Punching shear is one of the most complex phenomena in Reinforced Concrete (RC). More than 40 models exist for predicting the punching shear strength of RC flat slabs [1], and there seems to exist no consensus about the best model or the best approach. Punching shear failure is brittle, and it occurs with almost no warning, unlike flexural failure that normally shows visible signs of distress (large cracks for example) before losing the load-carrying capacity. The consequences of such a failure can be enormous if proper measures against progressive collapse are not taken, because punching failures can trigger progressive collapse of structures.
Looking at the relatively simple formulas provided by design codes such as ACI 318 [2] and Eurocode 2 [3], one can get the impression that punching shear is not that complex as a phenomenon after all. Well, think again! Look no further than the lack of consensus regarding the influence of concrete compressive strength. Eurocode 2 formula assumes that punching shear resistance is proportional to concrete strength to the power 1/3, but ACI assumes concrete strength to the power 1/2 is proportional to punching shear resistance. Then there is the control perimeter, etc., etc.
Nonetheless, design codes are generally safe, as demonstrated by the history of success throughout many years of designing flat slabs against punching shear based on these codes. The argument to be made based on the discussion above is that punching shear is a complex phenomenon and it is beneficial for structural engineers to study this topic a bit more in depth to really understand the limitations of the codes and to avoid being in a position of simply applying some code formulas without understanding the phenomenon.
One of the most intuitive theories out there that gives relatively good results (compared to well designed tests) is the so called Critical Shear Crack Theory (CSCT) [4]. Although this theory is only one out of more than 40 theories that exist, it is interesting for a practicing structural engineer to take a look at it because it provides a complete picture about the behaviour of flat slabs under concentric loading, including the interaction between flexural behaviour and shear behaviour. According to CSCT, punching shear occurs at the intersection of two curves:
- the load – rotation curve
- a failure criterion
as illustrated below:
This is cool because the designer can see whether flexural failure governs the behaviour or shear failure occurs before (i.e. for a smaller slab rotation) flexural yielding. For example, in Slab 1 in the figure below punching occurs after significant flexural yielding, whereas in Slab 2 punching occurs before yielding.
The guys at "EarthquakeApps" have developed a free Android app based on CSCT. It is meant to be used as a learning tool, not for design, and you can experiment it by clicking the link below:
or the following link: https://play.google.com/store/apps/details?id=blogndertimi.com.punchingshearcsct
Here is a very quick look how the app looks like:
Did you learn something new from this post? Share your thoughts in the comments and share this post with your colleagues.
References
[1] Koppitz R, Kenel A, Keller T. Punching shear of RC flat slabs – Review of analytical models for new and strengthening of existing slabs. Eng Struct 2013;52:123–30. doi:10.1016/j.engstruct.2013.02.014.
[2] ACI 318. Building Code Requirements for Structural Concrete (ACI 318-19) 2019.
[3] CEN. EN 1992-1-1. Eurocode 2 — Design of concrete structures. Part 1-1: General rules and rules for buildings. 2004.
[4] Muttoni A. Punching Shear Strength of Reinforced Concrete Slabs. ACI Structral J 2008;105:440–450. doi:10.14359/19858.