ON THE DIRECT STATIC PROBLEM OF A PLANAR RIGID BODY SUSPENDED FROM TWO CABLES

This paper presents a general solution to the direct static problem of a planar body suspended from two cables. First, the conditions for static equilibrium are stated and a mathematical formulation of the problem is derived. A twelfth degree univariate polynomial is then obtained using the resultant of two intermediate polynomials. It is shown that up to twelve real solutions can be obtained, thereby confirming that the polynomial is of minimal degree. Since the condition used in the derivation is necessary but not sufficient, the roots must be tested a posteriori for validity. Simple mathematical conditions are provided that allow such a verification. Finally, two examples are provided to illustrate the results and highlight the importance of the proposed root validation procedure.