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Punching shear is a phenomenon in flat slabs caused by concentrated support reactions inducing a cone shaped perforation starting from the top surface of the slab. Although generally preceded by flexural failure, punching shear is a brittle failure mode and the risk of progressive collapse requires a higher safety class in structural design.
One way shear is rate of change of bending moment. It's typically called beam shear. However two way shear is punching shear and its effect is two way. It's also called flat slab shear.