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Abstract

In this work, the stiffness equations for evaluating the internal stress of rigidly fixed portal frames (considering shear deformation) by the displacement method were generated. But obtaining the equations for the internal stresses required a parametric inversion of the structure stiffness matrix. To circumvent this problem, the flexibility method was used taking advantage of the symmetrical nature of the portal frame and the method of virtual work. These were used to obtain the internal stresses on rigidly fixed portal frames for different cases of external loads when shear deformation is considered. A dimensionless constant α was used to capture the effect of shear deformation in the equations. When it is set to zero, the effect of shear deformation is ignored and the equations become the same as what can be obtained in any structural engineering textbook. These equations were used to investigate the contribution of shear deformation to the calculated internal stresses and how they vary with the ratio of the flexural rigidity of the beam and columns and height to length ratio of the loaded portal frames.