Buckling of column connected to beam

[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?

Homework Equations

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]

 

[PhanthomJay]

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]

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?

 

[PhanthomJay]

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]

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?

 

[PhanthomJay]

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

 

[foo9008]

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 ?

 

[PhanthomJay]

Yes.

 

[foo9008]

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 ?

 

[PhanthomJay]

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

 

[foo9008]

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?

 

[PhanthomJay]

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

 

[foo9008]

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?

 

[PhanthomJay]

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]

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

 

[PhanthomJay]

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.

 

[foo9008]

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?

 

[foo9008]

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?

 

[foo9008]

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?

 

[PhanthomJay]

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]

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 ?

 

[fonseh]

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?

 

[PhanthomJay]

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.

 

[fonseh]

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 ?

 

[PhanthomJay]

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.