yield line - Yield Line of Reinforced Concrete Slabs 1....

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Yield Line of Reinforced Concrete Slabs 1. Problem description Figure 1 shows a group of slabs subjected to uniformly distributed loading. The cracking pattern of these slabs is examined and compared to the fracture line (or yield line) estimated from the classical yield line theory. CC C = Column B = Beam C C B B B C C BB B B B B B B B B Fig. 1 Reinforced concrete slabs under uniformly distributed loads
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2. Material properties The compressive strength of the culvert concrete is 28 MPa, while the yield stress of the reinforcement was 422 MPa. The applied element method follows a discrete crack approach, in which, the material is represented by a group of springs located at the surfaces of the element. The springs represent the axial and shear behavior of the material as shown in Fig. 2. Figure 3 shows the constitutive models adopted in the ELS. As for modeling of concrete under compression, Maekawa compression model 2) , as shown in Fig. 3(a), is adopted. In this model, the initial Young's modulus, the fracture parameter, representing the extent of the internal damage of concrete, and the compressive plastic strain are introduced to define the envelope for compressive stresses and compressive strains. Therefore unloading and reloading can be conveniently described. The tangent modulus is calculated according to the strain at the spring location. After peak stresses, spring stiffness is assumed as a minimum value to avoid negative stiffness. This results in difference between calculated stress and stress corresponds to the spring strain. These residual stresses are redistributed by applying the redistributed force
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yield line - Yield Line of Reinforced Concrete Slabs 1....

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