Application of Modified Bond Model to the capacity of Ruytenschildt Bridge

I recently gave a presentation in a session at the ACI Fall Convention on "Recent Developments in Two-way Slabs: Design, Analysis, Construction, and Evaluation". The session, in reality, turned out to be mostly aimed at shear problemns in slabs (which I enjoyed attending, of course).
This presentation combined the proof loading of the Ruytenschildt Bridge in Friesland, with my plasticity-based model that is under development.

The abstract of the presentation is the following:

The Ruytenschildt bridge in Friesland is a continuously supported concrete slab bridge, and was tested in two spans to failure in August 2014. The results of this experiment are valuable for the analysis of existing slab bridges and for analyzing the moment and shear capacity of reinforced concrete slabs and slab bridges.

Earlier analyses found that a large number of existing slab bridges in The Netherlands rate as insufficient for shear. However, these analyses did not take into account the beneficial effect of transverse load redistribution. Therefore, the Modified Bond Model was developed. This model covers beam shear, punching shear and flexure for reinforced concrete slabs.

The test results are now to compare to the predictions with the Modified Bond Model. Since the Modified Bond Model is independent of the failure mode, the maximum load that is found can be directly correlated to the maximum tandem load in the experiment. Comparing the test results on the bridge with the predictions based on the Modified Bond Model shows good correspondence. The results are also compared to a new proposal for vmin, the minimum shear stress at which shear failure takes place. For smaller value, a moment failure takes place.

While the presented results only show a comparison between 2 tests on an existing bridge and the proposed Modified Bond Model, the results indicate that the Modified Bond Model can become a useful tool for design and analysis of reinforced concrete slabs based on the principles of the theory of plasticity.

You can find the slides here:

Application of Modified Bond Model to the capacity of Ruytenschildt Bridge from Eva Lantsoght

Predicting the Shear Capacity of Reinforced Concrete Slabs subjected to Concentrated Loads close to Supports with the Modified Bond Model

For IABSE 2014, I published the first paper about the theoretical work about the Modified Bond Model from my dissertation.

The abstract of the paper is:

The shear problem is typically studied by testing small, heavily reinforced, slender beams subjected to concentrated loads, resulting in a beam shear failure, or by testing slab-column connections, resulting in a punching shear failure. Slabs subjected to concentrated loads close to supports, as occurring when truck loads are placed on slab bridges, are much less studied. For this purpose, the Bond Model for concentric punching shear was studied at first. Then, modifications were made, resulting in the Modified Bond Model. The Modified Bond Model takes into account the enhanced capacity resulting from the direct strut that forms between the load and the support. Moreover, the Modified Bond Model is able to deal with moment changes between the support and the span, as occurs near continuous supports, and can take into account the reduction in capacity when the load is placed near to the edge. The resulting Modified Bond Model is compared to the results of experiments that were carried out at the Stevin laboratory. As compared to the Eurocodes (NEN-EN 1992-1-1:2005) and the ACI code (ACI 318-11), the Modified Bond Model leads to a better prediction.

Predicting the Shear Capacity of Reinforced Concrete Slabs subjected to Concentrated Loads close to Supports with the Modified Bond Model from Eva Lantsoght

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: There is still life in "dead" slabs

The third proposition of my dissertation is the following:

The very large redistribution capacity of slabs is demonstrated, amongst others, by carrying out experiments on severely damaged and locally failed specimens that led, on average, to a capacity of about 80% of a virgin specimen.

or in Dutch:

Het zeer grote vermogen tot herverdeling van platen is onder andere aangetoond door proeven uit te voeren op zwaar beschadigde en lokaal bezweken laten, waarbij gemiddeld een capaciteit van ongeveer 80% van een onbeschadigd proefstuk gehaald werd.

This proposition is based on a story.

Initially, we were planning to do two or four tests per slab. For testing with the concentrated load in the middle of the width, we were planning two tests per slab: one at each support. For testing with the concentrated load near the edge, we were planning four tests: two close to every support (one east, and one west).

As we were testing our first slab, with loads in the middle of the width, we suddenly grew curious. What if we would test this completely damaged slab with the concentrated load near the edge? So, we wouldn't be loading exactly at the location of were the slab already failed completely, but at less than 1m away from the failed part.

And if I say "failed", I mean huge cracks. Like this case here, our cracks were 2cm wide, I could almost stick my fingers into it.



We didn't expect much from this experiment. We didn't plan to mark cracks, we didn't plan for load steps. We assumed we'd reach failure before 200kN (which would be the first load step in an experiment on a virgin specimen).

We were so wrong.

The load kept on increasing, and I started slowly moving towards the exit of the lab, as I thought we'd be seeing some extremely explosive failure, with all that energy held within the specimen.

We reached a large failure load, and the failure mode was very similar to an experiment on a virgin specimen - much to our surprise.

For that reason, we started to do 6 experiments per slab: either 2 "virgin" (or "uncracked") ones in the middle, and then 4 "cracked" ones at the edges, or the other way around.



This testing sequence meant of course more experiments, but also more data... and we used the comparison between the "uncracked" and "cracked" tests to see the effect of redistribution in slabs: we saw experimentally that the "cracked" tests had on average 80% of the capacity of an "uncracked" test.

In beams, the least bit of cracking might have a negative influence on the shear capacity, as we learned from experiments on beams that were also done in Delft [1].

Slabs, on the other hand, have the ability to redistribute forces. Even a local failure can't stop them from doing so. And that -again- is a reason why slabs behave structurally very different in shear than beams.

[1] Yang, Y., 2011, "Report of Experimental Research on Shear Capacity of Beams Close to Intermediate Supports," V. Stevinrapport 25.5-11-10, Delft University of Technology, the Netherlands, 58 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.

Project #tweetprop: On Slabs versus Beams

The first proposition of my dissertation is the following:

The two-dimenional shear-carrying behaviour of one-way slabs under concentrated loads close to supports should be treated differently than the one-dimensional shear-caryring behaviour of beams.

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

Het tweedimensionale afschuifdraagvermogen van in één richting dragende platen onder geconcentreerde belastingen nabij de opleggingen moet anders behandeld worden dan het eendimensionale afschuifdraagvermogen van balken.

This proposition is one of the main findings of my research, and a conclusions that I have previously published in the ACI Structural Journal as well as in a number of conference papers.

Let me break the justification of this proposition down into the observations, and the explanations based on the experimental evidence as well as theoretical reasons.

What did we observe?

In our shear experiments, we subjected slabs to a concentrated load close to the support. We studied the influence of different parameters on the shear capacity. Most shear experiments in the literature are experiments on beams, that typically have a small cross-section, that are heavily reinforced in bending and that are tested in four-point bending. Our understanding of how different parameters effect the shear capacity is thus mostly supported by these experiments. When we compared our experiments to the knowledge from beams, we found differences. The shear capacity of slabs depends mostly on geometric parameters. In beam shear experiments, the capacity depends strongly on the concrete compressive strength. For the range of concrete strengths that we tested, we did not see such a strong dependence.

To study how the behavior changes from beam to slab, we tested a series of specimens with an increasing width. We found how the dependence of the shear capacity on parameters changes as the specimen width changes. We also saw how different the cracking pattern is for slabs as compared to beams.

In this figure, we see the bottom face after an experiment of a specimen of 0,5m wide and a specimen of 2,5m wide. All other parameters are kept identical. The "beam" specimen only has horizontal cracks, while the "slab" specimen has a grid-like pattern of horizontal and vertical cracks following the rebar, but also has inclined cracks on the bottom that indicate shear distress, and even some punching damage.

How can we explain this?

Let's talk strut-and-tie models here. If we have a beam with a load close to the support, the load is carried by a compression strut between the load and the support - that's in the Eurocode as well.
But what happens when we apply this to a slab? If we have a concentrated load, we know that the forces can "fan out" in the width direction.

This figure shows why the influence of the distance between the load and the support is different for slabs as compared to beams. We see the top view of a slab subjected to a concentrated load. In a beam, our compression strut is the line of a/dl = 1 from the figure. In a slab, we have many struts that can develop - an entire fan of them. So, we can say that in a slab, we develop a three-dimensional strut-an-tie model. Now, two dimensions play a role in our shear capacity: the distance between the load and the support (a or av), and the width of the specimen. If we then apply this idea to the effect of the distance between the load and the support to the shear capacity, we see that we need to account for a sort of "average distance" for all these struts in a slab (a/dl > 1 on average), while for a beam this is defined only by a/dl = 1.

To conclude: we saw in our experiments a difference between slabs and beams in their dependency on parameters to define the shear capacity. This difference can be explained by acknowledging that slabs carry concentrated loads in what can be represented by a three-dimensional strut-and-tie model. As such, slabs have a two-dimensional load-carrying behavior, which is different from the one-dimensional load-carrying behavior in shear that we know from beams (and that is well-documented in the literature).

Applying Experimental Results to the Shear Assessment Method for Solid Slab Bridges

I recently presented a overview of the recommendations for shear assessment from my PhD research at Concrete 2013 in Gold Coast, Australia. In this paper and presentation, we looked at the our experiments, and how these led to the recommendations for shear assessment.

The abstract of the paper is the following:

"The combination of increased live loads and a more conservative shear capacity in the recently implemented Eurocodes, resulted in a large number of existing solid slab bridges in the Netherlands being shear-critical upon assessment. However, an enhancement of the shear capacity can occur in slabs under concentrated wheel loads due to transverse load redistribution. To quantify this effect, a comprehensive series of experiments on slabs and slabs strips under a concentrated load near to the support and under a combination of a concentrated and a line load was carried out. The experiments show the difference in behaviour for slabs, carrying the load in a two-dimensional way, as compared to beams in shear. The results from the laboratory research are used to develop recommendations, that are easily used in combination with the codes. These recommendations are implemented in a spreadsheet-based first-level assessment tool, the Quick Scan method. The assessment with this tool of selected cases of existing solid slab bridges shows that applying the experimental results into the assessment practice leads to an improved selection ability of the Quick Scan method."

You can find the slides here:

Applying Experimental Results to the Shear Assessment Method for Solid Slab Bridges from Eva Lantsoght

Paper published in the ACI Structural Journal

Our paper "Shear in One-Way Slabs under Concentrated Load Close to Support" is now available online at the website of the American Concrete Institute and will be published in the March/April 2013 version of the ACI Structural Journal.

Getting this paper in there was a long process. From the first drafts in December 2010, via the first submission in May 2011 and then revised submission and finally acceptance and receiving the print proofs - it's been an adventure. First babysteps into the real academic life?

The abstract of the paper is the following:
One-way slabs under concentrated loads are generally designed for shear by checking the beam shear resistance and the punching shear resistance over an effective width. Only a small number of test data regarding the shear resistance of one-way slabs subjected to concentrated loads is currently available. To be able to better evaluate the shear resistance of one-way slabs, a series of experiments was carried out on continuous one-way slabs (5 m x 2.5 m x 0.3 m [16.4 ft x 8.2 ft x 11.8 in.]) subjected to concentrated loads close to the supports, in which the load position, transverse reinforcement ratio, and concrete strength were varied. The test results are compared with code provisions and a method developed by Regan. The results show a different behavior in shear for slabs under concentrated loads than for beams.

ASCE Structures Congress 2011 - paper and presentation

Last month, I presented a paper at the ASCE Structures Congress 2011.

The full paper is published in the conference proceedings, as well as online in the ASCE library.
The abstract of the paper is:

When assessing the capacity of existing reinforced concrete slab bridges under the increased traffic loads prescribed in the current codes, shear may become the critical failure mode. To better evaluate the shear capacity of reinforced concrete slab bridges, a series of experiments is carried out on continuous one‐way slabs loaded close to the support. Eight continuous slabs of 5m × 2,5m × 0,3m are tested. The loading position is taken at different a/d ratios. Six slabs with a standard concrete mixture and two slabs with a higher strength concrete are tested. The influence of the loading history, the shear span to depth ratio and the concrete compressive strength is discussed. Conclusions on the influence of these parameters on the one‐way shear capacity of reinforced concrete slabs are drawn.

You can also find the slides I used for my presentation here:

Experimental study of shear capacity of reinforced concrete slabs

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