Tube steel question 3

[prblmfxr]

I have another structural steel question I hope you can help me with. Here is the current situation: We have a number of point loads on a structurally supported, one-way concrete slab. Our calculations indicate that the slab is overloaded due to the concentrated load pattern.

To correct this, our goal is to distribute the individual point loads over a larger area (actually over a larger width of floor, so that more of the slab will be effective in resisting the load).

We are proposing to place a TS section (say 4x2) on the floor, with the weak axis horizontal, probably with some sort of compressible bearing material between the steel and concrete to reduce any localized high stress areas.

I know this is defineitely a "band-aid" approach, but that is the way the client wants to do it.

Question 1: How do I size the TS for this situation?
The width of the point load (1 1/2&quot will be smaller than the width of the TS (4&quot. The length of the point load will be 3".

Question 2: Over what distance will the point load be distributed? In other words, if I have a 10 kip point load on top of the beam, over what distance can that 10 kip load be assumed to be uniformly distributed on the concrete floor? The beam will be continuous over a long distance, with point loads spaced 8' to 9' O.C. along the length of the beam.

Question 3: Any ideas for the compressible bearing material--i.e. ever deal with a situation like this before? We don't want to use grout because it'll be too costly.

Question 3: Referring to Q.'s 1&2, what if I used a W section instead?

Thank you in advance for any help you can give me. If you need additional information, please contact me. I look forward to hearing from you.

 

[breaks]

Q2 - For a point load on one-way concrete slabs, I usually distribute this load at a 45-degree angle downwards on both sides until you reach the horizontal projection of the reinforcing steel. So if the point load is 3" wide and rests on a 12" slab with a cover + bar radius of 2", the width I would distribute the load to would be 3" + 2 x (12"-2&quot = 23".

That's all I can answer off the top of my head. Good luck!

 

[dik]

If I understand the problem, the point loads are too great for distributing laterally to engage enough tributary width of the slab. I also understand that you are attempting to increase the tributary width by using an HSS 4x2 on the flat.

If this is the case, then unless you have a very thin slab, the effect of the 4x2 would be minimal and perhaps negligible... unless acting as a cateniary <G>. If the loads are on the 4&quot; wide surface, they may also collapse the tube wall. If you have the height, it may be possible to pour a concrete curb, or connect a steel beam so that composite action occurs (can even support the deadload to increase the effectiveness of composite effect).

To distribute the load laterally (effectively) stiffness is required; this only comes from sing something with depth or high E value like steel. This would be a real advantage for using a W Section... likely deeper to start with...

If the surface is irregular enough that you require a bearing material, then you might want to consider using 1/8&quot; untempered masonite or something of that ilk... with the smooth side to the steel section.

As for distribution, I've usually used 6 x T + bearing width, but not greater than .25 x S, where T is slab thickness and S is the Span. Example 6&quot; slab spanning 15' and 4&quot; bearing would be 6 x 6 + 4 = 40&quot; or .25 x 15 x 12 = 45&quot; max. Early work done by Westergaard shows that this approach is conservative. Also that the effects of concentrated loading dissipates fairly quickly and with the exception of loads close to the supports, has very little effect on the -ve moment. A bit of a caution, though, the elastic analysis of point loads can vary significantly from an analysis using yield line.

Trust this clouds it a little more...

 

[JAE]

Similar to dik:

Bridge engineers distribute concentrated loads on one-way slabs all the time. They use the AASHTO formula as follows:

The concentrated load is spread over a distance E

E = (4 + 0.06 x S) but not more than 7 feet (or, I would add, the center to center spacing of the posts).
S = span, ft.

Trying to analyze the &quot;help&quot; that the tubes provide would be a little difficult. The load would be distributed over a greater width, but the actual distribution depends upon the relative stiffness of the slab (along the tube) to the tube stiffness. The compressive stress distribution along the length of your tube would look somewhat like a wave, with the maximum being directly under the post, and the minimum being between the posts.

If you use the above equation, you may find that the concentrated loads are, in reality, already distributed over an adequate width.

We have recently studied a one-way slab at a dock in which forklift traffic was cracking the slab. With beams supporting it, there was a unique combination of stiffnesses between the slab and beams. We used a Finite Element analysis of the entire system to determine a more actual distribution of stresses with concentrated loads spaced around the floor. This might be your other option to better understand exactly how the concentrated loads are being distributed. Taking a small width of slab, such as 12&quot; or 24&quot; seems irrational as you know the slab will essentially deflect as a whole. And, per Hooke's law, where there's deflection, there's stress. Thus, you know the slab will tend to work as a unit.

You should also check punching shear through the slab per ACI 11.12.

 

[prblmfxr]

Thank you all for the informative and timely posts.

Dik--curious to where your formula comes from. Can you point me in the right direction?

JAE-- I'm not a highway engineer and not too familiar with AASHTO standards, but from what I've read, isn't the formula you gave based on tire loads--i.e. relatively wide point loads as compared to a 1 1/2&quot; x 3&quot; point load that I'm dealing with? If that's true, using that formula may be a little unconservative.

Any additional thoughts would be welcome.

 

[Ron]

Agree with JAE about the relative stiffness issue. If the stiffness of the tube is less than the stiffness of the concrete section, the distribution will not change significantly. You can prove this by plotting two deflection curves...one on the tube without the concrete, one on the concrete without the tube...then overlaying the concrete on the tube. If they don't intersect for the same span....no distribution!

What about slightly jacking the floor up, and pouring a curb with a little built-in camber? This would be inexpensive and provide you with a true ability to distribute the load. Would also combat the punching shear issue.

Ron

 

[dik]

Further to my note... the formula came from a wiser-older engineer of thirty years back... I checked it at the time... and, I'll have to dig through a couple of my texts to source it. The balance of this response is 'winging' it from memory.

A point load on a structured slab is similar to one on a slab on grade in that the effect is sort of 'local' and as JAE points out, it generates -ve moments transverse to the span. The stress curve is like a decaying sine wave, symmetrical about the point of load application. The actual moment at the point of application is significantly independent of the span distance, except in the larger picture [The moment has a maximum value ( P / (const + factor))] per unit width. As I recall, the point of contraflexure is approximately 1/3 of the span on either side of the point of application. The tributary width from the AASHTO's standards and the approach I've used conservatively reflect this 0.35 x 2 value and consider about 1/4 of it being effective.

The AASHTO value is less conservative than the approach I've used and has likely been used more often, with much heavier loads... I will take a gander at it and consider modifying my approach (I'm not familiar with AASHTO standards other than the truck loading diagrams)

My earlier response was incomplete with respect to checking for punching shear and spacing between point loads... never thought to include it in the posting. JAE's correct in the inclusion of these.

 

[JAE]

prblmfxr - Yes, you're correct that the AASHTO formula is used primarily for tires on slab spans of between 3 feet and 10 feet. With a small, concentrated load, you may have a condition where the source assumptions used in developing this formula (honestly - I am not completely familiar with its development) may not be entirely valid.

dik's formula may also be a similar attempt to rationalize how a concentrated load on a one way slab is spread out. My own preference is actually not to think of the load being &quot;spread out&quot; but rather how the slab will behave under the individual concentrated loads. If you have a load applied near midspan, for instance, on a long, one-way slab that spans about 6 feet, the slab will deflect in a way that looks like a combination of cylinder and bowl shapes. The cylinder shape is due to the one-way nature of the slab and how it tries to behave naturally under load. The bowl shape comes from the fact that the load is discreet. If you can visualize this shape you can see that the bending moment in the slab is obviously a maximum at the load, diminishing as it extends either way down the length of the slab...somewhere hitting zero. Hooke's law dictates that the warping in the slab equates to moment. But how far east and west does the moment extend?

In any case, I'd be safe and conservative. AASHTO and dik's formula perhaps give you a couple of estimations. This could give you at least a handle on how much slab is participating. An exact answer would be difficult.

 

[Gourile]

I agree with Ron. Distributing in the manner you described might probably of no use. If you have enough space to place a w-shape under your load, why don't you connect this section to the floor by means of -say drilling and expanding bolts- and then count on the composite behaviour of the floor and this w-Shape?
The degree of distribution for flexible material depends on the material properties in a long term view. A material that in short term seems to distribute the load in a good sense, may fail after a period of time.

 

[dik]

prblmfxr:
One source I have in my library is &quot;Reinforced Concrete Slabs&quot; by Park and Gamble, John Wiley, 1980, p111-p119. Another text is &quot;Handbook of Concrete Engineering&quot; by Fintel, Von Nostrand Reinholt, 1974, p96 (My texts have whiskers). The latter book has little description, but makes reference to work done by Woodring and Seiss.

I'll see if I can scan the pages of Park and Gamble (have to locate a scanner... my grandson did mine in about a month ago). Can you post your email address to dik@alpha.to?