Analysis of the shear force effect in the method of pneumatic hinge

The effect of transverse shear loading on the wrinkling and collapse loads of an air-supported cylindrical membrane is studied in this thesis. A transverse shear load causes shear stresses in the membrane and can be an important factor in the buckling process of a membrane structure.;At present the inflated cylindrical membranes are often used in the construction of large temporary shelters due to its light weight and simple erection. These structures are built by assembling elongated cylindrical pneumatic columns and creating in this way a closed space. A simplified approach to the analysis of wrinkling and collapse loads of a cylindrical air-supported membranes, subjected to axial loads and bending moments, was developed by Lukasiewicz and Balas in 1980s using the idea of "pneumatic hinges" (later called PHM method). In this approach the long cylindrical, inflated membrane is analysed utilising a beam model where the bending moment, normal force and the shear force are the factors deciding about the strength and buckling safety of the beam. It was found that the normal force and the bending moment in the cross-section of a pneumatic beam are the most important loadings deciding on the first wrinkling, creation of the pneumatic hinge (local large deformed area) and collapse of the membrane. The effect of shear stresses was neglected in that first approach.;PHM provides a simple and convenient tool for the industry for the design of structures built of air-supported membranes. A finite element software was developed using above mentioned ideas to check the buckling safety of this kind of industrial structures.;However, it is still necessary to determine the accuracy of PHM and the limits of its application due to that simplification. At present it can be done easily by comparing the results from PHM with the results of the advanced theory of membranes incorporating the possibility of wrinkling. Stanuszek (2003) developed a numerical method based on finite element technique to model the behaviour of wrinkled membranes. In that approach the cable analogy was introduced to define the wrinkling criteria in a triangular membrane element. The software developed by Stanuszek has been used to obtain the results from the finite element advanced method for comparison with the ones from experiment and PHM.;Several cases of membranes, with different loadings and boundary conditions are investigated in this thesis to verify the PHM. The main purpose focuses on studying the cases of cylindrical air inflated membranes loaded by transverse shear loadings. An experimental test has been performed with the membrane under the transverse shear load and distributed line load simulating the effect of the wind or the own weight. The experimental results were compared with the results of the calculations using the finite element analysis and PHM.;The comparisons indicate that PHM predicts the loads causing the first wrinkling and collapse loads with higher accuracy for the membranes loaded mainly by axial forces and bending moments. In the case of transverse shear loading, PHM predicts higher values of critical loads than the more precise finite element calculations. Also, it has been observed that the effect of the boundary conditions can reduce the value of the loads causing first wrinkling of the membrane structure. The main conclusion is that PHM can be used as a design tool for predicting the wrinkling and buckling of the membrane utilising a safety factor in the range of 2. It should be understand that PHM provides the upper limit loads for the ideal membrane causing first wrinkling. It gives more precise results while predicting the collapse loads. This is due to the fact that the first winkling phenomenon is strongly affected by the geometrical imperfections, boundary conditions and local deformations. Collapse loads correspond to the large deformations developed in the hinge area.;The PHM can be easily improved by adding the effect of the shear force in the formula for predicting the first wrinkling. The introduction of a safety factor is also recommended when the shear force causes local deformation and the first wrinkling critical forces are most affected.