Beam or truss mechanism for shear in concrete

Abstract

An unpublished study by Prof. A.W. Beeby shows the differences in strength capacity between a reinforced concrete beam without shear reinforcement and the same beam with a cut-out section at the middle of the span. The cut-out section exists at the bottom part of the beam while the reinforcement still remains. It remarkably turns out that the strength capacity of the beam with the cut-out section is 1.6 times larger compared to the reference beam. The reference beam fails by a flexural shear crack which does not arise in the beam with the cut-out section. On the occasion of Beeby’s experiments and the lack of a simple physical model for a flexural shear crack this thesis has the objective to clarify the difference between a beam and a truss mechanism and the failure due to flexural shear cracks. The study is based on a simple supported beam without shear reinforcement subjected to a oncentrated load with a three point bending test with a slendernessratio of 2.45 and a reinforcement ratio of 0.89%. An analytical study describes the difference between the beam and a simplified truss mechanism. Linear analyses show the differences in stress distributions and deflections. The study shows the same difference in strength capacity as the experiments of Beeby. In addition quite a difference is revealed in the displacements of both mechanism. The truss mechanism shows a larger deformation compared to the beam mechanism. Finite element modelling with DIANA has been used to gain better insight in the difference of the strength capacity. The models use a total strain fixed crack model. The Hordijk-curve describes the tensile properties and an ideal relation describes the compressive properties. The decrease of the poisson ratio and the shear resistance around a crack have been taken into account by a damaged based shear retention model and a damaged based crack model. The finite element models show differences of the strength capacity within the same level of Beeby’s experiments. The force mechanism in both systems is different before the flexural shear crack arises in the beam. After a flexural shear crack occurs both mechanism seems to change into a similar truss mechanism, but detailed analyses show important deviations from this expectation. Variation of the cut-out dimensions shows that a too small gap results in a flexural shear crack and a too large gap in the failing of the cantilever part. Gaps between these limits all change into a truss mechanism which reaches the same level of failure load as the basic truss. The decrease of stiffness of the beam results in more compressive stresses in the truss mechanism preventing the occurrence of the shear crack. If the shear crack does not occur in the beam it results in a higher strength capacity. A dedicated shaped beam which has initially exactly the shape of a shear cracked beam without the concrete part below the crack, has a different strength capacity compared to a regular shear cracked beam. The dedicated shaped beam proves that the crack shape itself has no influence on the ability of converting into a truss. It turns out that in the regular beam it is impossible to develop a perfect truss mechanism after a flexural shear crack due to the concrete that is still present beneath the crack. The concrete beneath the crack causes a different stress distribution in the top of the beam compared to the dedicated shaped beam without this concrete. A hypothesis is given for the failure of the shear crack. The acquired knowledge of the influence of the concrete beneath the crack and the stiffness of the beam allows other design possibilities. It is possible to design a concrete truss, if among other, the yielding of steel, crushing of the concrete and the deformation capacity of the truss are taken into account. Further research is for instance possible for unbonded reinforcement and beams with a descending height.