Entire Section: 1.201-e10 mm4

Does anyone know any method to calculate the Moment of Inertia for this section? Thanks a million for your help.

 

[jimstructures]

IES, Inc. at

http://www.iesweb.com

has a product called ShapeBuilder version 6.0 (I think) which will do that shape and it is available in a free demo version which is fully functional (i also think).

I have no connection with IES, Inc. except as a satisfied use.

Jim

 

[msquared48]

I agree. Shapebuilder worked for me too. Took a little bit of time to play with it to learn some of the nuances, but it generated a lot of pertinent information.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[RobertHale]

What is your concrete modulus? Assuming it is about 28.72 GPa then, I can get it pretty close (1.206e+10). you should just have to use the "effective width" of the angled portion 9.5mm/cos(36), giving about 11.74 mm. Then just use that number in the 1/12*b*h^3+A*d^2 calculation.

 

[iv63]

Attached are section properties for steel only. I have used AutoCAD’s MASSPROP command.
iv

 

[BAretired]

The trapezoidal section may be considered as composed of four pieces for the purpose of calculating area and moment of inertia...top plate, bottom plate and side plates.

Top and bottom plates are straightforward. The side plates may be considered as two vertical plates with a height of 711mm and a thickness of 9.5/cos36 or a single vertical plate of 19/cos36 = 23.485mm.

The area is 1981*13 + 25*608 + 23.485*711 = 75,651mm[sup]2[/sup], slightly less than found by iv63.

The moment of inertia and centroid may be calculated in the usual manner.

BA

 

[BAretired]

The area above should read 57,651, not 75,651.

BA

 

[JoshPlumSE]

I get the same basic answer with RISASection. That's assuming a ratio of Econc/Esteel of 0.12.

I get a slightly lower I value of 1.15E10 with my hand calc. That's not that difficult of a hand calc. The trickiest part is calculating the moment of inertia of the inclined web. It should be:

I(inclined) = (I_sa + Iwa)/2 + ((Isa-Iwa)/2)*cos(2*theta)

 

[ZeroStress]

Yup. What a relief! Thanks Robert and BAretired. Your idea of taking approximate thickness of the web parallel to axis of calculation is giving very close to what the actual answer is. Thanks to all.

=)

 

[SteelPE]

FYI, AutoCAD can calculate moment of inertia using some simple commands and as long as the section is homogeneous. I believe you create the homogeneous section in AutoCAD. Turn it into a region. Make sure the center of gravity align with the origin and then do a massprop command and it should give you the proper moment of inertial and radius of gyration about bot x and y axis. While you can use these numbers to calculate elastic section modulus you are on your own for plastic section modulus.... but it is helpful.

I hope this helps you.

 

[ZeroStress]

Yea I didn't have any problems in calculating the Plastic NA and then Plastic Section Modulus. But thanks SteelPE, I didn't know about this AutoCAD command before. Will give it a go, just wondering if AutoCAD Lite can perform this command too keeping in mind it doesn't have 3D capabilities.

 

[SteelPE]

Yes AutoCAD LT has this command (at least my version does). There are numerous threads posted on engineering tips about this. You may have some difficulty with the fact that it is a closed section. However, I think you can subtract on region from the next to form your hollow section. If that doesn't work you could always open up a small hole in your section so AutoCAD "thinks" the section is open to the hole. Remember, it must be a homogeneous section (meaning you will need to transform the concrete section to an equivalent steel section).

 

[ZeroStress]

Yea LT does have this command. I just created two regions, one with outside perimeter and one with inside. Subtracted them from each other and massprop gave really close results with the centroid at 0,0 coords.
This probably is much more easier then downloading any specific software for calculating properties. Ofcourse this wont give you detailed properties but still not bad. Thanks.