Do torsional shears add to overturning moment for shear walls? 2

[coolnes]

I have an 8 storey structure with a rigid diaphragm.

The lateral load resisting system is a RC core at the centre.

I only have to resist wind loads. No seismic.
Assume the building is square with plan dimensions of 100' x 100' and the core is 4 walls with dimensions of 20'x20'.
And the floor to floor height is 10'.

Let's say the wind load per floor is 10 kips. So each wall takes a shear force per floor of 5 kips.

Let's not consider torsion for a moment and look at only ONE of the shear walls.
The cumulative direct shear force at the bottom floor would be: V = 40 kips (= 10kips /floor * 8 floors / 2 resisting walls in that direction)
The overturning moment would be: M = 1800 kip-ft

Now consider torsion.
There will be some accidental torsion on the structure. My Canadian code says to use 10% of the width. e = 10ft
So the torsional moment per floor is 100 kip-ft
The cumulative torsional moment at the bottom floor is: T = 800 kip-ft.
Converting this torsional moment is equivalent to a shear force of 20 kips.

Now my questions are:

1. When designing a wall at the first floor, I would design for a M = 1800kip-ft and a total shear force Vtotal = 60 kips?
Or, should I take the shear force due to torsion, 20 kips x the floor height, and add this to the overturning moment so the loads become M = 2000 kip-ft and V = 60 kips?

2.
If you analyze it a different way, and you convert each storey's torsional moment to shear force per floor, that would add 2.5 kips to each wall per floor.
But if the shear force per floor is now 7.5 kips (= 5kips direct shear + 2.5 kips torsional shear), then the moment at the base would be: M = 2700 kip-ft. Quite a big difference compared to 1800 kip-ft or even 2000 kip-ft.
The total shear force at the bottom would still be 60 kips.

What is correct?

Thanks for your help.

 

[hokie66]

For one wall, using your numbers, I get (40 + 20) x 40 = 2400 ft-k.

 

[WillisV]

Torsional moments should be converted to additional shears at each floor and moments at the base would be cumulative based on the direct+torsional shear applied at each floor.

 

[coolnes]

WillisV,
That's what I suspected....

I was doing it wrong. I had taken the cumulative torsional moment and then converted that to a torsional shear and then used that multiplied by a single floor height to get an overturning moment due to torsion at that floor.

Instead what I should be doing is what you have stated.

 

[slickdeals]

Would'nt the torsional moment result in opposing shears for a shear wall, which would then end up canceling each other for overturning moments at the base? Am I missing something?

 

[hokie66]

slickdeals,
The torsional moments do offset globally, but when considering just one wall, the torsional moment adds or subtracts in a given load case.

 

[coolnes]

Slickdeals,

This is the way I understand it.

The torsional moment (twisting moment) is converted to a shear force per floor. Call it the torsional shear. This acts along all 4 walls in my example.

This torsional shear would ADD to the direct shear for one wall, because the torsional shear and the direct shear are in the same direction.

But for the other wall, the torsional shear is in the opposite direction as the direct shear.

However, I still have to design the individual walls for the combined effect of direct shear + torsional shear.

But for OVERALL or global building overturning, the torsional shears would cancel each other out.

 

[slickdeals]

Understood. The shears on each wall segment will be higher due to torsional shear + direct shear, but the overall overturning moment on the wall is independent of the amount of torsion in the wall. Right?

 

[hokie66]

Not exactly. The global overturning is unchanged by eccentricity, but the individual walls see increased shear. If a wall carries more shear, it also carries more moment. Of course, in a core it is more complicated than that, as intersecting walls form flanges, etc.

 

[AZengineer]

If the core is a monolithic concrete tube, then we are essentially analyzing a cantilevered tubular beam subjected to an eccentric point load at each floor. The analyses noted above assume all four walls act independently, which would be unusual for a core.

 

[hokie66]

AZengineer,
No, the analyses indicated above are precisely with all the walls acting as a tube. I don't think you can say anything is unusual in a core. There are concentric cores, eccentric cores, coupled cores...the imagination of architects is unlimited.

 

[coolnes]

Thanks for all your respsonses.

So just to sum up:

Torsional moments should be converted to additional shears at each floor and moments at the base would be cumulative based on the direct+torsional shear applied at each floor.

And using my example, for each wall:
The direct shear per floor = 5 kips.
The torsional moment per floor is 100 kip-ft.
This torsional moment converted to a shear force into each wall per floor = 2.5 kips.
Total shear force per floor = 7.5 kips

At the base of the wall, M = 2700kip-ft and V = 60 kips