Project #tweetprop: Shear capacity at the continuous support

The fourth proposition of my dissertation is the following:

The shear capacity of reinforced concrete members near to continuous supports is at least equal to the shear capacity near to simple supports, contrarily to the recommendations of NEN6720:1995

or in Dutch:

De dwarskrachtcapaciteit van gewapend betonnen elementen nabij doorgaande opleggingen is minstens gelijk aan de capaciteit nabij vrije opleggingen, in tegenstelling tot het NEN 6720:1995 voorschrift

The old Dutch Code (NEN 6720:1995 [1]) prescribes an increase in capacity for loads close to the support, but only if their are placed near to a simple support (or end support). This effect was expressed through the factor kλ, which was applied as an enhancement factor on the shear capacity.

In Eurocode 2 (NEN-EN 1992-1-1:2005 [2]), the effect of direct load transfer is taken into account by reducing the contribution to the shear stress at the support for loads close to the support. The code does not make a difference between simple and continuous supports anymore.

In our experiments, we tested with the concentrated load close to the simple support and close to the continuous support. These experiments taught us that the capacity at the continuous support is often larger than at the simple support, and that it is by all means safe to say that the capacity at the continuous support is at least equal to the capacity at the simple support. You can find the entire parameter analysis for the influence of the moment distribution at the support in §4.5 of my dissertation.

The experimental analysis shows that the shear capacity at the continuous support is at least equal to the shear capacity at the simple support. As such, the recommendations from the old Dutch code do not correspond to our experimental results.

[1] Normcommissie 351001, 1995, "NEN 6720 Technische Grondslagen voor Bouwvoorschriften, Voorschriften Beton TGB 1990 – Constructieve Eisen en Rekenmethoden (VBC 1995)," Civieltechnisch centrum uitvoering research en regelgeving, Nederlands Normalisatie-instituut, ; Delft, The Netherlands, 245 pp.

[2] CEN, 2005, "Eurocode 2: Design of Concrete Structures - Part 1-1 General Rules and Rules for Buildings. NEN-EN 1992-1-1:2005," Comité Européen de Normalisation, Brussels, Belgium, 229 pp.

Project #tweetprop: the Modified Bond Model

The second proposition of my dissertation is the following:

By combining two-way quadrants and one-way strips, the Modified Bond Model bridges the gap between the one-way and two-way shear approaches.

or in Dutch (as the propositions are in English and Dutch:

Door in twee richtingen dragende kwadranten te combineren met stroken die in één richting dragen overbrugt het Modified Bond Model de kloof tussen de methodes voor pons en dwarskracht

Admittedly, this proposition is more difficult to explain without dwelling upon all the technical details - but bear with me for this one, the lighter propositions will be up soon.

The Modified Bond Model is the theoretical model that I propose to determine the capacity of a slab subjected to a concentrated load close to the support. As its name suggests, it is a modification of the Bond Model by Alexander and Simmonds [1], which was developed for concentric punching shear in slabs.

In other words: while the Bond Model studies a single load (or column) on an infinitely large slab, the Modified Bond Model looks at the practical case of a slab with a certain geometry subjected to a concentrated load.

The Bond Model divides the slab into 4 strips, that branch out from the load, and 4 quadrants. All loading is carried from the slab to the column, via the strips. As such, the governing cross-section is the interface between the quadrants and strips. The capacity is defined as the sum of the capacities of the 4 radial strips.



The Modified Bond Model goes one step further. As we found in the experiments that the geometry is decisive for the shear capacity of slabs subjected to concentrated loads close to supports, we defined reduction factors that reduce the capacity of the strips. One of the advantages of the Modified Bond Model is that it is easy to calculate (you can do it by hand), and that it can incorporate a variety of different geometries.

So these ideas explain you the Modified Bond Model. But how does it bridge the gap between one-way and two-way shear approaches, and what is so cool about that?

Let me start by saying that our experiments, and thus the case of a slab subjected to a concentrated load close to the support, is a type of shear failure that is in-between the typical beam shear failure and punching shear failure modes. We see inclined cracks at the bottom face, but also punching damage and shear cracks at the side faces. The codes deal with these two failure modes in a very separated way, while in reality there is a transition zone. You can understand that it is thus important to find a method that describes this transition zone.

The Modified Bond Model does exactly that. The strips work in arching action, and the quadrants work in beam shear. The strips carry load in one direction (cfr. one-way shear) and the quadrants carry load in both directions (cfr. punching shear), off to the two strips that border each quadrant.

As such, the Modified Bond Model uses elements of one-way and two-way shear approaches, and helps us to describe the transition zone between pure beam shear behavior and punching shear behavior.

[1] Alexander, S. D. B. and Simmonds, S. H., 1992, "Bond Model for Concentric Punching Shear," ACI Structural Journal, V. 89, No. 3, pp. 325-334.