Sokov V. Strength of the thin-walled beam with broken edges considering elastic-plastic strains

In frames of the dissertation work there is the steel thin-walled beam with broken edges is investigated. The wall of this beam consists of two prismatic parts with the rectilinear transition from the smaller wall height to larger one, forming together with edges of prismatic parts the broken top line to which a free flange can be joined. By the lower rectilinear edge the wall is joined to the sheeting. The wall with broken edges without a free flange is called «beam-wall». There are presented the methodologies of optimal design and verification strength calculations of the beam-wall under static elastic and cyclic elastic-plastic deformation in the stress concentrator. Also there were developed expressions for definition of theoretical stress concentration coefficients in case of tension-compression and bending for a wide range of geometrical parameters of the beam-wall. It was concluded that theoretical stress factors’ magnitudes for tension-compression are always more than for bending for the same parameters. Optimal design of the beam-wall is provided on basis of theoretical stress factors’ expressions. There are characteristics of plastic zones, strains intensities and cyclic diagrams were ascertained depending on geometrical parameters and applied nominal load in the stress concentrator of the beam-wall. The material is ideal elastic-plastic without hardening. Cyclic diagrams in the stress concentrator were investigated for symmetrical and pulse cyclic nominal external loads. It was concluded that for symmetrical cycles of nominal loads the cyclic and static ranges of strains’ intensity are almost identical. If nominal load is nonsymmetrical then there is no relation between static and cyclic diagrams exist. For serial numerical calculations of elastic-plastic problem of the beam-wall there were used the volume finite elements. Using the volume model is connected with complex processes in the development of plastic zones when there is transfer from plane deformation to plane stress state. These processes depend on thickness. Additionally the volume model considers change of thickness in the stress concentrator under deforming. There were developed the dependencies for calculation of cyclic elastic-plastic strains’ intensity in the stress concentrator of the beam-wall. These dependencies are enabled in calculations of the beam-wall under its cyclic loading, and can be integrated into complex deformation criteria, approaches of fatigue assessment and damage accumulation. These dependencies were obtained for the symmetrical nominal cyclic loadings of constant amplitude. All elastic-plastic investigations of the beam-wall were examined under tension-compression. The elementary volume in the most tensed stress concentrator’s point of the beam-wall is in a linear stress state in case of elastic and elastic-plastic stress states. The classic Neuber’s formula can be used in the stress concentrator of the beam-wall when the relation of nominal pressure to the yield strength is less than 0.6. There were offered the relations for definition of elastic and elastic-plastic effective widths of a free flange in the dangerous cross section and for elastic effective width along inclined part of the beam with broken edges. The dangerous cross section located in the bend/kink of a free flange where the wall with smaller height adjoins inclined part. In so doing there is shear lag is considered in frames of strength calculations, taking into account influence of complex warping of a free flange in the inclined part. It allows providing calculations of investigated beam within usual Bernoulli’s hypothesis. Geometrical properties for this case have to be defined considering effective widths both free flange and sheeting girdle. The classic methodology of definition of effective width for a free flange can’t be used for inclined part due to its complex warping. It was proved that components of the strain stress state (SSS) involved in calculation of effective width have to be determined in the neutral layer, where there are no bending normal stresses caused by the local warping of a plating. These stresses don’t have to be considered in calculation of effective width. It was proved that the location of the neutral layer can be accepted on the middle surface of a free flange, despite that its real position is arbitrary. It was proved that for definition of effective width on the inclined flange part it is necessary to use the projected components of the SSS into inclined plane of a free flange. The investigations concerning effective width were examined under tension-compression which consider the most unfavorable occasion and provide obtaining of reliable strength estimation. Keywords: thin-walled beam, concentration coefficients, optimal design, elastic-plastic deformation, fatigue durability, shear lag, effective width.