How to analyze a built up section under beam-column conditions?

[TSG024]

I am currently designing a self-stressing precast concrete form, also known as a stressing bed. The pre-stressing steel is subjecting the form to ~2300 kN of load at a 90 mm eccentricity above the centroid of reinforcing steel. The form is supported by two W 250 x 33 sections on the bottom and two HSS 152 x 102 x 4.8 sections at the top, and the combined Ix is 1421 x 10^6 mm^4. So far I've analyzed it as per 13.8.2 of CSA S16-09, but I'm concerned about the compression being added into the HSS sections (the centroid for their area being 440 mm away) that they see an additional load of ~400 kN, which is pretty frightening margin.

If anyone has similar experiences with analyzing something like this (even remotely) or is confident my approach is adequate I would appreciate hearing from you.

 

[BAretired]

How can anyone be confident your approach is adequate from the description you have given?

BA

 

[TLHS]

I have no idea what your arrangement looks like, but if this is a combined section you shouldn't be using 13.8.2 because it isn't a Class 1 or 2 I shaped section. You should presumably be using 13.8.3

 

[Ingenuity]

TSG024,
With a picture being worth a thousand words, your 144 words above would be well served with a sketch...

 

[TSG024]

I've attached a quick sketch to this post, sorry for not including enough detail earlier. I'm doing a couple of these beds and this is another with an addition HSS 102x102x9.5 nearer the centroid.

TLHS: I did use 13.8.3, typo. Thanks!

To clarify:

My approach was to combine the moments of inertia of the resisting elements, taking the I of each section relative to the determined centroid. This gave me 1421 x 10^6 mm^4. I also determined the Section modulus by taking I/c where c is the distance to the HSS 152x102x4.8 nearest the top, being the most extreme fiber (459 mm). From here, I was able to find Mr = (phi)(S)(Fy). Compression was found according to 13.3 and I'm confident with that. I am mostly hesitant with this approach because, simply put, I can't find anything similar to it anywhere. If anyone has similar examples, or notices an error in this methodology, please reply.

These forms were developed a long time ago, they've been in for decades and this is only to determine their maximum capacity with an additional factor of safety as appropriate.


Also, I'm new to posting here, this is a position I just started last week and I graduated 2 months ago. I'm still learning and appreciate your patience.

 

[TLHS]

Unless there's something else happening that I don't understand, your analysis method doesn't work. For something to be treated as a combined section the way you're treating it, there has to be shear flow between the components and they have to deflect as a unit so that sections remain plane with themselves as they bend. Each of your members is independent. As such, they can buckle or bend independently, rather than buckling as a unit. This will reduce your compression capacity quite a bit.

On the plus side, the members likely won't see any appreciable bending. The eccentricity will be taken by the distribution of the compression across the various members. (i.e. you could attack it by spreading compression equally across the members and then using the 'eccentricity' to make a couple moment across your members that you add or subtract)

 

[TLHS]

Also, you're going to have to think carefully about how the load distributes to each of those members. It's indeterminate, and you may find that the stiffness of your form or whatever plate is transferring load may be such that the outer row of columns sees a reduced or negligible load.

 

[TSG024]

Ahg...

Let me clarify further. To make an actual form it's got 1/4" skin along the whole length and all the member are adequately able to transfer shear. You make a really good point though, I should also check the capacity of that (but have been told it's not going to govern).

The whole bed is braced every 600 mm. It's 28.5 m long and is braced so frequently that F_e = 850 000 kN. I've been told by the supervising engineer that it'll be limited by compression/bending and that it's basically fully braced.

While we're at it, I should also mention the header is basically a 840x1850x200 mm block of steel. It's definitely rigid on both ends from that.

 

[BAretired]

The 1/4" skin should be included in your cross section and in your calculation of section properties of the combined section. You should also confirm that the welds which attach the skin to each of the members is adequate to transfer shear flow.

BA

 

[TSG024]

I was instructed to exclude the skin reinforcement from the section properties. The skin does not bear against the header, there's around 20 mm of separation. For this reason I didn't include it in the cross section.

Thanks for your feedback.

 

[dhengr]

TSG024:
That is an awful engineering (?) sketch, such as it is. It shows almost no basic understanding of your real engineering problem, or how to approach it. If your supervisor says everything is fully supported, then ask him about the next steps in the solution, he can see it, we can’t from here. If you want any help here at E-Tips, from afar, you have to show a basic, well proportioned sketch of how the whole bed is arranged, and the parts connected to each other, including the sides, bottom and end bulkheads. Not just six compression elements, in space, relative to each other. Plans, side view, then some real cross sections. Scan them, and then attach them as PDF files so we can print them and study them a bit, not just squint at them through a bunch of kiddy crap. You keep dribbling out a fact a day, and we keep guessing. If we could see what was really going on, and your problem explanation was adequate, we would likely come to the conclusion that the .25" side sheets don’t add much to the compressive strength of the bed, as your boss suggested.

If the end bulkheads are stiff enough and prevented from rotating, and all of the six compression members you show are adequately braced, then treat the six compression members more like springs, with the total load ‘P’ being taken by each in proportion to their relative compressive stiffness. Of course, the stiffness of the bulkheads, their movements and deflections, and the eccentricity of the tensioning forces vs. these reacting forces must be brought into play too. Remember, from your first Strength of Materials class, Δ = PL/AE.

 

[BAretired]

I was instructed to exclude the skin reinforcement from the section properties. The skin does not bear against the header, there's around 20 mm of separation. For this reason I didn't include it in the cross section.

If there is an element of "skin" which is horizontal, you can't exclude it when calculating properties. It could have a profound effect in moving the c.g. of the section. But whether a horizontal plate exists or not, the proper procedure is to consider all parts of the combined section.

The 20 mm gap at each end will affect the stress in the immediate vicinity of the end blocks (which you call headers) but elsewhere, the stresses will be determined by the applied force, its eccentricity and properties of the overall section including plates (skin).

BA

 

[TSG024]

Thanks BA. I'll get the appropriate dimensions for the skin and talk to my boss about. Shouldn't the gap area be taken as the most critical section? The skin reinforcement should only increase the capacity if it's taking load too, no? Just logically it should decrease the eccentricity of the load because it's mostly above the depicted c.g.?

In the mean time I'm trying dhengr's suggestion of treating them as individual columns and taking stiffness into account. The issue I'm finding with this so far is how the moments in each column will distribute across the skin. This was not meant to be done by hand.

Again, sorry about the quality of the sketch, but I'm not going to scan/upload proprietary documents in my second week.

 

[TehMightyEngineer]

Again, sorry about the quality of the sketch, but I'm not going to scan/upload proprietary documents in my second week.

Smart. However, you can probably safely upload a portion of the drawing with all proprietary details removed. It's entirely your call though.

Maine EIT, Civil/Structural.

 

[BAretired]

Shouldn't the gap area be taken as the most critical section? The skin reinforcement should only increase the capacity if it's taking load too, no? Just logically it should decrease the eccentricity of the load because it's mostly above the depicted c.g.?

The gap area is likely not the most critical section because it may be considered a bearing stress. The permissible bearing stress is much higher than axial combined with bending (check your CSA S16).

You are probably correct in your second sentence, but in an earlier post you said:
"These forms were developed a long time ago, they've been in for decades and this is only to determine their maximum capacity with an additional factor of safety as appropriate."

Accordingly, I would say that your analysis should be as precise as possible. If you wish to add an additional factor of safety, that is fine but do it at the end of the process, not half way through.

BA

 

[dhengr]

TSG024:
Nobody’s asking you to give away the crown jewels. But, you could do some sketches which fairly represent the real conditions, so that an experienced engineer could see and understand what’s going on. And, don’t use the system you just used, that’s not an engineering sketch. You would be surprised how much an experienced and knowledgeable engineer can glean from a few good sketches. From what you’ve said, the .25" side sheets are there primarily to retain/form the conc. sides. If they were axially loaded to any extent, they would just buckle btwn. their supports, thus the 20mm gap btwn. them and the end bulkheads, to allow some slight end bulkhead movement. These aren’t text book problems any longer, with min. info., to make you learn one subject item, formula or method. They require considerable experience and judgement, which you will gain over time. You just won’t get meaningful answers if you can’t give enough info. and full enough details to tell the whole story. You should practice looking at a problem and asking yourself, what info. do I need to solve this problem, what info. am I missing, what assumptions can I reasonably make, etc.? Where is the precast conc. in your tangle of six axial steel members? How are the axial members braced without the bracing intersecting the conc. member?