Flanges formulas

Operational blanks shall be of the same thickness as blind flanges or may be calculated by the following formula (use consistent units) ... 

Unstayed flat heads and covers can be designed by very specific rules and formulas given in this subsection. The stresses caused by pressure on these members are bending stresses, and the formulas include an allowance for additional edge moments induced when the head, cover, or blind flange is attached By bolts. Rules are provided for quick-opening closures because of the risk of incomplete attachment or opening while the vessel is pressurized. Rules for braced and stayed surfaces are also provided. 

In this formula, w is the weight in tons per axle b is a coefficient of flange friction (0.03 for passenger cars) V is the speed in miles per hour C is the air drag coefficient (0.0017 for locomotives, 0.00034 for trailing passenger cars) and A is the cross-sectional area of locomotives and cars (120 sq ft for locomo-Uves, 110 sq ft for passenger cars). 

This issue was addressed in 1979 by McBride and Jacobs. Jacobs was from Fluor in Houston. The principle was to calculate stresses in two distinct areas, membrane and bending. Membrane stresses are based on pressure area times metal urea. Bending is based on AISC beam formulas. The neck-and-shell section (and sometimes the flange as well) is assumed as bent on the hard axis. This is not a beam-on-elastic-foundation calculation. It is more of a brute-force approach. 

It has been found by tests as well as by mathematical analysis that the torsional resistance of a section, made up of a number of rectangular parts, is approximately equal to the sum of the resistances of the separate parts. It is on this basis that nearly all the formulas for noncircular sections have been developed. For example, the torsional resistance of an Tbeam is approximately equal to the sum of the torsional resistances of the web and the outstanding flanges. In an I-beam in torsion the maximum shearing stress will occur at the middle of the side of the web, except where the flanges are thicker than the web, and then the maximum stress will be at the midpoint of the width of the flange. Reentrant angles, as those in I-beams and charmels, are always a source of weakness in members subjected to torsion. 

As an effect of the bend radii the unfolded dimensions of a blank cannot be determined as the sum of the over measured flange dimensions. The difference between both is referred to as the bend allowance BA). The BA can be determined experimentally. For mild steel the DIN6935 standard also offers a series of heuristic formulas. The standard uses the assumption that the neutral fibre (fibre with no effective strain) is showing... 

Head types fall into one of three general categories hemispherical, torispherical, and ellipsoidal. Hemispherical heads are analyzed as spheres and were covered in the previous section. Torispherical (also known as flanged and dished heads) and ellipsoidal head formulas for stress are outlined in the following form. 

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