Lateral stability/torsional resistance of steel box girder with lattice walls

[skewl]

I am designing a steel box girder with lattice walls due to geometric/constructability/maintenance reasons. The box girder is built in 2 "c-channel" sections with connection plates connecting the two halves at the top and bottom flanges at a set (to be determined) spacing. The box girder spans 30m and cannot be laterally supported at any point along the span.

I have the following questions:
1) Is this section L-T stable?
Closed sections are typically L-T stable, but in this case, there will be "openings" at the top and bottom flanges. I see this as two unstable L-T members laterally braced to each other, and I cannot wrap my mind around how the connected section will be stable (even though my supervisor believes it will be).

2) How do you evaluate the torsional constant (J) of this section?
The only reference I can find is from "Torsion in Structures (Kollbrunner & Basler 1969)", where a formula is given to find the thickness (t*) of an equivalent plate (see attached PDF). However, the equivalent thickness (t*) appears to be very small.

 

[WARose]

1) Is this section L-T stable?

Just eyeballing it....I'd say: yes. But you can calculate the LTB [Lateral Torsional Buckling] value between the plates (based on that cross section) to make you feel better.

2) How do you evaluate the torsional constant (J) of this section?

Me personally, I'd use this:

For multiple pieces in a (open) cross section: J= ∑(bt[sup]3[/sup]/3)

where:

b=length of each cross-sectional element
t=thickness of each cross-sectional element

This formula is (of course) a approximation....but I have found it to be sufficient in most cases.

 

[ProgrammingPE]

It looks like you might be using the weak axis instead of the strong axis for your moment of inertia in your spreadsheet. If you switch it up, your equivalent thickness becomes 1.56 mm which seems much more reasonable.

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[skewl]

Just eyeballing it....I'd say: yes. But you can calculate the LTB (Lateral Torsional Buckling) value between the plates (based on that cross section) to make you feel better.

Just for my clarity (I am still a structural noob), I assume you mean checking the resistance of the member by assuming the length of the unbraced beam equivalent to the spacing between the plates? Also, if considered the whole section globally, can one-half of the section L-T buckle and then "drag" the other half with it?

For multiple pieces in a cross section: J= ∑(bt3/3)

Unfortunately, this would not give me sufficient J and moment resistance, hence my senior engineer's advice to consider the section as a closed section.

It looks like you might be using the weak axis instead of the strong axis for your moment of inertia in your spreadsheet.

Well, I feel dumb . You appear to be correct and this solves my issue with the torsional properties.

 

[WARose]

Just for my clarity (I am still a structural noob), I assume you mean checking the resistance of the member by assuming the length of the unbraced beam equivalent to the spacing between the plates?

I'd check it at full length (at first) and see what it gives.....in reality the value is going to be some sort of composite between the two cross sections. But if it works with a minimal cross section at max unbraced length.....that simplifies things.

Also, if considered the whole section globally, can one-half of the section L-T buckle and then "drag" the other half with it?

If it buckles? Yes. But you shouldn't be issuing anything that buckles. The forces the plates will see should be from externally applied loads. If it is getting significant axial load.....there are procedures for that (I usually rely on a old AISC Journal article).

Unfortunately, this would not give me sufficient J and moment resistance, hence my senior engineer's advice to consider the section as a closed section.

I don't follow. Are you saying the difference between the formula I gave and the more analytical one you are using is significant? Or are you saying you need the connection plate to get to a J you need? If so, why do you need that J? Rotational stiffness? Moment capacity?

 

[skewl]

Hi WARose,

I have not yet calculated the "J" of the section based on the equivalent plate thickness, but I assume I will have a larger "J" if the section is "closed". I need the "J" for the moment capacity.

Case 1: If I can use the larger "J_closed" (for a closed section) and a warping constant "C_w" equal to zero (for a closed section), then I will achieve the necessary moment resistance at L=30m.

Case 2: If I use the smaller "J_open" and a warping constant "C_w" for an open section, then I can achieve the necessary moment resistance if I can assume each half of the girder is sufficiently braced at each connection plate location. However, each half section would not be able to stand on its own under self-weight (let alone under any other applied load) if the unsupported span is the full length (30m).

This girder has no axial loading but has applied span load above the shear center of the section, hence it introduces a destabilizing LTB effect. As I am typing this post, I realize this situation is very common in other steel bridge constructions. The steel girders may fail in LTB during construction before the steel girder and concrete slab becomes composite, so designers would laterally brace the steel girder against each other. If the connections plates provide sufficient lateral bracing, then I can be confident the two halves of the girder together would be stable (Case 2).

Let me know if any of the assumptions I made are inaccurate. I think I have a good understanding of the problems now after the discussions here. Thanks!

 

[WARose]

Ok I think I follow you now. Your OP made it sound like you were just trying to figure capacities and the mechanics of this.....but now it looks like you need all you can get out of this for capacity. (I.e. the short cuts I was recommending aren't enough.)

 

[Lomarandil]

Away from my reference library right now, but CalTrans studied this and issued a useful paper in relation to retrofits for the old bay bridge.

----
just call me Lo.

 

[human909]

1) Is this section L-T stable?
Closed sections are typically L-T stable, but in this case, there will be "openings" at the top and bottom flanges. I see this as two unstable L-T members laterally braced to each other, and I cannot wrap my mind around how the connected section will be stable (even though my supervisor believes it will be).

Your hesitation seems warranted. "Closed section are typically L-T stable," that is true, but this isn't a typical close section. This is very narrow and long span so even with continuous plates it wouldn't guarantee L-T stability. (I haven't don't any calcs on this just speaking in general given the depth to breadth ratio and the span.

 

[skewl]

This is very narrow and long span so even with continuous plates it wouldn't guarantee L-T stability.

The depth to width ratio is about 3. Can you kindly point me to some references regarding the effect of the depth to width ratio on L-T stability? Intuitively it makes sense, which is why I initially took a double-take. But I would like to know if there are any guidance on this.

 

[phamENG]

kwlbridge - AISC added LTB for rectangular tubes in 360-16. Section F7/4.

 

[skewl]

That is exactly what I was looking for, thank you!

 

[Eagleee]

Interesting situation. Probably the most accurate method of assessing the capacity of your built up beam is to do some finite element analysis (either a linear buckling analysis to get the critical moment or a full nonlinear analysis in which the initial imperfection seeded in the beam geometry follows the shape of the critical buckling mode...this option of course includes the linear buckling analysis to get the mentioned shape).

just for information purposes, as it seems from the above that you are designing acc. to US codes, the snippets below are from a book called ECCS New Design Rules in EN 1993-1-1 for member stability. In showing the background to the establishment of LTB formulas for beam columns that are used in the Eurocode, some guidelines are given with respect to susceptibility to LTB. If you are wondering what the difference is between 'Method 1' and 'Method 2', the story is a long one, but the bottom line is that they both look at the same thing, and both are accepted in the European code.