AbstractGeneralized analytical approach, with exact stress solutions, to buckling problems of in‐plane loaded plate with and without stiffeners has been presented through the case of locally distributed direct stresses. Several mathematical models have been chosen to represent high webs of steel girders under the patch load. Initially, the basic model has been built to simulate a girder used in the experimental research where the external load is equilibrated by support reactions. The second, more complex model included shear stresses along vertical stiffeners with a task to equilibrate the external loads, simulating a single web segment between the stiffeners of a long girder. The upgrade of the second model by adding a longitudinal stiffener resulted in the third model. Considering the complexity of stress distributions within the plate under such a demanding load, an analytical model for these problems has not been presented earlier. For the first time the influence of flexural stiffeners' rigidity on the plate buckling has been analysed with the exact solutions for in‐plane stress distributions, for simply supported plate. Results confirm the high quality of the analytical solution for the first and the second model and speak in favour of this approach and its potential for further upgrading in the case of the third model.
