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.

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

Shear and Punching 101: Distance in the codes

 I recently received a message with the following question:

Normally when we treat the problem of determination of shear stress in slabs, a critical section at a distance of half the effective depth of slab is taken from the support (like columns). Can you explain why this is recommended in many Codes?

Since I think this issue is not very clear in the background of the building codes, I'd like to share what I found while executing my literature review here.

There are two reasons for a distance of d/2 away from the column:
- for punching, you determine the punching perimeter at a certain distance (depending on the code). There is no physical explanation for the distance itself, although researchers like to relate this distance to the inclination of the shear crack that would result from the root of column to the top of the slab where the punching cone intersects (for the case of a flat slab floor for example).
If you look at the background of the codes, for example ACI 318, you find that the chosen distance is based on a better statistical result for the resulting punching perimeter in combination with the ACI formula as compared to test results (work done by Moe, 1961 [1]).
- for shear, we assume direct transfer of the load from its point of application to the support for loads that are at a distance d/2 to d from the column (also depending on the considered code). This direct transfer is by means of a compressive strut, which is of course much stronger than a section in shear.

[1] Moe, J. (1961). Shearing strength of reinforced concrete slabs and footings under concentrated loads, Portland Cement Association Research and Development laboratories, Skokie, IL.

fib Symposium 2011 - paper and presentation

Last week, I attended the fib Symposium 2011 in Prague, and presented some of my experimental results in the Friday morning session on Construction Technology.

The full paper is published on the CD proceedings, and the short version of 4 pages is published in the printed version of the proceedings. The abstract is the following:

Reinforced concrete one-way slabs subjected to concentrated loads are designed for shear by checking beam shear over an effective width and punching shear. Only a limited number of test data regarding the shear capacity of one-way slabs subjected to concentrated loads is available. To better evaluate the shear capacity of reinforced concrete one-way slabs, a series of experiments has been carried out on continuous one-way slabs (5m x 2,5m x 0,3m) loaded close to the support. The influence of the shear span to depth ratio is discussed. Conclusions about the influence of this parameter on the one-way shear capacity of reinforced concrete slabs and possible explanations for the difference with beams are provided. Test results are compared to the Eurocode provisions and a method to calculate shear capacity from the literature. A higher shear strength is found as compared to the Eurocode. As a result of these experiments expressions resulting in a higher theoretical shear strength for the design of one-way slabs under concentrated loads are recommended.

The keywords were: Shear, One-Way Slabs, Effective Width

Here are the slides I used for my 12 minute presentation:

Experimental study of shear in reinforced concrete one way slabs subjected to concentrated loads

View more presentations from elantsoght.

As you can see, I added the tables with the experimental results which I used in the paper as a few extra slides at the end of my presentation. I didn't want to go over all the numbers during my talk, but I wanted to be prepared for more detailed questions. And in fact, I had a question about the flexural capacity of the tested slabs, so I could simply show the table with the reinforcement ratios and explain how we designed the reinforcement.

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

View more presentations from elantsoght

The riddle of shear failure

Long ago, when I was an engineering student at Vrije Universiteit Brussel, I did not even realize that my research topic (of which I think I probably could spend a lifetime in researching it) was actually an unanswered question.

I remember taking Concrete Structures in Brussels. This class is the only concrete design class which is offered to civil engineering master students. No offense, I'm only pointing this out to show how different (or less design oriented and much more math and basic principles oriented) the Belgian engineering education is.
When the topic of shear in reinforced concrete beams was discussed, we quickly looked at the equation for the concrete part Vc and then immediately went into two methods of determining the necessary amount of stirrups. The superposition of the concrete part and the steel part was not questioned. The Eurocode 2 formula for the concrete contribution was explained term by term: k is the factor to take into account the size effect,.. To me, it appeared as if there was no problem at all with shear. We have a design formula for shear in beams, which is the holy grail for all shear design.

Two and a half years later, I arrived at Georgia Tech with my two volumes of lecture notes on reinforced concrete from Brussels. Together with my advisor from Georgia Tech, I looked at the material I had covered previously. He looked at the material, and every now and then he would say how "French" my material appeared to him. Even though, according to him, I had covered all topics, he advised me to take the master's course in reinforced concrete, to get used to the strange units and the ACI code.
When shear in concrete was treated, I heard about exotic mechanisms as "aggregate interlock" and "dowel action" for the very first time. I saw an equation for the concrete part Vc which did not look like the Eurocode 2 formula at all. In the lecture notes, the graphs from the ACI committee 326 from the 1960s were shown in which the ACI code formula which was proposed then was compared to a number of shear tests on beams. The scatter was still very large, and gave a coefficient of variation of (order of magnitude) 20%.
For one second the idea crossed my mind that this was because the ACI code formula was much easier and more compact than the Eurocode 2 formula, which looked more exact to me. But shortly afterwards, I started to realize that our current design methods for shear in beams are empirical methods. These methods are the result of shear tests, carried out on small, slender, highly reinforced concrete beams. Extrapolating the results of this types of beams could be questioned. It is therefore not unlogical that it became common practice to use generally conservative rules for shear, to avoid the sudden shear failure and make sure beams (and other structural concrete elements) fail in flexure, since signs of distress appear at load levels below the failure load.

After my job interview at TU Delft, I started to think about the topic for my master's research project course. In correspondence with my future advisors from TU Delft and my advisor from Georgia Tech, we decided to study punching shear in slabs. This problem is related to shear in beams, but works in two dimensions (as a slab has an extra dimensions as compared to a beam). I discovered how much we actually don't know about shear and torsion, and every paper I read just raised more questions. I found it quite exciting to discover that there are still so many questions to be researched.

A year and 5 months ago I started my research at TU Delft. I'm studying both shear in beams and punching shear in slabs and try to see how these mechanisms are interrelated and can occur in bridge decks. Every day I'm learning more, and every day I am formulating more questions to be solved.

However, when I try to explain some of my former classmates from Brussels what I am doing in Delft, I only get some blank stares. Is shear a problem? We have an equation for that in Eurocode 2! And then I tell them about the absurdly high scatter I get when I compare my test data to the calculated values from the code, after which I usually receive a very puzzled look.

* The title of this post is taken after G.N.J. Kani's famous article published in the ACI Journal Proceedings from 1964 (The riddle of shear failure and its solution)

If I had a time machine...

This post has been inspired by an idea from the daily post blog:

If you had a time machine that only let you spend one hour in a different time, what date would you go to?

I would set the time machine and "fly" (or what verb should you use for this?) back to some time in the mid 1960s to the University of Toronto to spend one hour discussing with Dr. Kani.

Just as many other researchers in the late 50s and 60s, he studied shear in reinforced concrete, which is also the topic of my research. I've read the few papers he wrote, as well as the book which was published more than a decade after his death. Most of all, though, I was impressed by the discussion and closure which resulted from his paper titled "the riddle of shear failure and its solution."

The discussion and closure were about 30 pages long, and when I was reading this, I got a glimpse of how it must have been to attend a live discussion with those pioneers in shear research. So many good ideas, so much enthusiasm sparks out of their writing. I have the impression those must have been thrilling times.

I'd love to go back in time, with the results and ideas that I have, and discuss with a researcher like Dr. Kani. I'm sure I would learn so much in that hour's worth of time.