Shear capacity of slabs and slab strips loaded close to the support
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The document summarizes research on the shear capacity of concrete slabs and strips loaded close to supports. Three key findings are: 1) The shear span to depth ratio has a smaller influence on shear capacity in slabs compared to beams due to three-dimensional load spreading in slabs. 2) Increasing the size of the loading plate increases the shear capacity more for wider slabs, as it allows stresses to spread over a larger area to form three-dimensional stress patterns. 3) Code design methods like Eurocode and the French National Annex conservatively predict the shear capacity of slabs, while a method by Regan that considers punching shear and enhancement close to
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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.
Bridging the gap between one way and two-way shear in slabs
The shear capacity of slabs under concentrated loads is particularly of interest for bridge decks under concentrated live loads. Often, one-way shear will be analyzed by considering the slab as a wide beam (without taking advantage of the transverse load redistribution capacity of the slab) and two-way shear by considering the punching area around the load. Since experiments showed that the failure mode of slabs under concentrated loads is a combination of one-way and two-way shear as well as two-way flexure, a method was sought that bridges the gap between traditional one-way and two-way shear approaches. The proposed method is a plasticity-based method. This method is based on the Strip Model for concentric punching shear and takes the effects of the geometry into account for describing the ultimate capacity of a slab under a concentrated load. The model consists of “strips” that work with arching action (one-way shear) and slab “quadrants” that work in two-way shear. As such, the resulting Extended Strip Model is suitable for the design and assessment of elements that are in the transition zone between one-way and two-way shear.
MODIFIED BOND MODEL FOR SHEAR IN SLABS UNDER CONCENTRATED LOADS
Slabs subjected to concentrated loads close to supports, as occurring for truck loads on slab bridges,
are less studied than beams in shear or slab-column connections in punching. To predict the shear
capacity for this case, the Bond Model for concentric punching shear was studied initially.
Modifications to this model resulted in the Modified Bond Model, which takes into account the
enhanced capacity from the direct transfer of the load to the support, is able to deal with moment sign
changes as occurring near continuous supports, and can take into account the reduction in capacity,
resulting from the geometry when the load is placed close to the edge. The model is then compared to
the results of experiments on slabs subjected to concentrated loads close to supports. As compared to
the Eurocode and the ACI code, the Modified Bond Model leads to a significantly better prediction of
the experimental results. The Modified Bond Model is one of the few models available to describe the
shear capacity of slabs subjected to concentrated loads close to supports and can be used for design
and assessment.
Recommendations for the Shear Assessment of Reinforced Concrete Solid Slab Br...
As a result of the heavier live load models and more conservative shear approaches prescribed by the recently implemented Eurocodes, a large number of existing reinforced concrete solid slab bridges in the Netherlands were found to be shear-critical. The beneficial effect of the transverse load redistribution in slabs under concentrated loads is not taken into account. To quantify this effect, a comprehensive number of experiments was carried out. These results are used to formulate recommendations for the assessment practice for the case of solid slab bridges. The recommendations focus on the effective width over which the axle load can be distributed and its lower bound, the beneficial effect of transverse load redistribution and the influence of the yield strength of the reinforcement on the lower bound of the shear capacity. These recommendations are implemented in the “Quick Scan” method, leading to a significant reduction of the shear stresses.
Effective Width in Shear of Reinforced Concrete Solid Slab Bridges under Whee...
For the assessment of reinforced concrete slab bridges in the Netherlands, the shear stress resulting from the dead loads and live loads is determined in a spreadsheet or from a finite element model. In a spreadsheet-based approach, an assumption for the distribution of the loads from the wheel prints is necessary. When finite element methods are used, it is necessary to determine over which length (a multiple of the effective depth) the peak shear stress can be distributed for comparison to the design shear capacity.
To recommend a load-spreading method, experiments were executed on slab strips of increasing widths. The shear capacity did not increase with the increasing width upon passing a threshold. This threshold is compared to different load spreading methods, indicating that a distribution from the far side of the wheel print is to be preferred. This recommendation is also supported by the results of a statistical analysis and the stress distribution in nonlinear finite element models.
To find the distribution width in a finite element method, a numerical model is compared to an experiment on a slab subjected to a concentrated load in which the support consists of a line of 7 bearings equipped with load cells measuring the reaction forces. These measurements were compared to the stress profile at the support from the model, showing that the peak can be distributed over 4 times the effective depth.
These recommendations for the effective width and distribution width are research-based tools that replace the previously used rules of thumb resulting from engineering judgement.
Shear and moment capacity of the Ruytenschildt Bridge
In August 2014, the Ruytenschildt Bridge, a reinforced concrete solid slab bridge, in Friesland, the Netherlands was tested until failure. One of the goals of the experiment is to analyze the failure mode of the slab bridge under a tandem of 4 wheel loads and to compare the capacity of the full bridge structure to the predicted results, to have an idea of the residual strength of existing bridges. The methods used are experi-mental (testing of the bridge to failure in two of its five spans) and analytical. The analytical work involved predicting the bending moment capacity, the shear capacity and the punching capacity of the bridge. In both spans, the bridge failed in flexure. The total capacity during the experiment was significantly higher than pre-dicted. The results indicate that the traditional rating procedures for shear are very conservative when applied to slab bridges that benefit from transverse load redistribution.
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For an initial design or assessment of a reinforced concrete solid slab bridge, spreadsheet-based or hand calculations are typically used. The shear stress is compared to the shear capacity as prescribed by the code. The distributed loads result in a uniform shear stress at the support. Concentrated loads are less straightforward to take into account. It is known that transverse load redistribution occurs in slabs. To explore the topic of transverse load redistribution, experiments on elements subjected to a concentrated load close to the support were carried out. These elements had an increasing width, starting at 0.5 m and increasing with steps of 0.5 m up to 2.5 m, so that the effect of transverse load redistribution could be studied. The threshold effective width resulting from the experiments was then compared to load spreading methods, in order to give recommendations for the practical use with concentrated loads. It was found that the load spreading method as used in French practice is to be preferred. As compared to load spreading methods that were used previously, the French load spreading method results in smaller shear stresses at the support. This result allows for more economic designs and provides a better assessment tool.
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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.
Bridging the gap between one way and two-way shear in slabs
The shear capacity of slabs under concentrated loads is particularly of interest for bridge decks under concentrated live loads. Often, one-way shear will be analyzed by considering the slab as a wide beam (without taking advantage of the transverse load redistribution capacity of the slab) and two-way shear by considering the punching area around the load. Since experiments showed that the failure mode of slabs under concentrated loads is a combination of one-way and two-way shear as well as two-way flexure, a method was sought that bridges the gap between traditional one-way and two-way shear approaches. The proposed method is a plasticity-based method. This method is based on the Strip Model for concentric punching shear and takes the effects of the geometry into account for describing the ultimate capacity of a slab under a concentrated load. The model consists of “strips” that work with arching action (one-way shear) and slab “quadrants” that work in two-way shear. As such, the resulting Extended Strip Model is suitable for the design and assessment of elements that are in the transition zone between one-way and two-way shear.
MODIFIED BOND MODEL FOR SHEAR IN SLABS UNDER CONCENTRATED LOADS
Slabs subjected to concentrated loads close to supports, as occurring for truck loads on slab bridges,
are less studied than beams in shear or slab-column connections in punching. To predict the shear
capacity for this case, the Bond Model for concentric punching shear was studied initially.
Modifications to this model resulted in the Modified Bond Model, which takes into account the
enhanced capacity from the direct transfer of the load to the support, is able to deal with moment sign
changes as occurring near continuous supports, and can take into account the reduction in capacity,
resulting from the geometry when the load is placed close to the edge. The model is then compared to
the results of experiments on slabs subjected to concentrated loads close to supports. As compared to
the Eurocode and the ACI code, the Modified Bond Model leads to a significantly better prediction of
the experimental results. The Modified Bond Model is one of the few models available to describe the
shear capacity of slabs subjected to concentrated loads close to supports and can be used for design
and assessment.
Recommendations for the Shear Assessment of Reinforced Concrete Solid Slab Br...
As a result of the heavier live load models and more conservative shear approaches prescribed by the recently implemented Eurocodes, a large number of existing reinforced concrete solid slab bridges in the Netherlands were found to be shear-critical. The beneficial effect of the transverse load redistribution in slabs under concentrated loads is not taken into account. To quantify this effect, a comprehensive number of experiments was carried out. These results are used to formulate recommendations for the assessment practice for the case of solid slab bridges. The recommendations focus on the effective width over which the axle load can be distributed and its lower bound, the beneficial effect of transverse load redistribution and the influence of the yield strength of the reinforcement on the lower bound of the shear capacity. These recommendations are implemented in the “Quick Scan” method, leading to a significant reduction of the shear stresses.
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For the assessment of reinforced concrete slab bridges in the Netherlands, the shear stress resulting from the dead loads and live loads is determined in a spreadsheet or from a finite element model. In a spreadsheet-based approach, an assumption for the distribution of the loads from the wheel prints is necessary. When finite element methods are used, it is necessary to determine over which length (a multiple of the effective depth) the peak shear stress can be distributed for comparison to the design shear capacity.
To recommend a load-spreading method, experiments were executed on slab strips of increasing widths. The shear capacity did not increase with the increasing width upon passing a threshold. This threshold is compared to different load spreading methods, indicating that a distribution from the far side of the wheel print is to be preferred. This recommendation is also supported by the results of a statistical analysis and the stress distribution in nonlinear finite element models.
To find the distribution width in a finite element method, a numerical model is compared to an experiment on a slab subjected to a concentrated load in which the support consists of a line of 7 bearings equipped with load cells measuring the reaction forces. These measurements were compared to the stress profile at the support from the model, showing that the peak can be distributed over 4 times the effective depth.
These recommendations for the effective width and distribution width are research-based tools that replace the previously used rules of thumb resulting from engineering judgement.
Shear and moment capacity of the Ruytenschildt Bridge
In August 2014, the Ruytenschildt Bridge, a reinforced concrete solid slab bridge, in Friesland, the Netherlands was tested until failure. One of the goals of the experiment is to analyze the failure mode of the slab bridge under a tandem of 4 wheel loads and to compare the capacity of the full bridge structure to the predicted results, to have an idea of the residual strength of existing bridges. The methods used are experi-mental (testing of the bridge to failure in two of its five spans) and analytical. The analytical work involved predicting the bending moment capacity, the shear capacity and the punching capacity of the bridge. In both spans, the bridge failed in flexure. The total capacity during the experiment was significantly higher than pre-dicted. The results indicate that the traditional rating procedures for shear are very conservative when applied to slab bridges that benefit from transverse load redistribution.
Practical Application of Transverse Load Redistribution in Reinforced Concret...
For an initial design or assessment of a reinforced concrete solid slab bridge, spreadsheet-based or hand calculations are typically used. The shear stress is compared to the shear capacity as prescribed by the code. The distributed loads result in a uniform shear stress at the support. Concentrated loads are less straightforward to take into account. It is known that transverse load redistribution occurs in slabs. To explore the topic of transverse load redistribution, experiments on elements subjected to a concentrated load close to the support were carried out. These elements had an increasing width, starting at 0.5 m and increasing with steps of 0.5 m up to 2.5 m, so that the effect of transverse load redistribution could be studied. The threshold effective width resulting from the experiments was then compared to load spreading methods, in order to give recommendations for the practical use with concentrated loads. It was found that the load spreading method as used in French practice is to be preferred. As compared to load spreading methods that were used previously, the French load spreading method results in smaller shear stresses at the support. This result allows for more economic designs and provides a better assessment tool.
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In August 2014, the Ruytenschildt Bridge, a reinforced concrete solid slab bridge (reinforced with plain bars) in the Friesland province in the Netherlands was tested until failure. One of the goals of proof loading and testing this bridge to failure, was to study the failure mode of existing slab bridges. The combination of smaller shear capacities as prescribed by the Eurocode in combination with the heavier live load models, has raised concerns with regard to a number of existing slab bridges in the Netherlands. As the shear capacity of existing bridges is under study, the results of testing an actual slab bridge until failure are used to compare to the results of testing half-scale slab specimens in the laboratory, and the conclusions resulting from those experiments. In this paper, the results of the predictions based on the first order of approximation rating procedure from the Netherlands for shear, the Quick Scan method, as well as based on predictions of the failure mode and the average predicted capacity are compared to the experimental results. The predictions show a possibility of shear failure in the second span of the bridge. The experiment showed that both spans of the bridge failed in flexure. The observed failure mode is important, as some of the results indicate that the solid slab bridges, currently under discussion with regard to their shear capacity, fail in flexure in reality. Flexural failure is considered a ductile failure compared to the brittle failure mode in case of a shear failure.
Defining loading criteria for proof loading
As the bridge stock in The Netherlands and Europe is ageing, various methods to analyse existing bridges are being studied. Proof loading of bridges is an option to study the capacity when crucial information about the structure is lacking. This information could be related to the material (for example, the effect of alkali-silica reaction on the structural capacity) as well as to the structural system (for example, the effect of restraints at the supports or transverse redistribution capacity). When it is decided to proof load a bridge, the question arises which maximum load should be attained during the experiment to approve the capacity of the bridge, and which criteria, based on the measurements during the test, would indicate that the proof loading needs to be aborted before reaching the maximum desired load (the so-called stop criteria). To define the required loading criteria, a review of the literature has been made, finite element models of existing viaducts have been made, and on these viaducts, proof loading tests have been carried out. These bridges were heavily instrumented, with a goal of learning as much as possible about the structural behaviour during proof loading. As a result of the analysis and experiments, recommendations are given for proof loading of bridges with respect to the required maximum load and the stop criteria.
These recommendations are important, since they form the basis of a guideline for proof loading of existing concrete bridges that is under development in The Netherlands.
Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs
For the assessment of existing structures and the design of new structures, it is important to have a good understanding of the flow of forces, here applied to reinforced concrete solid slabs. Two analyti-cal methods are used: finite element models with 3D solid elements and a plasticity-based model that is suita-ble for hand calculations, the Modified Bond Model. The slabs that are modeled are half-scale models of rein-forced concrete solid slab bridges. As the Eurocode live load model prescribes more heavily loaded trucks in the first lane, the load model is asymmetric. For the finite element models, limited use is made of the redistri-bution capacity of the slab. For the Modified Bond Model, the influence of torsion and the edge effect need to be taken into account. The results of these studies improve the current state-of-the-art for analysis and design of reinforced concrete slabs.
Application of Modified Bond Model to the capacity of Ruytenschildt Bridge
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.
Load testing of reinforced concrete bridges in the Netherlands
As the bridge stock in The Netherlands and Europe is ageing, various methods to analyze existing bridges are being studied. Load testing of bridges is an option to study the capacity when crucial information about the structure is lacking. This information could be related to the material (for example, the effect of ASR on the capacity) as well as to the structural system (for example, the effect of restraints at the supports or transverse redistribution capacity).
When it is decided to load test a bridge, the question arises which maximum load should be attained during the experiment to approve the capacity of the bridge, and which criteria, based on the measurements during the test, would indicate that the test needs to be aborted before reaching the maximum desired load (the “stop criteria”).
A number of reinforced concrete slab bridges have been load tested over the course of the past few years. These load tests were pilot cases, in which the bridges were heavily equipped with sensors, to study the bridges’ behavior at critical positions for bending moment and shear. The test results were then extensively analyzed, and compared to the stop criteria available in the currently used codes and guidelines.
As a result of the analysis and experiments, recommendations are given for proof loading of bridges. These recommendations are important, since they will form the basis of a guideline for proof loading of existing concrete bridges that is under development in The Netherlands.
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issue of the force transmission from the embedded steel pro le to the surrounding concrete
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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.
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Shear capacity of slabs and slab strips loaded close to the support
- 1. Shear Capacity of Slabs and Slab Strips Loaded Close to the Support Eva Lantsoght
- 5. Experiments Test setup Size: 5m x 2,5m x 0,3m Continuous support, Line supports Load: vary a/d and position along width
- 12. Size of loading plate Introduction (1) AASHTO loading truck Tire contact area: 510mm x 250mm EN 1991-2 load model 1 400mm x 400mm
- 13. Size of loading plate Introduction (2) 45 ° load spreading 45 ° load spreading – French practice Influence size of loading plate on shear capacity?
- 17. Overall width and Effective width Test results (1)
- 19. Overall width and Effective width Test results (3) Comparison cracking pattern BS2T1 and S9T1
- 21. Comparison to Code Methods Results (1)
- 27. Contact: Eva Lantsoght [email_address] +31(0)152787449