Analysis and Design of a Tapered-Section Column 1

[MrFurleyEIT]

I have got a question about the analysis and design of tapered-section columns, either in a pre-engineered building, or in a steel structure. What is the best way to approach this? What is the theory behind it?

Now, I have done some design for columns for purely axial loads, and for beam-columns for axial compressive and bending loads. I am pretty comfortable with W-shape columns, but am not too familiar with tapered-section columns.

I remember my boss asking me to evaluate a tapered-section column, and I was kind of stumped!

I guess the reason I am not entirely sure is because the section of a tapered-section column, by its very definition, changes constantly along its entire length. Which area, and hence, which rx, ry, Ix, Iy, Sx, Sy, etc. should I use?

Also, a tapered-section column is as if it were several members in one single column, and their properties varying as the column go upwards or downwards. Appreciate if someone could provide the theory behind the analysis and design of a tapered-section column, relevant formulas, a worked example, e.g. Relevant references with page numbers would also be most welcome.

Thanks a lot.

 

[COEngineeer]

How tapered are we talking here? I am not trying to give advice because I dont have the experience but I remember taking structural analysis where you plug in the area, I, etc. in term of X and solve it using integration method ( to get deflection). You also have shear and moment diagram along the column then you just look at the shear and moment vs x-section+reinforcement. Or just model it using computer program.

OR just use the worst case scenario but be more generous with buckling.

Thats my 2 cents with my little experience.

Never, but never question engineer's judgement

 

[271828]

AISC/MBMA will publish a new design guide for these in the next few months. That'll be your answer for the long haul.

For the short term, you can help yourself a lot by observing that ry and rt are almost constant over almost any unbraced length. Several other props are too.

The main difference is that rx varies significantly, which affects the strong-axis buckling load. You can calc Ix at about 2/3 the way from the small end and not be too bad off.

Q should be taken as the worst along the unbraced length.

See Appendix 7 for analysis requirements.

 

[prex]

Look in the first site below under Stability -> Columns -> Tapered : you'll be able to compare the critical load for a column with tapered section to that of a prismatic one with a section taken somewhere along the axis.

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[WillisV]

Agree with 271828 - there has been significant research and development put behind the new AISC/MBMA design guide which has been in final draft for a while now. This guide will also focus heavily on using the Direct Analysis Method in conjunction with the tapered column/beam design.

 

[271828]

It is funny.

I think the new DG will really help a lot of folks with this subject. I did my thesis on tapered members years ago and it was really a zoo back then. All that "B" business that the MB guys mostly just ignore.

The subject of tapered member stability bracing still needs work, though. I don't think they touch up on this at all in the new DG. That junk's hard enough for prismatic members.

I love metal bldgs. Might get back into those someday. Definitely the highest ratio of technical difficulty to glamour that I can think of.

 

[csd72]

A few references:

http://www.jcem.vgtu.lt/upload/civil_zurn/sapalas et al paper.pdf

http://scholar.lib.vt.edu/theses/available/etd-358103049751491/unrestricted/etd.PDF

csd

 

[darkwing888]

For design:
You must use the applicable design code such as the 1989 ASD Steel Manual Appendix F7 p.5-102 and Commentary p.5-191...or maybe the 1999 LRFD Steel Manual Appendix F3 p.103 and Commentary p.268...or use StaadPro with the appropriate parameters defined. I would prefer to use StaadPro so I could optimize the solution quickly. StaadPro uses the 1989 ASD Steel manual.

For theory:
Do some research.

 

[haynewp]

I don't think the AISC ASD/LFRD specs were intended to be applied to tapered metal building frames. I would get a copy of MBMA for guidance.

 

[flyby911]

what i see is logic is....

1)for analysis you can model the frame or whatever it is by computer and you can define the column section as tapered..

2)for buckling calculations use the properties of an intermediate section between the min and the max sections

3)for design and checking stresses use the section which suffers the max moment or/and normal forces and that's not an option (it's a necissity)

note:
if you wanna be very accurate..the tapered columns can be modelled as slightly inclined columns because the actual (structural) centerline of the column is in the CG of the section so when it's tapered from one side only the centerline is inclined

 

[darkwing888]

haynewp - Please tell me why you should not use AISC for a tapered column.

 

[haynewp]

Because it is set up for prismatic sections. I didn't say "should not".

 

[darkwing888]

Oh really.

 

[darkwing888]

I wonder why the AISC committee that developed the tapered section code provisions even bothered to do so.

 

[271828]

The 2005 AISC provisions aren't set up *exactly* for tapered member, but very few modifications are needed to make them applicable.

When the new AISC/MBMA DG is available, it'll be the way to go for sure.

For now, to my knowledge, all one can do it modify the Spec. equations. It should be noted that metal bldg companies use the AISC 89 Spec. and mostly ignore the tapered member stuff. To my knowledge, they mostly just use the prismatic provisions and do things like check Q at numerous places along the span, use the worst rT in the unbraced length, etc. At least some metal bldg guys have been programming the 2005 stuff for quite some time now and are just doing the smae thing with that Spec.

It's helpful to not that several of these limit states are really section-by-section checks such as flange local buckling. Also, like I typed before, rt and ry are nearly constant for any reasonable tapered unbraced length. Cw will vary, but I doubt by much. J will vary somewhat, but I doubt it is a big player in the LTB Fcr equation.

The strong-axis column buckling check is the main one to worry about because rx varies enough to cause the calc to be way too conservative if the small end is used, but too unconservative if the big end is used. If a section in the middle, about 2/3 the way across is used, then the strong-axis elastic buckling load is very well approximated. The new DG will give an exact equation for this location.

Shear strength is not greatly affected.

Analysis requirements in Appendix 7 apply perfectly for tapered members and alleviate the need to calculate Kx which could be trouble with tapered members.

Stability bracing provisions are garbage even for prismatic, so tapered member folks are even worse off. The prismatic provisions will certainly be used by everybody.

 

[271828]

"I wonder why the AISC committee that developed the tapered section code provisions even bothered to do so."

Are you referring to the upcoming AISC/MBMA Tapered Member DG or the AISC 89 (or 93 or 99) Appendix F stuff with all the "B" factor business?

 

[271828]

Oh duh, darkwing, hayne is, no doubt, referring to the 13th Ed. Spec. which does not include the tapered member stuff that showed up in every Spec. from (at least) 89 to 99.

People hated that stuff so much that practically nobody used it. Instead, they just came up with home-grown modifications of the prismatic stuff. That void, along with the urgent needs of the metal bldg people, prompted the development of the upcoming DG which IS a reasonable implementation. The advent of the Direct Analysis Method really helped this stuff come together. Before, coming up with Kx was sheer craziness.

 

[haynewp]

271828 is correct

 

[darkwing88]

Below is an excerpt from the NUCOR Product and Engineering Manual 3.0 Specification Guide. It says they use AISC 9th Edition. I don't see any design latitude mentioned (i.e. proprietary design methods using research papers, etc.) At this point, I don't know of a reason not to use the AISC 9th Edition for web-tapered members.

2. Design
2.1. Design Criteria
2.1.1. All structural steel sections and welded plate members shall be designed in accordance with the Manual of Steel Construction – Allowable Stress Design, 9th Edition, American Institute of Steel Construction, Chicago, IL; and the latest edition of the Structural Welding Code – Steel, ANSI/AWS D1.1, American Welding Society.
2.1.2. All light gage cold-formed structural members and exterior covering shall be designed in accordance with the Cold-Formed Steel Design Manual, 2002 Edition, American Iron and Steel Institute. All standards for the welding of coldformed members are based upon the latest edition of the Structural Welding Code – Sheet Steel, ANSI/AWS D1.3, American Welding Society.
2.1.3. The primary and secondary framing and covering shall be designed for all
applicable loads and combinations of loads as set forth in:
2.1.3.1. The specified governing building code for the order under consideration. This may be any of the standard model building codes currently published, such as: the International Code Council’s International Building Code(IBC); the Building Officials and Code Administrators’ National Building Code (BOCA); the International Conference of Building Officials’ Uniform Building Code (UBC), or the Southern Building Code Congress International’s Southern Building Code(SBC). Additionally, many orders may be within states or municipalities that have their own amendments to the governing model code or that have their own independent code. In this case, loads, deflection criteria, and load combinations will be determined in accordance with this governing local code. Specification of loads and codes and design responsibility shall be as stated in Article IV,
“Common Industry Practices”, of the 2002 Edition of the Low-Rise Building Systems Manual from MBMA. These “common industry practices” will apply regardless of the state, local, or model code chosen.
2.1.3.2. In lieu of appropriate state, local, or model codes, Article I., “Design Practices” of the 2002 Edition of the Low-Rise Building Systems Manual from MBMA shall be used to determine loads and load combinations.
2.1.3.3. Design loads shall not be less than those specified in Article IX entitled “Wind,Snow, Seismic, and Rain Data By County”, of the Low-Rise Building Systems Manual, MBMA, 2002 Edition, if there is not a controlling state or local code. If the controlling state or local code specifies values that are less than those found in Article IX, the state or local code takes precedence.
2.1.4. The appropriate code shall be specified at the time of the building quotation.