Why

Many Engineering Systems

Are Not Sufficiently Safe

© Lev Gelimson

The specific character of the strengths of solids extremely loaded make it necessary, to authentically know the domain of the safe combinations of the loads. It is not sufficient to determine a usual safety factor as a limiting stress divided by an equivalent stress. This safety factor concept has been initially proposed for uniaxial stress states of solids simply (proportionally) loaded. Otherwise, it normalizes no loading, geometrical, and rheologic parameters themselves (really determining the stress states of solids) but their result, an equivalent stress, as their composite function via the principal stresses by a limiting criterion. Moreover, experiments give only a limiting surface whose equation can be represented in distinct forms. They lead to many very different definitions of a usual safety factor. For unlimiting states, this factor can then take on any positive values (while the state is invariant) and hence has no objective sense. Furthermore, if loading is not simple, then the principal stresses are not obliged to vary proportionally with each other.

Further a usual safety factor does not show by what maximum number each of the loads can be multiplied or divided independently of one another so that, by the most dangerous realizable combination of such modified values of the loads, the stress state at the most dangerous point of the solid becomes limiting. It is especially dangerous that in such a case a usual safety factor gives values much greater than realistic ones. Let us consider two examples.

Example 1: The principal stresses are 250 MPa, 240 MPa, 210 MPa; the limiting one is 235 MPa.

The usual safety factor by the theory of maximum shearing stresses is

235 MPa / (250 MPa - 210 MPa) = 5.9

whereas

5.9 * 250 MPa - 210 MPa / 5.9 = 1439 MPa

and thus much greater than 235 MPa.

Example 2: A bar with strengths 100 MPa in tension and 800 MPa in compression is contracted and stretched by two pairs of forces independent from each other and causing the stresses

-500 MPa + 400 MPa = -100 MPa.

The usual safety factor is

800 MPa / 100 MPa = 8

whereas

-500 MPa * 8 + 400 MPa / 8 = -3950 MPa

(much more dangerous than -800 MPa) and

-500 MPa / 8 + 400 MPa * 8 = 3137.5 MPa

(much more dangerous than 100 MPa).

The main idea to realistically determine the reserve of a system under consideration is separately taking the reserves of its original parameters into account, each of these reserves being expressed via a common additional number. It is obtained from the condition that, by the worst realizable combination of the values of these parameters arbitrarily modified within the bounds determined by the corresponding reserves, the state of at least one element of the system becomes limiting, no element of it being in overlimiting state.

The additive approach to obtaining reserves develops, generalizes, and extends the relative error whereas the multiplicative approach develops, generalizes, and extends the reserve factor.

In the simplest case of the equal reserves of all initial parameters, in example 1 we obtain the additive reserve 1.423 and the multiplicative reserve 1.5 instead of the above usual safety factor 5.9.

In example 2 we obtain the multiplicative reserve 1.25 and 2 in tension and compression, respectively, instead of the above usual safety factor 8.

These realistic reserves are significantly less than the usual ones unwarrantedly optimistic.

The generalized reserve determination method in fundamental mechanical and strength sciences allows rationally controlling the authentic reserves of structures strength.

For formulae and details, see the scientific website of the author and especially his works under "Strength".