Block Shear failure is usually the failure which combines both the tensile strength on one plane and the tensile strength on one or more planes. Shear lag is used to denote the uneven stress which is distributed over its connected members in some of their elements like flange, web, leg, etc. The Block Shear Failure may occur, if the strength of the metal which are connected together are not fairly strong enough. These kind of failures are not familiar and may occur very rarely.
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In simple words block shear failure means, say that two metal sheets are joined together by four bolts. Here block shear failure may occur, if the metal sheet breaks or tears due to high tension, to keep in mind that the four bolts are held strong in their places. Due to the block shear failure, only the metal breaks in various possible ways. To visualize this concept, have a look at thid video - https://www.youtube.com/watch?v=J-tzdceowZY . As mentioned above, you can see that the two metal pieces are well attached by the strong four bolts and due to the high tension only the parts of the metal plates breaks which resulting in separating the two pieces. As mentioned, the bolts are very strongly held in its place.