Bezpieczeństwo Liny jako Złożonego Elementu Konstrukcyjnego - W. Piekarski (Engineering Transactions)
In composite structural elements subject to tension, such as ropes, cables, sets of wires or bars in r.c. structures etc. the number n of component elements has an essential influence on the safety of the structure. The object of the present considerations is a rope composed of n wires. The strength of the i-th wire is a random variable obeying the probability distribution law for the type of steel used and independent of the strength of the remaining wires. Thus in a rope of n wires we are concerned with n independent random variables. The strength Ri of the rope (which is a random variable) is therefore a sum of n independent random variables. Hence the mean strength R of the rope is the rithmetic mean of the mean strengths R of separate wires [the Eqs. (3) and (5)1 and the dispersion of the strength is yn times smaller than that of the wires [the Eqs. (6), (6) and (6')]. Due to the reduction of strength dispersion the rope (which constitutes a structural part composed of 71 wires) shows greater safety than that of a single wire.