Slenderness ratio for column having different cross sections
Slenderness ratio for column having different cross sections
(OP)
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
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






RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
BA
RE: Slenderness ratio for column having different cross sections
Can you tell me what procedure you use to make it extremely easy?
RE: Slenderness ratio for column having different cross sections
BAretired - The file is pdf and has japanese characters. I'am reattaching it anyway.
RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
The procedure I have used is Newmark's Numerical procedures. Page 122 of "Theory of Elastic Stability" (second edition) by Timoshenko contains a simple example using this method. For a more complicated case, you would divide the member into many more sections.
I believe, although I have not done it myself, that the method could be set up on a spread sheet if you had a lot of similar problems to solve. Happily, these things don't seem to occur too frequently.
BA
RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
I looked at the referenced book but have couple of comments on using it for the application I need:
1) On figure 2-43(b)in page 113, the shown system is opposite to the one I have. For deteriorated pile the thinner section is in between the two thicker ones. So I can not directly use the values at Table 2-10 to obtain the factor "m" since I1/I2 will be greater than 1.
2) It's also a question on if this method could be applied on timber columns. Other factors comes to the play when analyzing the stability of timber column(Fce, Cp, etc.).
I setup a spreadsheet to calculate the stability of a constant section timber column. I think a conservative approach to model the deterioration is to assume that the entire length have this minimized diameter. I realize this may under estimates the actual capacity of the pile but still not sure how to apply the deterioration in the middle for the reasons stated above.
RE: Slenderness ratio for column having different cross sections
http://www.seaofsc.org/Alex's%20Corner.htm
and use this spreadsheet
POLYNOM
Great Alex. I have never seen such nice guy. Every time I go to his page, my heart is ponding and my credit card is shivering that now I got to pay but ! ! !
RE: Slenderness ratio for column having different cross sections
You cannot use the values in Table 2-10 but you can follow the example on page 122, except that your value for EI will be smaller in the central section than the ends.
If you want more accuracy, use more sections each with the appropriate EI. Using the Newmark method is very straightforward and easy to carry out.
BA
RE: Slenderness ratio for column having different cross sections
The procedure is the same whether the middle is bigger or smaller, you just change the ratio of I1/I2 as req'd.
RE: Slenderness ratio for column having different cross sections
Table 2-10 considers only I1/I2 ratios less than 1.0 so you can't use the table, but using the transcendental equation on p. 114, a solution is available by using the appropriate value of I1 and I2 for k1^2 and k2^2.
BA
RE: Slenderness ratio for column having different cross sections
I don't have Timoshenko's book at the moment until Monday. But, if I'm not wrong, I thought the example was for an axially loaded horizontal beam. If it was, can this method be used for a column similarly. I recall the procedure in that example included calculating the reations at the ends of each segment of the beam (I may be wrong though). I'm not sure if the same procedure can be applied to the columns.
RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
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.
BA
RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
BA
RE: Slenderness ratio for column having different cross sections
Is there any difference if the example on P.120 is used on other end support conditions (i.e. one ende free and the other is fixed), which may be more representative to the column
RE: Slenderness ratio for column having different cross sections
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
RE: Slenderness ratio for column having different cross sections
RE: Slenderness ratio for column having different cross sections
Not if the other end is free.
BA
RE: Slenderness ratio for column having different cross sections
Attached is the pile sketch
RE: Slenderness ratio for column having different cross sections
It is not a simple problem.
BA
RE: Slenderness ratio for column having different cross sections
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Slenderness ratio for column having different cross sections
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.
RE: Slenderness ratio for column having different cross sections
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
RE: Slenderness ratio for column having different cross sections
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.
RE: Slenderness ratio for column having different cross sections
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
RE: Slenderness ratio for column having different cross sections
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