Slenderness ratio for column having different cross sections

[Awre]

Hello,

I was researching a way to calculate the effective slenderness ratio for column having different cross sections. The application I need to perform this on is to estimat the axial loading capacity for a deteriorated timber pile in marine environment. The pile diameter is 12" and necks down to 7" then back to 12".
I came across an article which I thought may help (but in Japanese "attached" which I don't understand!).
I was hoping if somebody advices on an english source on this topic. Any idea on estimating the axial load in this condition or calculation example are also appreciated.

Thanks

 

[BAretired]

adfo,

A column of length L hinged at each end and symmetrical about the midpoint will have the same critical load as a column fixed at the midpoint and free at each end but the two half columns may not buckle in the same direction.

I'm not sure if I answered your question or not.

BA

 

[csd72]

If one end is fixed then the buckling capacity would be substantially larger than a 7" column.

 

[BAretired]

csd72,

Not if the other end is free.

BA

 

[Awre]

I'll see if I can setup a spreadsheet for it, the method is a bit lengthy. I may try STAAD. I don't have NDS added to STAAD, not sure if it exists for STAAD

Attached is the pile sketch

 

[BAretired]

The top of pile is free. The base of pile is embedded in soil, so where is the point of fixity? I think it depends on the flexural rigidity of the pile as well as the modulus of elasticity of the soil. You could consider it a beam on an elastic foundation, axially loaded.

It is not a simple problem.



BA

 

[IDS]

Is there any reason for not just doing a buckling analysis in a frame analysis program?



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[csd72]

BAretired,

Think of the cantilever from the fixed end and how much less that will buckle if it was 9" not 7" then translate this into an effective reduction of the buckling length.

It will still be the 7" section in the middle that will be the first thing to fail but this will be significantly stiffer against buckling.

 

[BAretired]

csd72,

If we are comparing hinged/hinged to hinged/fixed, then I agree the critical load will be higher in the latter case if L is the same.

If we are comparing hinged/hinged to free/fixed, then the critical load will be lower in the latter case if L is the same.

In the actual structure, it appears that one end is free while the other end is restrained against rotation but not fixed. If L is the length from top of pile to the soil below the water, the effective length of the pile, assuming a constant EI will be greater than 2L.

For the tapered shape shown in adfo's latest post, there is insufficient information to determine whether the critical load is controlled by the 12" section at the bottom or the reduced section higher up.

BA

 

[vandede427]

Structural EIT,

If you're reading theories on Elastic Stability at home in your spare time, then you're too deep into engineering.

Put down the pencil and go to a baseball game. Play some Xbox.

 

[msquared48]

BARetired:

A minor point here...

You said above that "The orientation of the member is not relevant. An axially loaded member is the same whether it is vertical, horizontal or at any other angle."

If you discount the weight of the member, this is true. But when you set a compression member on it's side, gravity self-weight loads need to be considered in the buclking model as this will cause lateral instability in the direction of the gravity load, increasing the P delta effect and reducing the ultimate buckling load.

Mike McCann
MMC Engineering

 

[BAretired]

Mike,

You are quite right. I was considering that the only force acting was axial. The example performed by Timoshenko did not consider any load normal to the member. It was taken as horizontal more for the convenience of displaying the calculations than anything else.

If a normal load is considered to be acting simultaneously with the axial load, the same technique can be used (Newmark's Numerical Procedures) but the moment at each station will be increased by the gravity load moment.

BA