Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 / "Brescia" to "Bulgaria"

where F is some unknown function. Launhardt found that, for stresses always of the same kind, F = (t-u)/(t-f_max.) approximately agreed with experiment. For stresses of different kinds Weyrauch found F = (u-s)/(2u-s-f_max.) to be similarly approximate. Now let f_max./f_min. = ?, where ? is + or - according as the stresses are of the same or opposite signs. Putting the values of F in (1) and solving for f_max., we get for the breaking stress of a bar subjected to repetition of varying stress,

f_max. = u(1+(t-u)?/u) [Stresses of same sign.]

f_max. = u(1+(u-s)?/u) [Stresses of opposite sign.]

The working stress in any case is f_max. divided by a factor of safety. Let that factor be 3. Then Wöhler's results for iron and Bauschinger's for steel give the following equations for tension or thrust:?

Iron, working stress, f = 4.4 (1+½?)

Steel, working stress, f = 5.87 (1+½?).

In these equations ? is to have its + or - value according to the case considered. For shearing stresses the working stress may have 0.8 of its value for tension. The following table gives values of the working stress calculated by these equations:?

Working Stress for Tension or Thrust by Launhardt and Weyrauch Formula.