Synopsis

For dimensionning of bridges and crane-lines the construction of influence lines for bending moments on all supports is the basis of the calculus. Following the Maxwell’s roule an artificial refraction would be applied at the observer point of a size 1 (tg φ0 + tg ψ0 = 1). Using the angle transporting coefficients the inclinations of these influence line is determined successively on all supports. For avoiding the backward transporting, used by Cross-method, we make use of “reduced stiffnesses”. The base formulas for them are:

The grade of the restraining:

u = Σ reduced stiffnesses of adjoined bars / Σ reduced stiffnesses of adjoined bars + full stiffness of the considered bar

The reduced stiffness: tr = (3 + u) J / L;

[3 for a bar with a hinge

4 for a full restraining]

The bending moment transporting coefficient:

KM = - u / 2;

The angle transporting coefficient: 

Kφ = - 1 - u / 2

Beginning by the end of the framework all stiffnesses, all restraining grades and all angle transport coefficients are calculated progressively. They are different for each direction. The proceeding appears by the sketch. For designing the yielding line, a numerical diagram follows. For the computation of the uniform loading we have to multiply the sum of both deflection angles by the factor: q L2 / 12