{"id":2745,"date":"2025-02-13T16:58:59","date_gmt":"2025-02-13T15:58:59","guid":{"rendered":"https:\/\/jureknawrocki.com\/?p=2745"},"modified":"2026-02-24T12:07:52","modified_gmt":"2026-02-24T11:07:52","slug":"inzynier-d-s-obliczen-czy-tylko-uzytkownik-programu","status":"publish","type":"post","link":"https:\/\/jureknawrocki.com\/en\/inzynier-d-s-obliczen-czy-tylko-uzytkownik-programu\/","title":{"rendered":"Pipe stress engineer or just an program user only"},"content":{"rendered":"

Below is a long post. Understanding it allows you to distinguish between an ordinary software user that program clicking without understanding how it works, and a pipe stress engineer who has an above-average knowledge of what hypothesis underlies the strength of materials. If you belong to the second group, then this post is for you. <\/p>\n\n\n\n

PRINCIPAL STRESSES AND STRESS HYPOTHESES<\/mark><\/strong><\/strong><\/p>\n\n\n\n

Let us imagine a material element subjected to tension as shown in the figure below. The a \u2013 a plane is directed at an angle alpha to the direction of the force F acting on the plane A, generating a tensile stress S. The force F can be resolved into two components: Fn<\/sub> \u2013 normal and Fs<\/sub> \u2013 tangent to the plane a \u2013 a. These components cause normal stresses sigma and tangential stresses theta with values \u200b\u200bdescribed by the formulas below:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

It is obvious that for a constant value of the force F, the normal and tangential stresses depend only on the angle of inclination of the plane. The maximum tangential stress theta will be for sin 2 alfa = 1 (which corresponds to the angle a = 450<\/sup>) half the value of the tensile stress of the sample. The maximum of the normal stress sigma will of course occur for the angle alpha = 00<\/sup>, and its minimum for angle alpha = 900<\/sup>. Stresses in such planes are characterized by the absence of a tangential component and are called principal stress.<\/p>\n\n\n\n

Traditionally, principal stresses have been determined using a series of simple constructions from analytical geometry called Mohr's circle, an example of which is given below.<\/p>\n\n\n\n

Let us assume that the normal stress sigmax<\/sub> and shear thetaxz<\/sub> are greater than zero and can be shown in the sigma-tetea coordinate system below. We put the value of the normal stress sigmax<\/sub> on the s-axis, and at its end the tangential stress value thetaxz<\/sub>.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

We draw a circle of radius R, the beginning of which is half the value of the normal stress sigmax<\/sub>. We determine the maximum and minimum principal stresses, where the circle intersects at the points of zero tangential stress theta. In the last step, we determine the directions of their action.\u00a0<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Principal stresses (here sigma1<\/sub>, sigma2, <\/sub>sigma3) <\/sub>are the starting point for the two hypotheses used in the pipeline calculations. <\/p>\n\n\n\n

The first one is the hypothesis of the specific work of purely shear deformation formulated and published in 1904 by the outstanding Polish professor M.T Hubera (1872-1950)<\/a> more widely known as the hypothesis R. Misesa (1883-1953)<\/a>, who published it only nine (!) years later, in 1913. Both were under the resumption of the same ruler, Franz Joseph I, except that the former was a Pole born in a tiny town in Podhale, and the latter an Austrian living in the capital of the Empire in Vienna. Whether this was the theft of the century that the Austrian aristocrat got away with is difficult to decide now. However, there was something to fight for, because the hypothesis of the specific work of purely shear deformation, which was the crowning achievement of many European scientists throughout the 19th century, is the same as Maxwell's four equations for our electromagnetic civilization. This is the fudamental basis of the science of strength of materials. <\/strong><\/mark> <\/strong> <\/mark><\/p>\n\n\n\n