Choise of theta_v in Equation 8.1.10.4a AS3600-2009

[kww2008]

The code seems to allow a value of phi of 45 degrees to be used in Equation 8.1.10.4 (a) (i) (A), namely "V* cot(theta_v)/phi". This assumption gives a smaller value of "V* cot(theta_v)/phi" than if the theta_v value is determined using 8.2.10 (b) (ii), namely "theta_v = 30 + (V*-phiVu_min)/(phiVu_max -phiVu_min) x 15".

For a given V*, assuming 45 degrees for theta_v will give more steel in the stirrups and less steel in the support anchorage for all beams other than beams with V*=phiVu_max.

Does this mean that when using this clause, one can use either a theta_v value determined using 8.2.10 (b) (ii) or a theta_v of 45 degrees ?

 

[asixth]

What is the support anchorage? Are you referring to flexural reo? In which case the shear provisions should not drive you to use less flexural reo.

Using a theta_v of 45 degrees will give you less shear capacity than a theta_v of 30 degrees. Yes, depending where the V* lies relative to the Vu_max than you can use a value closer to 30 deg.

 

[kww2008]

asixth,

The "support anchorage" is the amount of anchorage of positive moment main reinforcement at a support to enable the beam to develop V* at or close to the support, where V* is the design shear action effect. This is based on the truss analogy theory to ensure consistency in the flow of forces close to the supports.

The amount of anchorage to be provided must satisfy T* >= V* Cot(theta_v)/phi where phi=0.8, and phi=0.8 is the value suggested in a Powerpoint presentation by Ian Gilbert on "Detailing of reinforcement in concrete structures" in 2012.

One does not need to anchor the "full amount of flexural steel required at the maximum moment region" into the support. You just need to provide sufficient to satisfy the requirement of Clause 8.1.10.4.

 

[rapt]

kww2008,

That is what the code says. I cannot understand what the doubt is. It specifically says either
45 degrees
or
a variable value depending on the value of V* relative to Vmin and Vmax.

Whatever value is chosen is then used to determine the end anchorage of the flexural reinforcement. It should also be used to determine the offset of the moment diagram for development of reinforcement at any location, rather than simply using.

45 degrees allows no redistribution if shear. The variable strut angle allows for redistribution of shear due to cracking. With redistribution, you need less shear reinforcement but the development requirements of the reinforcement are greater so you need to extend your flexural reinforcement further.

 

[kww2008]

asixth,
Thank you for your comments, and getting the ball rolling. Literally, according to the code one can use either 45 degree or a value determined using V*, Vumax and Vumin (referred to as the determined value from hereon).

The definition of theta_v is tied to clauses 8.2.10 (a) and (b), and using 45 degrees is conservative (as pointed out in the earlier version of AS3600) when use with these two clauses. One will always get a lower extimate of V_us in Clauses 8.2.10(a) and (b) when using theta=45 degrees when compare with using the determined value.

But when assuming theta_v of 45 degree and use with clause 8.1.10.4 (a)(i), the tensile force required to be anchored is smaller than the value determined using the determined value. While the standard states that a theta_v=45 degree can be assumed when use with 8.1.10.4 (a) (i), I am not sure of the background to this, and hence my query.

I am not familiar with the redistribution of shear as shear behaviour in my mind relates to non ductile behaviour.

Hope others can add to this discussion.

 

[rapt]

kww2008,

If you want a detailed explanation of it, you are not going to get it here.

A simple search on Google for "variable strut angle" will give you heaps of articles describing it. Or get a hold of Collins and Mitchells work on compression field theory and the Canadian Code shear rules or Walravens work shear rules in Eurocode 2.

 

[kww2008]

Thanks Rapt. Will read up about variable strut angle.

 

[Trenno]

I have nothing to add to this thread, but I will say Collins and Mitchell's seminar on Shear Design this year was very interesting and informative. They both spoke very well and opened everyone's eyes up.

They were also massive fanboys (understandably) of the Canadian Code over our Australian code. Seemed as though the Canadian code deals with shear design quite effectively.

ALso it was funny/interesting to hear...

"I'm sorry, but concrete does not bottle like that..." (In reference to our strut and tie sections)

 

[kww2008]

Trenno,

I attended Collins and Mitchell's seminar too. It was, as you pointed out, informative and interesting. The Compression Field method is a more rational approach and is supported up by many years of research activities.