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Structural Engineering and Mechanics
  Volume 11, Number 4, April 2001, pages 423-442

Second order analysis of planar steel frames considering the effect of spread of plasticity
Liang-Jenq Leu and Ching-Huei Tsou(R.O.C.)

Abstract     [Full Text]
    This paper presents a method of elastic-plastic analysis for planar steel frames that provides
the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of
distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for
the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column
element, which is achieved by the following procedures. First, nonlinear equations describing the
relationships between generalized stresses and strains of the cross-section are derived analytically. Next,
nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise
integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by
differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix
is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric
stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can
readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear
analysis procedures. The accuracy of the proposed method is verified by several examples that are
sensitive to the effect of spread of plasticity.
Key Words
    second-order analysis; steel frames; spread of plasticity; flexibility matrix.
Liang-Jenq Leu and Ching-Huei Tsou, Department of Civil Engineering, National Taiwan University, Taipei, 10617 Taiwan, R.O.C.

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