Behaviour of concrete membrane elements in the crack formation phase
Author: Simon Karrer
Language: English
Abstract
The deformation capacity of membrane elements can generally be calculated based on existing mechanical models. All these models are exclusively derived for membrane elements with stabilised cracking. Stabilised cracking of a membrane element is characterised by a fully developed crack pattern which means that no new cracks form, even if the applied stress level and the deformations are further increased. However, many membrane elements do not have a fully developed crack pattern for service and even ultimate loads. The application of existing models in the crack formation phase may lead to an overestimation of the deformation and load-bearing capacity. It is therefore questionable whether the existing models can be applied in the crack formation phase.
This Master's Thesis characterises the crack formation phase of concrete membrane elements by analysing the results of four large-scale experiments loaded in pure shear and instrumented with Digital Image Correlation (DIC). New visualisation plots are developed based on the accurate and comprehensive crack measuring data. The crack width opening rate has been developed to illustrate whether a crack further opens and at which rate. This parameter gives insight into the crack opening development and indirectly into the stress distribution in concrete at a particular measuring step. In order to investigate the influence of cracks on the macroscopic level, further new parameters such as the total crack length and total crack area have been developed. The crack area is the product of the crack length times the average crack width. Secondary cracks (i.e., those cracks with small openings that are not relevant for the comparisons with mechanical models) can be selected in an automatic manner based on the crack area concept. An approach to automatically compute the crack spacing based on the total crack length is proposed.
In addition to the existing empirical provisions for minimum shear reinforcement in the design code SIA 262 and the fib Model Code 2010, two preliminary approaches are developed that are based on an equilibrium formulation at a cracked membrane and failure mechanisms, respectively. By following the approach based on failure mechanisms, the minimum shear reinforcement is highly dependent on the amount of longitudinal reinforcement. This finding contrasts with existing empirical design code provisions. Further research is needed to find out under which conditions the membrane elements might have sufficient deformation capacity to reach the plastic solution.
Further research is also required to clarify whether existing models can be applied in the crack formation phase. The conducted characterisation of the crack formation phase opens the way to perform tailored analysis with mechanical models such as the cracked membrane model (CMM) to simulate both the crack formation and the stabilised cracking phases. In such analyses, a variable crack spacing in the crack formation phase should be considered, in line with the experimental observations. This would allow for a reliable calculation of the deformation capacity of membrane elements also in the crack formation phase.