Size effect on punching shear strength: differences and analogies with shear in one-way slabs

Size effect has been theoretically and experimentally acknowledged as a phenomenon influencing the shear and punching shear strength of concrete structures, with reducing unitary shear strength for increasing member sizes. For members failing in shear, as beams or one-way slabs without transverse reinforcement subjected to uniform loading, size effect has shown to have a variable influence, with low significance for failures governed by limit analysis (strength or yield criterion) and large influence for members failing in a brittle manner. When the response of a member failing in shear can be reasonably approximated by a linear behaviour (i.e. linear relationship between the acting shear force and the crack widths), the predictions of Linear Elastic Fracture Mechanics (LEFM) can be applied to asymptotically large specimen sizes. This phenomenon can for instance be demonstrated by the Critical Shear Crack Theory (CSCT) and leads to a dependence of the shear strength with the power -1/2 of the size of the specimen. Nevertheless, in actual structures failing in shear (as slabs or shells), the structural response is normally characterized by some level of redundancy and capacity to redistribute internal forces in the longitudinal and transversal directions. In this case, the relationship between the acting shear force and the crack widths is not linear (with lower crack widths associated to larger shear strengths) and the influence of size effect on the shear strength is milder than that predicted by LEFM. With respect to punching (shear failures due to concentrated loads in two-way slabs), a similar behaviour is observed with respect to size effect. A low dependency can be observed when limit analysis governs whereas, for brittle failures, size effect becomes significant. In this case, it can be observed that the behaviour of slabs is highly nonlinear (as for redundant members failing in shear), and the crack openings are to a large extent dependent on local and structural tension-stiffening effects. This deviates the actual behaviour from the one predicted by LEFM and modifies the influence of size effect, which becomes less significant than according to LEFM. In this paper, this phenomenon is investigated by means of the CSCT, providing a consistent frame to analyse size and strain effects accounting for realistic slab responses.

Assessment of Shear Strength for Existing Bridges with Low Amounts of Shear Reinforcement

Miguel Fernández Ruiz, Aurelio Muttoni, Michael Markus Rupf

Design of concrete girder bridges has significantly evolved during the last decades. This has been particularly relevant with respect to shear design, motivated by changes in actions and design models. As a consequence, assessing the shear strength of existing bridges leads in many cases to unsatisfactory safety levels. Furthermore, many existing bridges do not comply with current code regulations with respect to minimum amounts of shear reinforcement. This situation can lead to expensive retrofitting and strengthening of a significant number of existing bridges. The assessment of the shear strength of these bridges has thus become a significant task for structural engineers. Design codes are not always appropriate for assessing the strength of existing bridges. They propose safe models providing sufficient accuracy for design of a wide number of structures. However, these models do not account for some particularities of prestresses bridges and neglect a number of shear-transfer actions that can be relevant for their strength. This is typically the case of shear carried by the inclination of the compression chord, the increase of the stress in the tendons or the effective strength of concrete in the web of cracked prestressed girders. Accounting for more realistic approaches for these parameters may significantly increase the estimated strength of a structure with respect to code provisions, avoiding in many cases unnecessary retrofitting or strengthening. In this paper, the results of a tests campaign carried out at Ecole Polytechnique Fédérale de Lausanne on 10 prestressed concrete girders (10 meters long, 0.78 m high) are outlined. The specimens were provided with very low amounts of shear reinforcement and some of them present defective stirrup anchorage to simulate realistic conditions of existing structures. The experimental results are discussed with reference to the stress field method where the role of the different shear-transfer actions is investigated and compared to current code provisions.

fib Symposium Tel-Aviv 20132013

Seismic behavior of lightly reinforced concrete squat shear walls

Christian Greifenhagen

This thesis addresses the seismic evaluation of existing buildings. In particular, it focuses on the seismic behavior of lightly reinforced shear walls that are not designed to withstand earthquake actions. A shear strength envelope for the assessment of deformation capacity of these non-ductile walls is presented. The approach is the result of experimental investigations and analytical modeling. Existing models for plastic hinges in beams are enhanced in order to determine drift capacity of lightly reinforced concrete shear walls. The static-cyclic behavior of non-ductile, reinforced concrete shear walls is investigated by testing four small-scale specimens of shear span ratio equal to 0.8. The design of the specimens includes reinforcement ratios, and axial force levels in existing shear wall buildings. Although the specimens were expected to fail in brittle shear, low to moderate ductile response is obtained. The deformation capacity, not the shear strength, is found to be restricted by shear failure. It is observed that inherent shear strength of concrete and the concrete compression zone are the principal contributors to the shear capacity of lightly reinforced shear walls. It is also observed that low reinforcement ratios and moderate levels of axial force can efficiently prevent brittle response in shear. The analytical model consists of a plastic hinge over the entire height of the low-rise shear wall. Proposals are made for the strain distribution inside the plastic hinge. Explicit relationships between drift and base shear are established and it is found that the model accurately predicts the envelope curve of static-cyclic loading. The shear strength envelope is formulated by using the analytical model. Criteria for the failure modes of diagonal tension, of concrete crushing, and of sliding enclose the shear strength envelope. In addition, inherent shear strength forms the lower bound of this envelope. The contributions of reinforcement and concrete to shear capacity are formulated in terms of initial strength and strength decay. Accurate prediction of both the ductility supply and the drift capacity obtained in static-cyclic tests is observed. Validation of the shear strength envelope on full-size walls prevalent in existing buildings shows potential for further application. The proposal contributes to more realistic evaluation of shear strength in selected situations where available methods are too conservative. Hence, it allows for both avoiding costly seismic strengthening in such situations and better allocation of resources where they are really needed.

EPFL2006

A mechanical model for failures in shear of members without transverse reinforcement based on development of a critical shear crack

Francesco Cavagnis, Miguel Fernández Ruiz, Aurelio Muttoni

In this paper, a mechanical model consistent with the main assumptions of the Critical Shear Crack Theory (CSCT) is proposed for shear design of slender concrete members without shear reinforcement. To that aim, the shear force that can be transferred through the critical shear crack by aggregate interlock, residual tensile strength and dowelling action as well as due to the inclination of the compression chord are calculated by integration of fundamental constitutive laws accounting for the critical shear crack opening and kinematics at failure. The pertinence of the assumptions is validated through comparisons to detailed test measurements to assess their validity. The model allows predicting the failure load, the deformation capacity and the location of the critical shear crack leading to failure. The results are checked against large datasets and the model is finally used to discuss on the influence of the various parameters on the governing shear-transfer actions. The results are eventually used to propose improvements on the CSCT failure criterion for shear, relating the shear strength and its associated deformation capacity.