# Buckling Calculation for I-Section Joists w/ Ball-Jointed Ends

• jazzchan
In summary: For your buckling calculation, you may need to look at the effective area which takes into account the end conditions and the moment of inertia of the entire beam. In summary, the conversation discusses calculating the compressive load and buckling of an I-section joist with ball-jointed ends. It also touches on the necessary calculations and considerations for tension and compression.
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

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:
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

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.

Dear FredGarvin

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

regards,

jazz

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

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

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

## 1. What is buckling and why is it important?

Buckling is a phenomenon in which a structural element, such as an I-Section joist, experiences sudden failure due to compression forces exceeding its capacity. It is important to understand buckling because it can lead to catastrophic failures in buildings and structures, posing a threat to human safety.

## 2. How do you calculate the buckling capacity of an I-Section joist with ball-jointed ends?

The buckling capacity of an I-Section joist with ball-jointed ends can be calculated using the Euler's formula, which takes into account the length, moment of inertia, and modulus of elasticity of the joist. This formula gives the critical buckling load, which is compared to the applied load to determine if the joist is at risk of buckling.

## 3. What factors can affect the buckling capacity of an I-Section joist?

The buckling capacity of an I-Section joist can be affected by various factors such as the length of the joist, the cross-sectional shape and dimensions, the material properties, and the end conditions (e.g. fixed, pinned, or ball-jointed). Other factors, such as temperature, axial load, and lateral support, can also influence the buckling behavior.

## 4. How can buckling be prevented in I-Section joists with ball-jointed ends?

To prevent buckling in I-Section joists with ball-jointed ends, engineers can design the structure with appropriate load-bearing capacity and stiffness, use bracing and lateral support systems, and carefully consider the end conditions of the joist. Regular inspections and maintenance can also help detect any signs of buckling and take preventive measures.

## 5. Are there any limitations to the buckling calculation for I-Section joists with ball-jointed ends?

Yes, there are some limitations to the buckling calculation for I-Section joists with ball-jointed ends. The calculation assumes ideal conditions and does not account for factors such as imperfections in the joist, residual stresses, and dynamic loads. Therefore, it is important to use engineering judgment and consider other factors when analyzing the buckling behavior of a joist.

• Classical Physics
Replies
5
Views
1K
• Mechanical Engineering
Replies
1
Views
1K
• Mechanical Engineering
Replies
2
Views
266
• Mechanical Engineering
Replies
13
Views
3K
• Classical Physics
Replies
5
Views
700
• Mechanical Engineering
Replies
3
Views
3K
• Engineering and Comp Sci Homework Help
Replies
5
Views
3K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Classical Physics
Replies
16
Views
2K
• Classical Physics
Replies
1
Views
4K