Query on Web Shear Cracking of Prestressed Beams

[kww2008]

In AS5100.5, the equation for web shear cracking is V_uc = V_t + P_v, where V_t is the shear force which, in combination with the prestressing force and other action effects, would produce a principal tensile stress of 0.33 sqrt(f'c) at the centroidal axis or the intersection of flange and web, whichever is more critical.

As V_t above is ULS, I suspect the corresponding M (when V=V_t)to use for calculating the normal stress at web-flange interface is also at ULS. Is this observation correct ?

 

[rapt]

No, it should be the service moment.

 

[IDS]

The code clause says:

Vt = shear force which, in combination with the prestressing force and other action effects at the section, would produce a principal tensile stress of 0.33 f′c at either the centroidal axis or the intersection of flange and web, whichever is the more critical.

and the commentary says:

In calculating Vo, the corresponding values of M* and V* can vary, depending upon the loads and load positions. Maximum moment and corresponding shear, and maximum shear and corresponding moment should be calculated and the resulting minimum value of Vo used.

The Commentary does not comment on the applicable moment to use when calculating Vt, but I don't see any reason why it would not be M* (i.e. the ULS moment) associated with V* that gave the worst case, rather than the SLS moment.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

It has been based on the service moment for the last 36 years. Unfortunately I am out of the office this week and do not have my reference material available to provide references.

 

[IDS]

If that's the case that's something to add to your list of things to clarify in the next version of the code!

But I still don't see the logic of it, and the British Code (BS 5400) is quite explicit that Ultimate Moments should be used for checking web shear cracking.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

Clarifying this,

V* and M* should come from the same load combination. These will result in flexural and shear stresses which have to be equated to the principal tensile strength using Mohr's circle to givethe V and M condition at the principal tensile strength and this V is then the Vut.

So it is not rleated to M* but the combination of V* and M* and you need to calculate the fraction of V* and M* (possibly greater than 1) that solves the equation.

 

[kww2008]

Thank you Doug and "Rapt" for the interesting discussions.

Now I understand that V_ut should be determined using unfactored loads as V_ut represents a capacity, not a load.

However, I am not sure whether to use the load combination V* and M*, or the load combination V_ser and M_serv, as V*/M* can be slighty different from V_ser/M_ser for a given load combination.

I have a floow on query relating to the loads to use to calculate M_ser and V_ser. I am considering an indeterminate structure. I can think of two ways to determine V_ut, and one is probably more appropriate:

First way: Use the primary prestressed moment in the section to produce the initial stresses and included the secondary prestressed effect as applied load to produce additional stresses. This gives me an estimate, say V_ut1, maintaining the ratio M_ser/V_ser, where M_ser and V_ser include the secondary prestressing effect.

Second way(which I have not done the calcs): Use total (primary plus secondary) prestressed moment in the section to produce the initial strsses, and not to include the secondary prestressed effect as an applied load effect. Say, this gives V_ut2, maintaining the ratio M_ser/V_ser, where M_ser and V_ser do not include the secondary prestressing effect.

Estimated V_ut1 is likely to be different from V_ut2, as the first way considers the secondary prestressing as an applied "load", which the second way doesn't.

Which of the two ways is correct/more appropriate

 

[kww2008]

Further, to my last posting, I found M_ser/V_ser quite different to M*/V*. Not sure if I have mistakes in the calcs ...

 

[rapt]

The primary prestress is kept separate from the applied moment. The applied moment only includes the secondary prestress which is assumed in design to be an applied load.

so you calculate the flexural stress with P/A +- P e y / I +- M* y / I. And shear stress with V* Q / I bw

Where M8 and V* only inlcude the secondary prestress.

Yes, you will get a slightly different result using unfactored load combinations. If you want to be conservative, use the worst result.

 

[kww2008]

Thank you "Rapt" for your posting.

Would the below (where V*/M* or V_ser/M_ser does not include the prestressing effects) be more appropriate ?

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The primary prestress and secondary prestress are kept separate from the applied moment. The applied moment is from all applied loads other then the primary and secondary prestressing.

Calculate the flexural stress with (P/A +- P e y / I) +- (Msec y / I) +- M* y / I. And shear stress with V* Q / I bw

Where M* and V* exclude both the primary and secondary prestressing effects.

There will be a slightly different result using unfactored load combinations. To be conservative, use the worst result.
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[rapt]

No. Secondary prestress is part of the external loads and is included in M* and V*!

I would suggest you purchase a good book on application of AS3600!

 

[kww2008]

Thank you "rapt".

I have not come across a book with an example showing the calculation of design shear capacity for an indeterminate prestressed concrete beam. All those I have read so far have examples for shear design of simply supported beams only.

Has anyone come across a book or technical paper with an example showing the calculation of shear capacity for an indeterminate prestressed beam to AS3600?