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[kajal.chopra]

Hi Kedar,

Thanks for the reply.

1.Can you kindly explain point 6 b) of your post? That is, the force passing from the column to the slab due to rigid diaphragm action in an intuitive sense?

2. What if the column is very stiff say a basement column of high rise commercial building?

Kajal

[Kedar]

Hi Kajal


Plz note


1.The Column and slab are integrally casted.i.e. they are note separate  entity.

2.The horizontal/shear force applied by tendon is shared in proportion with the stiffness of slab/column system.This is obvious.

3.This shear force will cause BM in column due to small displacement
and axial shortening of slab.


Lets consider simple/quick calculation just to demonstrate how shear force is distributed between slab and column


Considering the previously posted example
consider practical sizes of system


the slab thickness = 350 mm
the column ht = 4200 mm
Column size 900mm x 900mm
column grid = 11m x 11m



Shear force =532 kN


1.Axial stiffness of slab(s suffix)

AsE/Ls
=350E

where
As= tributory length across span x thickness
=11000 x 350

2.Horizontal Reaction/shear  at the base of column(c suffix) due to unit deformation

12EIc/Lc^3
=8.86E


Total stiffness at joint = 350E+8.86E
=358.86E


The shear resisted by column

=532 x (8.86/358.86)
=13.13 kN


The shear resisted by slab in form of axial compression
=532 x (350/358.86)
=518.87 kN


It can be seen that
slab takes 97.53% of shear
column takes 2.47% of shear


Assumptions are made
wherever necessary.


regards
Kedar

[kajal.chopra]

Thank you so much for the reply.

But it does have an impact when column is very stiff.

Example:

Say the slab is 150mm thick

Column is 1000mm x 1000mm and 3 m long.

Now:

AE/L of slab = 150 E

12 EI / L^3 of column= 12 E (1000x 1000^3/12) / 3000^2 = 37.03E

Shear = 532 KN

Now, shear taken by slab= 532x 150 / 207 = 385

shear taken by Column = 147 KN.

There could be a scenario like this.Right?

[Kedar]

Hi Kajal


The  of system you are describing is
is difficult to exist in practice.


Since one would go for regular beam,slab & column system
why it is necessary to provide post tensioned slab for 3m span?


If at all one want that kind of structure just for the sake of it you need to account all forces i.e. shear in column and all.


Same is applicable for other system elements you
proposed.


regards
Kedar

[kajal.chopra]

I mentioned 3m as height of the column.

Axial stiffness of slab = 11,000 x 150 / 11,000 E = 150 E

Note: i assumed column height as 3m instead of 4.2m what you assumed.

This could be a practical system infact?

[Kedar]

Hi Kajal


Can you plz check calcs
posted by you?



regards
Kedar

[kajal.chopra]

I do not find anything wrong there?

[Kedar]

Hi Kajal


Plz check summation of stiffness

=150E+37.03E
=187.03E

(not 207E)

so other forces will change.


plz correct me if I am wrong.


regards
Kedar

[kajal.chopra]

Ok, right. In that case shear taken by column is: 106 KN.Can it be neglected?

[Kedar]

Hi Kajal



It all depends on your judgement and calcs.
and how you want your structure to preform.


If you feel shear needs to be accounted
you can as simple as that..



regards
Kedar