Static engineering v -- stress/buckling

In summary, the least second moment of area is the measure of how much a shape's total second moment of area is smaller than its total first moment of area. The shape with the smallest second moment of area is the most slender.
  • #1
oxon88
176
1

Homework Statement



A column has the dimensions shown below...

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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
 
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  • #2
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.
 
  • #3

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


--------------------------------------------------------------------------------------


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
 
  • #4
ok. so i worked it out.

the answer is 5.94m
 
  • #5
Last edited:
  • #6
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?
 
  • #7
any ideas?
 
  • #8
useless forum...
 
  • #9
We are not allowed to answer your homework questions for you.
 
  • #10
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...
 
  • #11
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
 
  • #12
I am just wondering if this thread is still active as I am studying this question and facing similar problems to those on here
 
  • #13
David J said:
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. :frown:

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. :wink:
 

1. What is static engineering?

Static engineering is a branch of engineering that deals with the analysis, design, and stability of structures and systems that are at rest or in equilibrium. It involves the study of forces and stresses on stationary structures to ensure their safety and stability.

2. What is stress in static engineering?

In static engineering, stress refers to the internal force that resists the deformation of a structure. It is caused by external forces acting on the structure and can lead to structural failure if it exceeds the strength of the material.

3. What is buckling in static engineering?

Buckling is a type of structural failure that occurs when a structure is subjected to compression forces and it suddenly collapses due to the instability of its components. It is a critical issue in static engineering and can be prevented by properly designing structures to withstand compressive forces.

4. How is stress calculated in static engineering?

In static engineering, stress is typically calculated using the formula stress = force/area. This means that stress is directly proportional to the applied force and inversely proportional to the cross-sectional area of the structure.

5. What are some common methods for preventing stress and buckling in static engineering?

Some common methods for preventing stress and buckling in static engineering include choosing appropriate materials with high strength-to-weight ratios, designing structures with proper bracing and support, and conducting thorough stress and buckling analyses during the design process.

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