Abstract
The initial axial forces of members—whatever caused by prestress or external loads—may strongly change the mechanical properties of pin-jointed bar assemblies, to enhance, or even establish their structural stiffness. The structural responses under external disturbance cannot be calculated accurately if the influence of initial axial forces has not been considered appropriately. In this paper, an analytic theory considering the effect of initial internal forces is developed on the basis of linear elasticity hypothesis. The fundamental formulas proposed finally include generalized equilibrium equations and generalized compatibility equations, both of which have square coefficient matrices of full rank being transposed with each other. Generally, this method can be regarded as an extended version of a traditional force method considering the stiffening effect of initial internal forces. Compared with the matrix force method, it has a wider application scenario since few redundant simplifications are employed in the derivation of the formulas. In comparison with the displacement-based algorithm, the proposed method has the inherent advantages of the force method—the physical concepts of each item in equations are fairly explicit; and the combination coefficients of self-stress states and mechanisms are determined simultaneously in solving the structural responses. Thus, it is very helpful for us to essentially comprehend the principle that the pin-jointed bar assemblies resist the external loads.
Highlights
Pin-jointed bar assemblies are becoming increasingly popular in structural engineering.The concepts of statical and kinematical determinacy are key to understanding the mechanics of these kinds of structures
The fundamental formulas proposed in this paper are more complex than the ones of the matrix force method, they are applicable to static analysis of a general pin-jointed assembly based on the assumption of small deformation and linear elasticity, which will be further verified through several numerical examples
Numbered from 12; (d) the members numbered from theto members numbered from formulas of theof static the pin-jointed assemblies,bar considering the Thefundamental fundamental formulas theanalysis static of analysis of the bar pin-jointed assemblies, influence of initial axial forces of members, are derived based on the assumption of small deformation considering the influence of initial axial forces of members, are derived based on the assumption of and elasticity, which of the generalized equations and the generalized smalllinear deformation and linearconsist elasticity, which consist ofequilibrium the generalized equilibrium equations and compatibility equations
Summary
Pin-jointed bar assemblies are becoming increasingly popular in structural engineering. The force method has its inherent advantages: the physical concepts of each item in equations are fairly explicit; the essential structural and kinematic properties, e.g., the rigid body motions or infinitesimal mechanisms, the states of self-stress, etc., can be explained clearly from the orthogonal subspace of the equilibrium matrix. It has made the matrix force method complementary to the displacement-based method and irreplaceable in the design of pin-jointed bar assemblies.
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