The Process of Progressive Limiting State and Determination of the Residual Strain Energy of a Structure Based on the Force Method

A methodology for investigating the progressive limiting state of the structure is proposed. To solve this problem, the criterion of critical strain energy levels in the form of the force method is used. The criterion for violation of the limiting state of the structure is a change in the state of self-stress of the structure. The problem is posed as an eigenvalue problem and the values of the maximum values of the design parameters are found for the flexibility matrix. The resulting forces correspond to a critical level of energy. They can be used to find the maximum possible value of the strain energy of the structure. By subtracting from it the amount of work of external forces, it is possible to determine the residual load-bearing capacity of the structure. An example of calculating a simple statically indeterminate truss structure is demonstrated. It clearly shows the change in the energy of deformation of the structure, its self-stress, and the possibility of modeling the progressive limiting state of the structure. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.