# Buckling calculation

1. May 11, 2005

### jazzchan

Dear all,

I have a question are as follows:

It is a I-Section joist, the question is find the compressive load could it take with ball-jointed ends.

i want to know what is ball-jointed ends ?? is it mean the base of the I-Section joist ??

if yes, what is the surface area i need to consider ?? only the area of ball-jointed ends ?? or whole area ??

Besides, the compressive load is mean the buckling ??

Thanks and best regards,

Jazz

2. May 11, 2005

### brewnog

Ball joint ends are such that the supports for your member cannot support a moment.

How is the member loaded? If it is in compression along its axis (in which case you have a 'column' or a 'strut'), it is likely to fail by buckling, especially if the member is quite long. You can use the Euler formulae to calculate the buckling load, based upon the Youngs Modulus (E), Second Moment of Area (I), length of your strut (L), and the applied end conditions (in your case, pinned ends). For this situation, the Euler load (and excuse my lack of Latex skills) is:

W=(Pi^2)EI / L^2

For one fixed end, and one pin jointed end, this load is doubled, if both ends are fixed the load is quadrupled.

Let us know if you don't follow.

Last edited: May 11, 2005
3. May 11, 2005

### jazzchan

Dears,
the detail question is as follow:
An I-section joist has total height 160 mm, total width 120 mm, and the thickness throughout of 5 mm. It is 4m long. It made of steed with yield stress =280MN/m2 and E=210GN/m2.

a) when loaded only in tension along its axis, what tensile load could it take at yield?

b) what compressive load could it take with ball-jointed ends? check buckling and yield.

my problem is
in part a)
i think i can use yield stress=P/area to find the tension.

in part b)
I didn't not understand what is the meaning of compresive load could it take with ball-joint ends ?? Is it mean the compressive load apply at the base of the I section and at x axis ??

thanks and regards,

kk

4. May 11, 2005

### FredGarvin

In regards to part A: Yes. You can use $$\sigma = \frac{P}{A}$$ and use the yield strength as $$\sigma$$

Pt B: The compressive load failure modes you need to look at are compressive yield (which is different than tensile yield) and buckling. The ball joints are in reference to what to use for your effective length of the column. $$F_{BUCKLE} = \frac{\pi ^2 E I}{L_e ^2}$$ . Like Brewnog mentioned, it is in relation to the column being able to sustain a bending moment at the ends. Most text have a table listing different end conditions and the associated effective lengths. You still use the area of the column in your calculations.

5. May 11, 2005

### jazzchan

Dear FredGarvin

in your last sentence, the column means the area only base part of the I-Beam ?

regards,

jazz

6. May 11, 2005

### brewnog

The cross sectional area of your beam plays a part in your calculation of I, - the Second Moment of Area.

7. May 11, 2005

### jazzchan

I know that it is necessary t ofind the min Ixx or Iyy for second moment of the area.

I think I should use the whole I-section beam to for area calculation.

thanks a lot

8. May 11, 2005

### brewnog

With your simple tension and compression calculations, take the area to be the cross sectional area of the I beam.