Yield line Theory for Concrete Slabs Subjected to Axial Force

Tim Gudmand-Høyer*

*Corresponding author for this work

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This paper treats the subject Yield line Theory for Concrete Slabs Subjected to Axial Force. In order to calculate the load-carrying capacity from an upper bound solution the dissipation has to be known. For a slab without axial force the usual way of calculating this dissipation is by using the normality condition of the theory of plasticity together with the yield condition. This method is equivalent to the original proposal by K. W. Johansen. This method has shown good agreement with experiments and has won general acceptance. In this paper the dissipation in a yield line is calculated on the basis of the Coulomb yield condition for concrete in order to verify K. W. Johansen’s method. It is found that the calculations lead to the same results if the axes of rotation are the same for adjacent slab parts. However, this is only true if the slab is isotropic and not subjected to axial load. An evaluation of the error made using K. W. Johansen’s proposal for orthotropic rectangular slabs is made and it is found that the method is sufficiently correct for practical purposes. For deflected slabs it is known that the load-carrying capacity is higher. If it is assumed that the axis of rotation corresponds to the neutral axis of a slab part and the dissipation is found from the moment capacities about these axes K. W. Johansen’s proposal may be used to find the loadcarrying capacity in these cases too. In this paper this is verified by comparing the results with numerical calculations of the dissipation. Also for deflected slabs it is found that the simplified method is sufficiently correct for practical purposes. The same assumptions are also used for rectangular slabs loaded with axial force in both one and two directions and sufficiently good agreement is found by comparing the methods. Interaction diagrams between the axial load and the transverse load are developed at the end of the paper for both methods. Different approaches are discussed. Only a few comparisons between experiments and theory are made. These indicate that the theory may be used if a proper effectiveness factor is introduced and the deflection at failure is known. If the deflection is unknown an estimate of the deflection based on the yield strains of the concrete and the reinforcement seems to lead to acceptable results.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark, Department of Civil Engineering
Number of pages116
ISBN (Print)87-7877-136-6
Publication statusPublished - 2003
SeriesDTU Civil Engineering Report

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