Short Column Deflection

[kylelo]

A short column is said to depend on material strength only. But you know deflection still occurs. It may be negligible, but I'm computing the corresponding strain of concrete at mid-height with respect to the upper and lower region. If concrete fails at a strain of 0.003 at mid-height. What formula do you use to compute for the strain at the upper region. I'd like to compare them. Please see color diagram of the strains attached herewith.

 

[kylelo]

More specifically. Is the eccentric loading interaction diagram for a short column at mid-height only or throughout the span? I'm assuming the compressive strains at mid-height is greatest and getting smaller at top and bottom. Do you hold this position too?

 

[Ron]

What is inducing bending in your column? Eccentricity? Variable cross-section?
Generally this is a concern for bending elements, not columns with no lateral loading.

If loading is axial, then buckling should be checked.

 

[kylelo]

It is column of exterior wall with eccentric loading and falls under short column (not slender column). But in the computations of interaction diagrams and especially compression blocks, they assume it occurs in all parts of the short column (from top to bottom with same value). But I think it actually occurs in mid-height only, with varying and larger compression blocks further away (as the compression strain gets less), right?

 

[BAretired]

A short column loaded eccentrically top and bottom must be designed for the factored axial load Pf and the moment, amplified for the effects of member curvature. The amplification factor is given in CSA A23.3 and presumably in other concrete codes as well.

BA

 

[paddingtongreen]

The maximum compressive stress and therefore, rate of strain, is at the bottom. it is frightening that you might think it otherwise.

Unless, of course, you are holding back important information, perhaps the eccentricity at the top is matched by the eccentricity of the support at the bottom.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[kylelo]

In a typical beam, the maximum moment occurs at midspan, and it is where the first tensional crack occurs.

In a typical column, the maximum moment occurs at mid height, and it is where the first compression failure occurs (reaching strain 0.003).

Can how can moment be maximum at the bottom of the column?

 

[frv]

kyelo,

In a typical beam (and especially in a typical concrete beam) the maximum moment most certainly does not occur at midspan. In a typical column, a similar situation occurs, but in addition you are adding the self-weight of the column at the bottom of the beam. I echo paddington's comment.

 

[paddingtongreen]

kylelo, a beam is loaded along its span, your column is not. You have a moment at the top plus the applied axial load. as you move down the column, the axial load increases by the weight of the column. If you have the P-delta effect in there it modifies this only slightly for a short column. if this were an homogenous material, you would have:
P/A + or - M/Z with P/A increasing as you go down the column. If P/A is greater than M/Z at the top, it doesn't go into tension art all.

I still find it scary that you could not see for this yourself. You are in need of a mentor.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[BAretired]

It really depends on how the short column is loaded. If the load at each end is applied with eccentricity 'e', what kylelo is saying is that the eccentricity at mid height will be larger than 'e' because of column bending. That will cause maximum compressive stress at mid height. The weight of column is presumed small compared to the axial load.

BA

 

[paddingtongreen]

I did leave that door open in my first post although I wasn't thinking pinned base. My thinking though was that the axial load would have to be high to cause a significant moment.

I do dislike these incomplete descriptions, they lead us down the garden path until we draw out the details, bit by bit.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[msquared48]

My thought too is that there will tend to be more "natural" as opposed to "designed" fixity at the ends of a short column as opposed to a long one for columns sections of the same size, due to the greater potential for lateral deflection in the longer columns.

Mike McCann
MMC Engineering

 

[MJB315]

Kylelo,

What are you trying to check? Are you designing an actual corner column for a building, or are you asking the question in the abstract?

I ask, because I'm thinking along the same lines of Paddingtongreen. It does not matter how a "typical beam" or "typical column" behaves...because the definition of "typical" varies so widely.

If this is an actual building element that you are designing, be sure to satisfy the design checks required by the governing building code. Know your first principals, and know what those design checks are based upon-- but do not design a building element just based an elastic FEM model with likely unrealistic end conditions and say that it is adequate because the strain in the concrete is below 0.003.





"We shape our buildings, thereafter they shape us." -WSC

 

[kylelo]

MJB315, I'm not yet designing. Just a fresh grad and reviewing my lessons. If you will review any book on short column and that includes any books for engineering students. It is emphasized short column is only based on material strength. Then you will be taught about the interaction diagram and how to compute for balance failure where the eccentricity and axial is such that the ultimate compressive strain is balanced by the tension at opposite side of the column just when it yields. From this you get the section sizes based on the eccentricity and axial load interaction diagram. Most books on the section of short column doesn't emphasize how the eccentricity varies along the height just like what BA described below:

It really depends on how the short column is loaded. If the load at each end is applied with eccentricity 'e', what kylelo is saying is that the eccentricity at mid height will be larger than 'e' because of column bending. That will cause maximum compressive stress at mid height. The weight of column is presumed small compared to the axial load.

The above is what I have in mind and inquiring how the compressive stress at mid height differs to the top and bottom and how much the value it varies. This is for a column at exterior side of any building with beams framing to it in one side only or eccentric loading.

Paddington stated how the axial load increase as you go down the column. Now combined with the fact it is an exterior column with eccentric loading. Maximum compression stress occurs then just below mid height for the compression block at ultimate strength?

Now if the ultimate load is exceeded, the concrete crushing will be just below mid-height? Is this what occurs in tests and damaged buildings?

 

[hokie66]

Not getting into this argument, but for an edge or corner column in a building, column bending is not all due to gravity load eccentricity. Don't forget the lateral load imposed by shrinkage of the floor structure. Cracks are common on the outside face of columns in low rise buildings.

 

[paddingtongreen]

I don't, in real life, see eccentric supports for concrete columns. If the model has equal moment top and bottom, it is subject to circular bending from the moments plus a moment that is zero at the ends and maximum in the middle from the axial load by the deflection.

I question the constituents of the starting moments, big axial load small eccentricity or small load big eccentricity. If it is big load, small eccentricity, does the bending stress ever exceed the axial stress?

If you start off with the axial load by the eccentricity, call it P_xe, it causes a deflection which increases the moment to P(e+delta), this again increases the defection etc.

There is a way to calculate this, BA put up some papers with a successive approximation method which can be as accurate as you wish. I think one of the guys has it on a website. I don't know where I put my copy. We used to use the plain concrete shape and modulus for deflection calcs but I'm not sure what they do now.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[kylelo]

In short column, you often see the illustration in the file enclosed where (a) is a loaded column subject to eccentric compression (b) is the strain distribution at section a-a; (c) is the stresses and forces at nominal strength

The formula in short column for the compression block in the interaction diagram for combined bending and axial load on one side (please see file picture) is:

c = d * (strain of concrete/strain of bars and concrete)

where d is the distance from one edge to the bars of the other side

All references mention this and treating like this compression block is the same for the whole length of the column.

My inquiry is whether this only occurs at mid-height with the top and bottom having larger compression block. If true, how large is the difference and how do you compute for it? Could the compression block for example at the top most part of the column be 50% larger?

 

[JAE]

Moments in columns can vary in different manners depending on the framing system of the overall structure.

Many times, in tall structures, the columns experience more of a "bowtie" moment diagram with max. moments at the ends and zero moment in the mid-height.

Other types of buildings have max. moments near the mid-height. It all depends on the structure, the bracing system, whether you have moment frames, shear walls, etc.

There is NO general rule that says that columns have max. moments at particular locations.

The column design along its length would vary then as P/A varies down its length (a bit) and moment varies.

 

[kylelo]

Ok. Jae. But I'm talking of isolated column with slenderness ratio about 8 only which is considered a short column. A column is considered a Slender Column when it's slender factor becomes 15 (length of column divided by column depth). So for our discussion. Let's consider a short column only.

If you will do the experiment on an isolated short column with eccentric loading at a certain e. How much do you think the compression block vary between mid-height and the ends of the column? (this isolation experiment ignores the framing system of the overall structure, bracings, moment frame, shear walls etc, just for sake of discussion).

 

[JAE]

P load at an eccentricity of "e" results in a uniform moment down the length if the base is fixed.
If it is "pinned", then the moment is a triangle with max. at the top and zero at the bottom.

In reality, you are somewhere in between.