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This paper considers the application of the limit equilibrium method to the calculation of a double hinged circular arch loaded with a uniformly distributed vertical load. It is assumed that the arch has a rectangular cross-section made of a homogeneous elastic plastic material with different tensile and compressive yield strengths. The peculiarity of the limit state calculation is that the section works elastically until the transition to a plastic state of the entire section. If the action of the longitudinal force is not taken into account, in the limiting state a classical plastic joint is formed in the cross-section, which allows unlimited rotation relative to each other of the sections located infinitely close to the plastic joint. If the bending moment and the longitudinal force are taken into account simultaneously in the limit state, the possibility of unlimited rotation and unlimited linear displacement of the sections located infinitely close to the origin of the plasticity arises. In order to calculate the limit load for an arch, it is first necessary to obtain a dependence describing the strength area of the cross-section. This dependence relates the ultimate moment and ultimate longitudinal force for the section and is often referred to as the yield stress condition. In this paper the yield stress conditions for rectangular sections of arches with constant and variable stiffness are presented. Using yield conditions of the section and equations of balance of the arch it is possible to construct and solve an optimization problem for finding the minimum load which satisfies both equilibrium and yield equations. Thus, the target function of the problem is the value of ultimate load and the design variable is the coordinate of section which goes into the plastic stage. This problem was solved by means of spreadsheets. Also non-linear calculations of arches with constant and variable stiffness were performed in PC Lira-SAPR. Comparison of the calculation results showed their satisfactory convergence. [ABSTRACT FROM AUTHOR]

In the present paper a program THINWALLRES is explained to obtain the elastic and plastic resistance of thin walled HVH sections under many combinations of the internal forces: axial force N, shear forces Vz and Vy, bending moments My and Mz, bimoment B, warping torsional moment Tw (= Mxw) and Saint Venant torsional moment Tt (= Mxs). The program THINWALLRES can at the moment solve various HVH-sections (H – Horizontal upper flange, V – Vertical web, H – Horizontal bottom flange), i.e. I-sections and H-sections that can be monosymmetrical, channel sections and Z-sections. The background of the theory is briefly explained. The results provided by the program are the elastic normal stresses, shear stresses and von Mises stresses due to any combinations of eight internal forces. The plastic stress distribution under given internal forces, plastic factor and up to ten different interaction diagrams combinations may be obtained with THINWALLRES. The results in the form of diagrams are helpful in the safe and economic design of metal (steel and aluminium) thinwalled members of the Classes 1, 2 and 3. [ABSTRACT FROM AUTHOR]

In the present paper a program THINWALLRES is explained to obtain the elastic and plastic resistance of thin walled HVH sections under many combinations of the internal forces: axial force N, shear forces Vz and Vy, bending moments My and Mz, bimoment B, warping torsional moment Tw (= Mxw) and Saint Venant torsional moment Tt (= Mxs). The program THINWALLRES can at the moment solve various HVH-sections (H – Horizontal upper flange, V – Vertical web, H – Horizontal bottom flange), i.e. I-sections and H-sections that can be monosymmetrical, channel sections and Z-sections. The background of the theory is briefly explained. The results provided by the program are the elastic normal stresses, shear stresses and von Mises stresses due to any combinations of eight internal forces. The plastic stress distribution under given internal forces, plastic factor and up to ten different interaction diagrams combinations may be obtained with THINWALLRES. The results in the form of diagrams are helpful in the safe and economic design of metal (steel and aluminium) thinwalled members of the Classes 1, 2 and 3. [ABSTRACT FROM AUTHOR]

The problem of plane strain pure bending of a plate made of a linearly elastic–perfectly plastic material with a through-the-thickness gradient of strength properties and tension-compression asymmetry is considered. The gradient of strength properties was produced by accelerated one-sided cooling of the plates made of A32 ship steel from the austenitic temperatures. The purpose of the present work was to analyze the effect of various approximations of the strength gradient on the accuracy of determining the critical bending moment corresponding to the complete yielding of the sheets. [ABSTRACT FROM AUTHOR]

The paper studies pure bending of a strip (beam) containing through crack which is perpendicular to its axis and asymmetrical about the one. One of the crack tips is in the compressive stress zone and crack faces are in smooth contact near it. The other one is in the tensile stress zone and there is a striplike plastic zone on the crack prolongation line near this tip. The solution is reduced to linear conjunction problems using methods of complex analysis and complex potentials. The length of crack faces contact zone, the length of crack tip plastic zone and crack tip opening displacement are evaluated. Their analytical solution is found. The system of transcendental equations for calculating the length of crack tip plastic zone and parameter, that characterized the length of crack closure zone are established. Formula for calculating the crack tip opening in noncontact tip and dependencies for the stress tensor components on the line, where the crack located are wrote. Numerical analysis of crack tip opening in her noncontacting tip and the length of crack tip plastic zone from reduced external load and location of crack center relative to the axis of the strip (beam) is done. The parameter, that characterized the length of crack closure zone doesn't depend from external load is find numerically and a simple formula for its determination is given. The critical value of the bending moment of fracture of the beam (strip) with the contact crack is estimated based on the δк-model of fracture of crack bodies. [ABSTRACT FROM AUTHOR]

In article the design procedure of the bending moment and curvature in a plastic zone of elastic-plastic calculation of the framework of the cabin of the tractor is offered. The offered method procedure of the bending moment and curvature in a plastic zone together with the known methods of calculation of an elastic zone allow with count deformation of the design of the framework with an accuracy, sufficient for the framework of cabins of the tractor. [ABSTRACT FROM AUTHOR]