Structural Design_2012_yield_line.pptx - Chapter 1 u2013...

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Chapter 1 – Yield Line Analysis for slabs Concrete materials and structures chair.
Behavior of slabs loaded to failure in flexure Four or more stages: i. Before cracking the slab acts as an elastic plate, and for short time loads, the deformations, stresses and strains can be predicted from an elastic analysis. ii. After cracking and before yielding of the reinforcement, the slab no longer has a constant stiffness, because the cracked regions have a lower flexural stiffness, EI than the uncracked regions and the slab is no longer isotropic because the crack pattern may differ in the two directions. 2
Behavior of slabs loaded to failure in flexure 3 Although these conditions violate the assumptions in elastic theory, tests indicate that the elastic theory still predicts the moments adequately. Generally normal building slabs are partially cracked under service loads. iii. yielding of reinforcement eventually starts in one or more region of high moment and spreads through the slab as the moments are redistributed from yielded regions to areas that are still elastic. The progression of yielding through a slab fixed on four edges is illustrated in Figure (next slide)
Behavior of slabs loaded to failure in flexure 4
Behavior of slabs loaded to failure in flexure With further load, the regions of yielding known as yield lines, divide the slab into a series of trapezoidal and triangular elastic plates as shown in Figure (d) above. The loads corresponding to this stage of loading can be estimated by using yield-line analysis (plastic method analysis) iv. Although the yield lines divide the slab to form a mechanism, the hinges jam with increased deformation, and the slab forms a very flat compression arch as shown in Figure (next slide)(avail stiff support). This stage of loading usually is not considered in design 5
Behavior of slabs loaded to failure in flexure 6
Yield line method is a plastic method of analysis of slabs A yield line analysis uses rigid plastic theory to compute the failure loads corresponding to given plastic moment resistance in various parts of the slab A yield line method is an upper bound method whereas the strip method is lower bound method . Chapter 1 – Yield Line Analysis for slabs
Upper bound theorem : If, for a small increment of displacement, the internal work done by the slab, assuming that the moment at every plastic hinge is equal to the yield moment and that boundary conditions are satisfied, is equal to the external work done by the given load for that same small increment of displacement, then that load is an upper bound of true carrying capacity. Chapter 1 – Yield Line Analysis for slabs
Lower bound theorem : If, for a given external load, it is possible to find a distribution of moments that satisfies equilibrium requirements, with the moment not exceeding the yield moment at any location, and if the boundary conditions are satisfied, then the given load is a lower bound of the true carrying capacity.

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