Tensile strength reduction for insufficient thread engagement A FEM study of a wall-shoe assembly

Abstract: The purpose of this master thesis is to determine whether or not it exist, a model that can describethe reduction in strength, due to missing threads in a bond between a bolt and nut. And how thereduction in strength might effect a wall-shoe assembly, used to connect a wall to another wall or aconcrete base plate. This is done by firstly considering the strength of the entire wall-shoe assembly andthe strength of the bond between the nut and the bolt is then considered. The strength of the entire assembly is calculated using some simple analytical models. The strengthof the bolt is the limiting factor for the assembly given the analytical models. Four FEM-models arethen created, three to evaluate the strength of the bolt and nut assembly, for bolt sized from M6to M60 with thread engagement from one thread to seven threads.  An elastic model without a defined tensile stress limit is proposed. The maximum stress at the sharpgeometry changes (stress concentrations) are used to dimension the maximum allowed load accordingto the von Mises yield criterion.  The yield limit is implemented by introducing a elastic-plastic (without hardening) for three different materials. Where the maximum yield force is determined as the maximum reactionforce on the frictionless support boundary condition, when a displacement is applied. Material hardening is applied according to a bi-linear material model (with hardening). Thereaction force is evaluated and the maximum force and displacement can be determined using thedefinition of property class 8.8 that propose a yield limit of 80 percent of maximum load. The behavior of the anchor bolt when it is pulled out of the concrete was also modeled. To obtain anunderstanding of the pull-out behavior. The FEM-models makes it possible to formulate a simple reduction model, where the bolt failure loadis reduced by the calculated reduction factors. The reduction factors are dependent on the amountof missing thread due to damages or insufficient bolt height. The reduction factors are also highlydependent on the ratio between the rise and bolt diameter. The reduction factors are significantlysmaller when a perfect plastic material model is applied. The failure mode is dependent on the material model, when hardening is applied fewer threads areneeded to achieve bolt failure rather then thread failure, compared to when a ideal plastic materialmodel is applied. The reduction factors are not affected by the material yield limit, the maximal load is however highlydependent on the yield limit. The placement of the missing thread does not effect the reduction factors. They can therefor beused regardless of if threads are missing due to damage or due to partial thread engagement. A test of an M8 bolt was performed to attempt to validate the FEM-model. Due to some inherent flawsin the test procedure no clear conclusion, about the validity of the model can be made. It is howeverclear that missing threads induces risk of failure when tightening the assembly, since the bolt or nutcan be damaged without any clear signs that the assembly is compromised, leading to catastrophicfailure. Reducing the load with the reduction factor model should be done with caution.