Siła Krytyczna Ramienia Dźwigu przy Wyboczeniu z Płaszczyzny Zawieszenia - Dmitrijuk, W. (Engineering Transactions, 1967)
The usual method for computing the critical force of a bar with luffing rope for buckling out of the plane of suspension was, until recently, the same as for a bar fixed at its lower end the upper end remaining free. The fact that the luffing rope is deflected if the arm (jib) is deflected was not considered thus producing a restoring force, which increases the critical force. The case in which the bar is loaded by means of a cable: (rope) (that is by a force turned, after buckling, towards a fixed point) was discussed for a constant moment of inertia by W.J. FEODOSYEV [6] and for a moment of inertia variable with the square of x by R. ROSMAN [7]. The case of a bar with luffing rope and with a constant moment of inertia was considered by KOROBOV [8] and witha moment variable with the square of x - by KOGAN [9] and [1], The problems considered in the present paper are those of the same bar having a moment of linear variable with the fourth power of x, a moment variable in a jump-like manner and a moment partially constant, partially variable with the square of x.It will be seen that if the coefficient of influence of the luffing rope is k = 0 the bar is clamped at the lower and free at the upper end and if k = 1 the luffing rope influences the behaviour of the bar in such a manner that it behaves as if it were resting on two supports. On this basis two approximate equations are obtained. These equations can be used in practice for the determination of the critical force in the crane arm (jib).The second of these equations is a generalization of the equation recommended by the British Standard B.S. 2573, Part 1 for a crane with constant moment of inertia.