Collapse Analysis Of Frame Structures Research Articles

A modified member stiffness procedure for dynamic progressive collapse analysis of planar frames

A computer program for progressive collapse analysis of planar frames is under development. The software has a capability to analyze structures after failures of members in which failure can occur at one or both ends of a member. When an end of a member fails, the failed end separates from the main structure and becomes discontinuous. In this paper, a modified member stiffness procedure with releases of end forces to track the response of a failed end is discussed. The procedure utilizes a condensation process of the element stiffness matrix of the failed member. An example in applying the modified member stiffness procedure is given to show that the assembly process for the stiffness matrix and the applied force vector of the main structure does not change. In addition, the Equation solver still determines the same number of unknown degrees of freedom. Accordingly, this approach provides a convenient, simple, yet efficient means of keeping track of all failed members for progressive collapse analysis of frame structures.

Structural collapse analysis of framed structures under impact loads using ASI-Gauss finite element method

The main objective of this study is to devise a technique, which, when implemented into finite-element codes, is efficiently applicable to impact collapse analyses of framed structures. In this study, the formerly developed adaptively shifted integration (ASI) technique for the linear Timoshenko beam element is modified into the ASI-Gauss technique by placing the numerical integration points of the two consecutive elements forming an elastically deformed member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. On comparison with the ASI technique, the ASI-Gauss technique proves its higher accuracy and efficiency in elastic range. Moreover, instead of applying impact loads in the form of nodal forces, we consider the impact phenomenon by means of contacts between the elements involved and the elemental contact algorithm is verified from the point of conservation of energy. Impact analyses considering member fracture with different sets of parameters are performed using a high-rise framed structure and a small aircraft. From the results obtained, we can observe propagation phenomena of impact loads and shock waves. Also, a proper difference in impact damage is obtained by different sets of parameters. The results also indicate that the mass of the aircraft has a stronger influence on impact damage than its velocity. Moreover, soon after impact, tensile stresses are observed in the columns that were compressed by dead loads before impact.

Modeling the Impact of Failed Members for Progressive Collapse Analysis of Frame Structures

During the past decade, increasing attention has been focused on the design of buildings to resist progressive collapse. Previously, the authors presented a nonlinear solution procedure for progressive collapse analysis of planar frame structures. In the current study, a modeling strategy to account for the impact of failed members against other structural components is developed to extend the capabilities of the initial models. Assumptions made in approximating the effects of impact on the overall behavior of frame structures are discussed. An example illustrating the importance of accounting for the effects of impact on predicting progressive collapse is also given. Results indicate that the impact velocity plays the most significant role in causing failure of intact beam elements.

Element-Size Independent, Elasto-Plastic Damage Analysis of Framed Structures.

The adaptively shifted integration (ASI) technique and continuum damage mechanics are applied to the nonlinear finite element analysis of framed structures modeled by cubic Bernoulli-Euler beam elements. A new form of evolution equation of damage, which is a function of plastic relative rotational angles, is introduced in order to remove the mesh-dependence caused by the strain-dependence of damage. The elasto-plastic damage behavior of framed structures can be accurately and efficiently predicted by the combination of the ASI technique and the new damage evolution equation. Some numerical studies are carried out to show the mesh-independence of the proposed computational method. presented the formulation for the damage analysis of RC frames by the lumped dissipation model and implemented it in the commercial finite element program. Florez-Lopez (10) gave a unified formulation for the damage analysis of steel and RC frame members. Inglessis et al. (13,14), and Febres et al. (16) conducted the analysis of steel frames considering damage and local buckling in tubular members. Addessi and Ciampi (18) proposed a new beam finite element based on damage mechanics and plasticity to analyze the cyclic structural response of plane frames. However, no discussion has been made for the mesh-dependence of the finite element solutions for the damage problem of framed structures in the existing literatures (6-18). The cubic beam element based on Bernoulli-Euler hypothesis is generally used in the finite element analysis of framed structures neglecting the effect of shear deformation (19). Toi (20) derived the relation between the location of a numerical integration point and the position of occurrence of a plastic hinge in the element, considering the equivalence condition for the strain energy approximations of the finite element and the computational discontinuum mechanics model composed of rigid bars and connection springs. The computational method identified as the adaptively shifted integration technique (21) (abbreviated to the ASI technique) was developed, based on this equivalence condition. The ASI technique, in which the plastic hinge can be formed at the exact position by adaptively shifting the position of a numerical integration point, gives accurate elasto-plastic solutions even by the modeling with the minimum number of elements. The ASI technique has been applied to the static and dynamic plastic collapse analysis of framed structures (21-24), through which the validity of the method has been demonstrated with respect to the computational efficiency and accuracy. In the present study, a new computational method is formulated for the elasto-plastic damage analysis of framed structures, based on the ASI technique for the cubic Bernoulli-Euler beam element and the concept of CDM. The non-layered approach, in which the stress-strain relation is expressed in terms of the resultant stresses and the corresponding generalized strains, is employed in order to reduce the computing time for the large-scale framed structures. A new form of damage evolution equation, which is expressed in terms of the plastic relative rotational angles and the effective element length instead of the plastic curvature changes, is proposed in order to remove the mesh-dependence of solutions in the damage analysis. The present method is applicable to the collapse analysis of framed structures including elasto-plasticity, damage initiation, its evolution and fracture. Numerical studies for simple frames are conducted to show accuracy, efficiency and the mesh-independence of the proposed method.

Efficient collapse analysis techniques for framed structures

An efficient computational procedure for collapse analysis of framed structures is described. The procedure makes use of co-rotating nonlinear beam–column elements, connected at nodes, that may develop plastic hinges. The formulation incorporates a series of novel features that greatly enhance the efficiency of the computations. The secant and tangent stiffness of the beam–column element are obtained from a six-component equilibrium format in explicit form as a nonlinear function of the normal force, and initial imperfections and shear flexibility are incorporated into the explicit format. The yield functions used in the plastic hinges are extended to the full generalized stress space in a form that optimizes the convergence rate of the iterative return algorithm, and the effective length of the plastic hinge is assessed from the moment distribution in the element. The equilibrium format of the beam–column element enables a simple explicit modification of the theoretical elasto-plastic tangent stiffness to obtain the corresponding algorithmic stiffness that accounts for the finite stress increments of the numerical algorithm. These features have been implemented into a finite element collapse analysis program RONJA, and two realistic offshore analysis examples are included to illustrate the performance of the computational procedure.

Adaptively shifted integration technique for finite element collapse analysis of framed structures

AbstractThe present study is concerned with the improvement of the previously proposed ‘shifted integration technique’ for the plastic collapse analysis of framed structures using the linear Timoshenko beam element or the cubic beam element based on the Bernoulli‐Euler hypothesis. In the newly proposed ‘adaptively shifted integration technique’, the numerical integration points for the evaluation of the stiffness matrices are automatically shifted immediately after. the occurrence of plastic hinges according to the previously established relations between the locations of numerical integration points and those of plastic hinges. By using the adaptively shifted integration technique, sufficiently accurate solutions can be obtained in the non‐linear frame analysis by two‐linear‐element or only one‐cubic‐element idealization for each structural member. The present technique can easily be implemented in the existing finite element codes utilizing the linear or the cubic beam element.

Adaptively Shifted Integration Technique in the Finite Element Collapse Analysis of Framed Structures

The present study is concerned with the refinement of the previously proposed 'shifted integration technique' for the plastic collapse analysis of framed structures using the linear Timoshenko beam element or the cubic beam element based on the Bernoulli-Euler hypothesis. In the newly proposed 'adaptively shifted integration technique', numerical integration points are automatically shifted immediately after the occurrence of plastic hinges according to the previously established relations between the locations of numerical integration points and those of plastic hinges. By using the adaptively shifted integration technique, sufficiently accurate solutions can be obtained in the nonlinear frame analysis by two linear element or only one cubic element idealization for each structural member. The present technique can be easily implemented with a minimum effort into the existing finite element codes utilizing the linear and the cubic beam element.

Shifted integration technique in one‐dimensional plastic collapse analysis using linear and cubic finite elements

AbstractThe present study is concerned with the physical explanations of the linear and the cubic finite elements for beams and axisymmetric shells through comparisons of their strain energy approximations with those of the Rigid Bodies‐Spring Models which are discrete elements suitable for plastic collapse analysis using the concepts of plastic hinges and hinge lines. The established conditions for the equivalence between these two modellings, which are given as the relations between the locations of the numerical integration points and those of the occurrence of plastic hinges, can be conveniently used in the economical plastic collapse analysis of framed structures and axisymmetric shells where the locations of plastic hinge formations are controlled by the movement of numerical integration points. Some numerical results are shown in order to prove numerically the obtained relations and to verify the validity of the proposed shifting technique of numerical integration points, which is identified as ‘the shifted integration technique’ in the present paper.

On the Shifted Integration Technique in the Finite Element Analysis of Framed Structures and Axi-Symmetric Shell Structures

The present study is concerned with the physical explanations of the linear and the cubic finite elements for beams and axisymmetric shells through the comparisons of their strain energy approximations with those of the Rigid Bodies-Spring Models which are the discrete elements suitable to the plastic collapse analysis using the concepts of plastic hinges and hinge lines. The established conditions for the equivalence between these two modelings, which are given as the relations between the locations of the numerical integration points and those of the occurrece of plastic hinges, can be conveniently used in the economical plastic collapse analysis of framed structures and axisymmetric shells where the locations of plastic hinge formations are controlled by the movement of numerical integration points. Some numerical results are shown in order to prove numerically the obtained relations and to verify the validity of the proposed shifting technique of numerical integration points, which is identified as 'the shifted integration technique' in the present paper.

Limit Analysis of Soil Structure by Rigid Plastic Finite Element Method

We investigate a numerical approach to analyze the limit state of soil structures, assuming that the mechanical property of the soil is rigid plastic. It is well known that the collapse analysis of frame structures can be formulated as the linear programming problem through the upper bound theorem of plasticity. Recently this method was extended to continuum. Since the nonlinear programming problem must be treated in this case, no well-established technique is found out in the literature. There also is a little theoretical confusion concerning the constraint conditions and the indeterminate pressure (total mean stress).In this paper, we firstly formulate the problem by using the upper bound theorem and secondly show that the minimization of the upper bound is equivalent to finding out the equilibrium state with the indeterminate pressure. The present numerical procedure is illustrated by typical problems, i. e., bearing capacity of shallow foundation and slope stability. Good agreement between the present results and well-known solutions confirms that our approach can be used as a general method for the limit analysis of soil structures.