Simplified Plastic Analysis for Reinforced Web Holes

A previous publication has presented a method of analysis for the ultimate strength of beams in the region of web holes reinforced. Experimental verification of the method has also been established. The analysis described in Ref. 1 is quite cumbersome, and it is the purpose of this paper to describe and substantiate an approximate, but much simpler, method of analysis. Attention is directed to plastic collapse of beams with both hole and reinforcement located symmetrically about the neutral axis. The analysis provides a method for construction of interaction diagrams relating values of the moment and shear which, acting together at the center line of the hole, will cause failure. The structural behavior of a beam in the region of a reinforced hole has been described elsewhere. The zone of the beam (web, flange, and reinforcement) above the hole in a region of positive moment carries compressive stress due to the primary moment, and additional normal stresses due to local bending resulting from Vierendeel action. In addition, the web carries the shear force. In Ref. 1 the shear and normal stresses in the web at failure of the beam are assumed to be related through von Mises yield criterion, and this considerably complicates the algebra of the solution. When the shear force being carried is significant, that is, when the shear-to-moment ratio at the hole is high, the normal stresses on a cross section through the web are small, and in the following discussion these stresses are ignored under such loading conditions. However, when the shear-to-moment ratio at the hole is low, the web contribution to the bending strength is not neglected.