Influence of Material Compressibility on Displacement Solution for Structural Steel Plate Applications

Displacement field calculations are necessary for many structural steel engineering problems such as cold expansion of holes, embedment of bolts and rivets, and installation and maintenance of external devices. To this end, rigorous closed form analytical displacement solution is obtained for structural steel open-hole plates with in-plane loading. The material of the model is considered to be elastic perfectly plastic obeying the von Mises yield criterion with its associated flow rule. On the basis of this solution, two simplified engineering formulae are proposed and carefully discussed for practical engineering purposes. Graphical representations of results show validity of each formula as compared with rigorous solution and other studies. 1. Introduction Displacement field calculation around stress concentrators in steel structural members is on-going engineering task which is necessary for a number of reasons. It provides the basis for specific industrial codes and regulations such as AISC or Eurocodes, makes substantial part of commercial software based on finite element method (FEM), and proves validity of initial stress solutions. In a large number of cases, structural elements utilized in civil, mechanical, and aerospace engineering require major repair or are out of service due to ductile failures originating at holes. To this end, two widely applied technological processes are of great importance, namely, cold expansion of holes to improve fatigue life of structural members [1] and embedment of bolts to achieve the optimum bearing area within the available hole [2]. For cold expansion process, the plate may reach purely plastic state upon loading. In contrast, for bolt connections, the plate surrounding the fastener in a global structural environment should be mostly in elastic state; that is, the plastic zone is inferior to elastic one. For mild and high strength steels, this difference in structural expectation from the technological processes may influence the methodology of displacement evaluation based on the same geometrical model of a plate with central hole subjected to internal pressure. Such a model is commonly used both in analytical and numerical calculations dealing with either cold expansion process (with its applications) [1, 3–7] or specifically with bolt connections [2, 8–10]. In spite of the fact that numerical analyses form a powerful tool in complex realistic engineering situations, analytical methods continue to occupy important role in preliminary engineering design due to their rigorous mathematical formulations and