Abstract:
In a spatial cable-truss system, a single upper or lower chord cable can be considered as a first-order system that is statically indeterminate and kinematically indeterminate. The solutions for forces and shapes can be determined separately by the grounds of equilibrium conditions or other known conditions. Based on the nodal equilibrium relationship, an analytical formula for the initial prestress distribution in a circular plan diagonal cable-truss, both with and without an inner hoop, was derived by assuming the self-weight and roof loads as equivalent nodal forces. The calculation process of force-finding and form-finding for cable-truss under self-weight and roof loads is provided. First, by assuming that the shape of the upper chord cables is known and by providing the initial prestress of the central vertical strut, the initial prestresses of all upper chord cables and vertical struts can be calculated. Next, with the initial prestress of the vertical struts known, the shape and initial prestress of all lower chord cables can be determined by specifying either the shape or initial prestress of one cable. Based on the same level of prestress in the central strut, the differences in the initial prestress distribution with and without considering the self-weight and roof loads were compared by using two diagonal cable-trusses with and without an inner hoop as illustrative examples. The calculation efficiency and accuracy of the force-finding and form-finding method were analyzed. The force-finding and form-finding method outlined accurately calculates the initial prestress and lower chord geometry of diagonal cable-trusses under self-weight and roof loads. This method is applicable to the practical engineering design of other types of spatial cable-truss systems.