Computing redistribution moments in the plastic stage by using linear analysis

  • M. A. FaroukEmail author
  • Majed Alzara
  • Mahmoud Samir El-kady
Technical Paper


In this research, a suggested linear model was investigated to analyze the plastic stage for indeterminate skeletal steel structures. The aim of this model is to facilitate the analysis of the structure element in the plastic stage without resorting to the complicated calculations of the material nonlinearity. The suggested model was represented by considering the full plastic sections in the element as a concentrated plastic hinge. The plastic hinge was modeled instead of the plastic zones as a pin support or an intermediate hinge with a rotational spring. Computing the stiffness of rotational spring was based on the acceptance criteria in the nonlinear static analysis according to FEMA 356 (2000). The linear structural methods can be used after that to calculate the deformations and moments in plastic stage. In this paper and due to the simple cases which are analyzed, the forced method of structural analysis can be used. But for structural elements which are more complicated than the present cases where the plastic hinges are separated on more positions, the finite element analysis is the best. The suggested model can be used to predict the mechanism of failure, to evaluate the deformations after occurring the plastic moment as well as to compute the elastic redistribution moments. The suggested model was verified by comparing the experimentally and analytically results of steel beam deformations which made by El Damatty (J Steel Compos Struct 3:421–438, 2003) with the obtained results of the suggested model, and the suggested model gave good results. Moreover, a W-shaped fixed steel beam was analyzed by finite element method by using ANSYS program, the suggested model and elastic analysis to compute the induced moments in plastic stage and evaluated the elastic redistribution moments. The suggested model gave matching values of the induced moments of the fixed compared with the finite element results.


Plastic hinge Finite element analysis Suggested model 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • M. A. Farouk
    • 1
  • Majed Alzara
    • 1
  • Mahmoud Samir El-kady
    • 1
    • 2
  1. 1.Civil Engineering DepartmentJouf UniversityAl-JoufSaudi Arabia
  2. 2.Structural Engineering Department, Faculty of EngineeringZagazig UniversityZagazigEgypt

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