Static engineering v -- stress/buckling

[oxon88]

Homework Statement

A column has the dimensions shown below...

Column material properties:

young's Modulus E = 200 GN m^-2

Yield stress = 140 MN m^-2

Homework Equations

a) what is the minimum length of the column at which buckling is likely to occur?

The Attempt at a Solution

i got an answer of: 2*((118.74 * Sqrt((2.33x10^3)/(2800x10^-3))) = 6850.56 M

 

[nvn]

oxon88: Your current answer is wrong. Try again. First, list relevant equations. And then show how you computed each numerical value used in your final equation.

By the way, MN*m^-2 is called MPa. And GN*m^-2 is called GPa. Always use the correct, special name for a unit. E.g., 140 MPa, not 140 MN*m^-2.

 

[oxon88]

Homework Statement

a) what is the minimum length of the column at which buckling is likely to occur?

The Attempt at a Solution

least second moment of area. I = (B^4 - b^4)/12 = (80^4 - 60^4)/12 = 2.33x10^6

area. A = B^2 - b^2 = 80^2 - 60^2 = 2800

σ = 140x10^6

E = 200x10^9

effective slenderness ratio. E.S.R = sqrt(pi^2.E/σ) = sqrt(pi^2.(200x10^9)/(140x10^6)) = 118.74

effective length. L = (E.S.R). Sqrt(I/A) = 118.74(sqrt(2.33x10^3)/(2800)) = 3427.7


effective length = 1/2 column length. = 3427 x 2 = 6854 mm


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I also tried another method and got the same answer...


Least value of radius of gyration. K = (1/2).sqrt((B^2+b^2)/3) = 1/2 sqrt((80^2+60^2)/3) = 28.868

effective length. L = (E.S.R x k) = 28.868 x 118.74 = 3427.73

effective length = 1/2 column length. = 3427 x 2 = 6854 mm

 

[oxon88]

ok. so i worked it out.

the answer is 5.94m

 

[nvn]

Your answer in post 4 is correct.

By the way, always leave a space between a numeric value and its following unit symbol. E.g., 5.94 m, not 5.94m. See the international standard for writing units[/color] (ISO 31-0[/color]).

 

[oxon88]

ok. So if the column was to be 5.94 m. What would be the mode of failure? and at what load would you expect the failure to occur?

I guess it would be buckling?

 

[oxon88]

any ideas?

 

[oxon88]

useless forum...

 

[nvn]

We are not allowed to answer your homework questions for you.

 

[Rafeng404]

Hi all, I have the same question and was getting the same answers originally. I assume that your new answer is based on changing the formula to a hollow tube. I was wondering without being told in the question how we are supposed to determine what shape it is... Or am I being a bit thick...

 

[forexpipz]

Wrong formula

The least second moment of area I about the xx axis is not what you stated so your value is incorrect. I get L = 5.236389088 m

 

[David J]

I am just wondering if this thread is still active as I am studying this question and facing similar problems to those on here

 

[SteamKing]

I am just wondering if this thread is still active as I am studying this question and facing similar problems to those on here

The last post was two years ago, so, no, it's not still active.

However, you can and should create your own, fresh thread. It's not like you can create only so many threads at PF before you run out.