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The basis for computer calculations
Published in Malcolm Millais, Building Structures, 2017
The flexibility method has the advantage that the primary unknowns are forces, which is the essential information required for the numerical analysis of structures, whereas for the stiffness method the primary unknowns are displacements. This may seem irrelevant, but in the complex procedures used in computer programs to solve hundreds or thousands of simultaneous equations, numerical errors can result. Here’s a simple example that shows what can happen:
Matrix flexibility method
Published in R.C. Coates, M.G. Coutie, F.K. Kong, Structural Analysis, 2018
R.C. Coates, M.G. Coutie, F.K. Kong
It was shown in Chapter 7 that one basic form of the stiffness method could be applied to a wide range of structures, with only minor adjustments to cope with each variant. The advantages of the method can be summarized as: A general-purpose program is easy to write. (a) (b) It requires a minimum of input data. It can be made entirely automatic. Its use requires no understanding of (c) structural mechanics. The method has a major disadvantage in that no account is taken of the degree of indeterminacy, and therefore there is little opportunity to benefit from the structural expertise of the operator. Equally, this will be seen as an essential concomitant of the advantage listed in (c) above. The time required to perform an analysis and the amount of computer storage necessary depends almost entirely on the number of degrees of freedom involved. The flexibility method has the potential advantage that it.recognizes the state of indeterminacy of a structure, and regards the number of degrees of static indeterminacy as the unknown. It allows the engineer to exercise his judgement over the details of the solution-such as the choice of releases. Structures having many degrees of freedom but few degrees of static indeterminacy should be much more economically analysed by the flexibility rather than the stiffness method. However, the flexibility method has the severe disadvantage that a general program is difficult to write. The full advantage ofthe method for skeletal analysis is only achieved if the matrix Frr can be set up directly, and although this can be done for plane frames, it is by no means as straightforward for other types of structure.
Exact solutions for thin-walled composite open section beams using a unified state space coupled field formulation
Published in Mechanics Based Design of Structures and Machines, 2022
Srinivasan Ramaprasad, B. Dattaguru, Gajbir Singh
Vlasov (1961) presented the first contour-based cross-sectional analysis method to study isotropic thin-walled beams with warping restraint effects and non-uniform torsion. Gjelsvik (1981) developed an isotropic beam theory by relating plate displacements to generalized beam displacements. Salim and Davalos (2005) accounted for elastic couplings and extended this to the linear analysis of open and closed section TWCB. Many authors developed analytical models for analyzing TWOSCB based on either stiffness (Chandra, Stemple, and Chopra 1997; Kim and White 1997) or flexibility method (Erkmen and Mohareb 2006) that correlates with the experimental data better.
Modeling of Behavior of Continuous Energy-Dissipative Steel Columns Under Cyclic Loads
Published in Journal of Earthquake Engineering, 2019
Yan-Wen LI, Guo-qiang LI, Jian JIANG, Fei-Fei SUN
For the displacement compatibility equation of flexibility method (Leet et al., 2002) at the cut, the sum of the four parts of relative displacements as shown in Figure 10 should be zero at any elevation z, i.e.: