# Buckling of column connected to beam

• foo9008
In summary, the conversation discusses the calculation of moment of inertia (Ixx and Iyy) at the column for determining the buckling load. The author clarifies that the cross section of the beam does not affect the buckling of the column and explains how the beam provides lateral support at the column midpoint. They also discuss the two forces applied and how the middle beam provides lateral support against weak axis buckling. Finally, they explain why the effective length for Pcr_y is 3000 and why there is no support provided by the beam against major axis buckling.
foo9008

## Homework Statement

In this question, we are interested inthe buckling of column, so we should calculate the moment of inertia (Ixx) or (Iyy) at the column,right?

## The Attempt at a Solution

Why the author calculate (Ixx) and (Iyy) using the cross sectional area of beam?
is it wrong?
And for critical load applied at y-axis (Pcr_y) , why the Le used is 3000 , why not 250mm?[/B]

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The author is using the column cross section in determining the buckling load of the column. The beam in the middle provides lateral weak axis column support at the column mid point.

foo9008
PhanthomJay said:
The author is using the column cross section in determining the buckling load of the column. The beam in the middle provides lateral weak axis column support at the column mid point.
do you mean the load is applied at the beam to detremine the buckling of column?
Since the column and beam are connected , so , we can use the Ixx or Iyy about the cross sectional area of beam to calculate the buckling of column?

Buckling loads in the usual sense are compressive axial loads. This problem asks what is the max compressive axial load that can be applied to the top of the column before it buckles. The cross section of the beam has nothing to do with the buckling of the column. The beams transfer vertical loads to the columns, yes, but the problem example wants to show how beams can reduce the effective length of the column when determining weak axis column buckling

foo9008
PhanthomJay said:
Buckling loads in the usual sense are compressive axial loads. This problem asks what is the max compressive axial load that can be applied to the top of the column before it buckles. The cross section of the beam has nothing to do with the buckling of the column. The beams transfer vertical loads to the columns, yes, but the problem example wants to show how beams can reduce the effective length of the column when determining weak axis column buckling
is It true that the load is applied in this direction?

Not true. The solution gives the max vertical load for P applied downward at the top of the column.

PhanthomJay said:
Not true. The solution gives the max vertical load for P applied downward at the top of the column.
do you mean the load is applied in this direction ?

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Yes.

PhanthomJay said:
Yes.
then , why we need to consider the moment of inertia about the cross sectional area of beam ? or i misunderstood something ? the 250mm x300mm is not cross sectional area of beam ?

That is the cross section of the column, which should have been more clearly shown,

foo9008
PhanthomJay said:
That is the cross section of the column, which should have been more clearly shown,
Can you explain why we need to consider the moment of inertia about the cross sectional area of beam? We are interested in the buckling of column, so we should consider the moment of inertia of the column, right?

Yes , the dimensions given are for the column. You do not need to consider the cross section of beam.

foo9008
PhanthomJay said:
Buckling loads in the usual sense are compressive axial loads. This problem asks what is the max compressive axial load that can be applied to the top of the column before it buckles. The cross section of the beam has nothing to do with the buckling of the column. The beams transfer vertical loads to the columns, yes, but the problem example wants to show how beams can reduce the effective length of the column when determining weak axis column buckling
why there are two force applied which is 771kN and 2138kN? only 1 force can be applied at the top and bottom portionof the column to determine the critical load of the column,right?

That is correct. Critical load is determined by using the lesser of the 2 values calculated. In this case, major axis buckling controls due to the higher l/r ratio.

foo9008
PhanthomJay said:
That is correct. Critical load is determined by using the lesser of the 2 values calculated. In this case, major axis buckling controls due to the higher l/r ratio.
can you explain why the Le for Pcr_y is 3000 ? i could only understand the Le for Pcr_x is 6000

The middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling. No such mid point support is provided against major axis buckling by this beam.

PhanthomJay said:
The middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling. No such mid point support is provided against major axis buckling by this beam.
，do you mean the beam divided the column into 2 parts?

PhanthomJay said:
The middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling. No such mid point support is provided against major axis buckling by this beam.
，do you mean the beam divided the column into 2 parts?

PhanthomJay said:
No such mid point support is provided against major axis buckling by this beam.
you already said that the middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling?
Why there's no support provided by this beam?

The beam is pinned to the column at one end and at the other end of the beam it is connected to a wall or another column which is not shown in the figure. Once again the beam keeps the column from deflecting in the direction of that beam so it cannot bulge out and buckle at that point. But since the beam is pinned to the column at that point, it can't prevent the column from buckling about the major axis since the beam would just rotate and not provide support on that direction, only the other direction along the beam. Assuming ideal pins here. So in reprieve, effective length is 6000 for major
axis buckling and 3000 for minor axis buckling.

fonseh and foo9008
PhanthomJay said:
The beam is pinned to the column at one end and at the other end of the beam it is connected to a wall or another column which is not shown in the figure. Once again the beam keeps the column from deflecting in the direction of that beam so it cannot bulge out and buckle at that point. But since the beam is pinned to the column at that point, it can't prevent the column from buckling about the major axis since the beam would just rotate and not provide support on that direction, only the other direction along the beam. Assuming ideal pins here. So in reprieve, effective length is 6000 for major
axis buckling and 3000 for minor axis buckling.
this seems an interesting topic to learn . You already said that the column cannot bulge out due to the pin . why for the bottom part , you said that the the beam can't prevent the column from buckling about the major axis ?

PhanthomJay said:
The middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling. No such mid point support is provided against major axis buckling by this beam.
The major axis here means the 6m ? We can see that there are 3 beam connected to the column(top , middle and bottom) , why you said that there's no No such mid point support is provided against major axis buckling by this beam?

fonseh said:
The major axis here means the 6m ? We can see that there are 3 beam connected to the column(top , middle and bottom) , why you said that there's no No such mid point support is provided against major axis buckling by this beam?
Looks like the original posts have been deleted, but the beam provides lateral middle support against weak axis buckling, but about the major axis of the column, it does not, because the beam can rotate out of plane assuming a ball type pin connection, and thus cannot restrain the column in that direction.

PhanthomJay said:
Looks like the original posts have been deleted, but the beam provides lateral middle support against weak axis buckling, but about the major axis of the column, it does not, because the beam can rotate out of plane assuming a ball type pin connection, and thus cannot restrain the column in that direction.
do you mean the middle beam can only support the weak axis buckling of beam until 3m only ?
So , we need to consider another case ( which is stronger axis buckling) for 6m column ?

fonseh said:
do you mean the middle beam can only support the weak axis buckling of beam until 3m only ?
So , we need to consider another case ( which is stronger axis buckling) for 6m column ?
yes, correct.

fonseh

## 1. What is buckling of a column connected to a beam?

Buckling is a structural failure that occurs when a column connected to a beam is subjected to compressive forces that exceed its ability to resist deformation. This can result in the column bending or collapsing.

## 2. What factors contribute to the buckling of a column connected to a beam?

The main factors that contribute to buckling are the material properties of the column and beam, the length and cross-sectional area of the column, and the magnitude and direction of the applied loads.

## 3. Can buckling be prevented in a column connected to a beam?

Yes, buckling can be prevented by ensuring that the column and beam are designed to withstand the expected loads and by using appropriate bracing or reinforcement to increase their resistance to buckling.

## 4. How is the buckling strength of a column connected to a beam calculated?

The buckling strength of a column connected to a beam is typically calculated using formulas or equations that take into account the material properties, geometry, and applied loads. Finite element analysis can also be used to determine the buckling strength.

## 5. What are some common methods for reinforcing a column connected to a beam against buckling?

Common methods for reinforcing against buckling include adding diagonal bracing or shear walls, increasing the column size or using a stronger material, and using moment connections between the column and beam.

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