Orthogonal load resolution and statical-kinematic stiffness matrix

The structural behavior of underconstrained systems is explored with an emphasis on statically indeterminate ones. The roles of the elastic stiffness and the statical-kinematic stiffness (induced by prestress or an equilibrium load) are investigated and compared. The linearized response of a prestressed underconstrained system is shown to go beyond the simple notion of the first-order stiffness induced by prestress and independent of the member stiffnesses. Some interesting features of structural behavior under a general load and stability under an equilibrium load are revealed and illustrated with an example of a quasi-variant pin-bar system. Finally, a comprehensive stiffness matrix with coefficients representing various sources of first-order stiffness is introduced, to replace, when necessary, the conventional elastic stiffness matrix. The comprehensive matrix is valid for structural systems of any type and is always invertible. © 1997 Elsevier Science Ltd.