Shear in Opening Corners of Tanks 1

[haceng]

thread167-245165
I'm from the UK and there is little guidance on this here. In the case where you have an opening corner, the rebar on the inside face will be resisting the bending and all of the tension. Therefore it is reasonable to assume the support is being provided at that location (not at the face)by the rebar. If you superimpose a shear crack line patern (adjusted so the support lines up with the rebar), you will see that it is quite reasonable to use the same rules for distance from the support as you do for a compressive support(d to ACI but 2d to BS8110 and EC2 but see following). In this case d should be the distance between the top and bottom reinf not the effective depth. BS8110 and EC2 differ at (av < 2d) from the support. BS8110 factors the CAPACITY by 2d / av, whereas EC2 factors the ADDITIONAL SHEAR by av/2d between 2d and 0.5d and by 0.25 closer than 0.5d. For a linearly varying increase in shear from 2d to the support the EC2 method results in a value at the support which is slightly over the value you would get at d which is quite conveniently similar to the ACI check position! You could also consider the rebar from the supporting wall as a shear leg and then check at d from there.
If you have a situation where the moment is small, the support will be shared by the rebars on both faces and the support will be on the centre line of the wall so the check position moves closer to the face. The check position will only be at the face if the support is taken as being at the far(outer)rebar which can only happen with a closing moment. Therefore, I believe those diagrams which show the failure point to be a 45 degree line between the corners are not appropriate to design case we normally see in tanks.
You must reduce the shear capacity as a result of any tension. BS8110 does not allow you to combine adjustment due to axial with closer than 2d factors but I believe that should apply to compression only as tension REDUCES the capacity but will not alter the shear line pattern, especialy as the tension is taken by the rebar and generally only increases the rebar stress by 15% say. EC2 does allow combination of effects.

 

[hokie66]

Don't know why your link didn't appear, but here it is.

thread167-245165

 

[haceng]

Here is a diagram which illustrates my opening thread - hopefully shear binders and inclined bars will not be required.

 

[hokie66]

haceng,
For closing joints, the critical shear plane is taken as occurring at some distance from the face of the support. As you pointed out, this distance varies somewhat between codes. But remember, this shear plane is just a model, as this type shear is actually diagonal tension which occurs on an angle, somewhere near 45 degrees.

For opening joints, the diagonal tension can actually extend INTO the support, so the span contributing to shear failure is larger than for closing joints, and we use the face of the support as the critical location.

I haven't looked at the ACI code in this regard and am not familiar with the UK code, but the Australian code says to take shear either 1) at the face of the support, or 2) at a distance d from the face, provided "diagonal cracking cannot take place at the support or extend into it". At an opening corner, diagonal cracking clearly can extend into the support.

 

[haceng]

Thank you for your comment. I agree that a diagonal flexural crack will go from inside corner to outside corner in an opening condition. If this crack is taken as the first shear crack, the tension reinforcement in the inside face of the supporting wall will resist this and will in effect be a shear leg. The shear load will be excatly the same as the tension load in the wall so the reinforcement should have been designed to take this.
If you then consider a possible shear failure line to be at 45 degrees (actually 30 deg is used in BS8110) from the bottom of the supporting reinforcement (now acting as a shear leg), you could argue that the load between the shear leg and a point d1 along the wall is taken by the shear leg. If the section is adequate in shear at the d1 distance, then no further legs should be required. If legs are required BS and EC2 specify that their centres are at 0.75d1.
This approach would enable the checking at d1 for an opening corner to an acceptable method. This is provided the corner to corner crack is properly resisted and d1 is the distance beteen As1 and As2 and is measured from the supporting shear leg not the face.

 

[hokie66]

Along the wall, I would always make the wall thick enough to resist the slab shear rather than use shear reinforcement.

 

[haceng]

The problem with that approach is that you end up with a wall thickness that is only required very locally and legs are a very efficient method. I have not uncovered any research tests that deal with the shear span in opening corners which is somewhat astounding considering how frequently it occurs. If there is any, I would like to see it. I would have though that once you are clear of the corner, the flexural cracks will revert to being at 90 deg just like at an internal support and provided the corner crack is resisted, the situation is then similar to a conventional compressive support. I am not convinced that just because you have a partial depth diagonal flexural crack at the corner (which is adequately resisted by reinforcement) the mode of shear resistance and shear span should be any different to that in a continuous beam.