Abstract
In this paper, the theoretical treatment of membrane stress states are developed for membrane structures and cable nets in order to present some formulas expressing nonlinear structural behaviours for the practical use as well as the background to numerical analyses and experiments. After discussing the nonlinear strain-displacement relations and the equilibrium equations with initial prestressing terms for shallow membrane structures from the view points of the expressions in the different coordinate systems : Cartesian and curvilinear coordinates, the nonlinear fundamental equations are derived for the cable nets of H. P. type with clamped boundaries. From the stress and deflection analyses of these equations by use of the first main deflection term (W=A_<11>cosπ/2ξcosπ/2η), the following formulas are introduced : (a) stress resultant-deflection relation (N_x-N_y∝A11and N_x+N_y∝A^2_<11>), (b) load-deflection relation of the third order algebraic expression. Next, these results are modified to the analyses of cable nets with cable boundaries, and the tension of boundary cable-deflection relation (T∝A^<4/3>_<11>) is formulated. The validity of these formulas are examined by comparing with the experimental results of cable net models.
