Hoop tension

The external diameter of the tube and its wall thickness determine the pressure which it will stand. Failure of a tube is due to the tension at the surface becoming too great. For a cylinder of internal radius r and external radius R, and vwth an internal pressure in the cylinder of P, the maximum circumferential (or hoop) tension S (see A. Morley, 1940) on the inner surface of the cylinder is... 

For distance down from the top tangent line that a thickness is good for, when the thickness of the top section is that required for hoop tension, use... 

True Stress. As set up in the forms for checking stresses and in the derivation of formulas for approximate thickness, the elastic strength under compound stress is determined by maximum principal stresses. This has been done because the ASME Code does not allow the use of true stress for hoop tension, and because some engineers will not allow the use on the longitudinal axis. 

Derivation of Equations. The principal stress of hoop tension is (PD)/2 for thin cylinders. Using the... 

When the plate size for the top section has been calculated for hoop tension, to find the approximate distance from the top tangent line that the plate is good for in axial tension, the value of O.bf may be used for (PI>/4) substituting in 4-27,... 

Hoop tension, Tg, will govern design of shell for. shallow bins T2 = p,R... 

Note For thin, circular steel bins, longitudinal compression will govern. The shell will fail by buckling from vertical drag rather than bursting due to hoop tension. 

Shki ls with Self-supportivi Roofs. A seIf-sup M r(-ing roof is one which is. supported only on its peripfiery, without added structural support. Such roofs cause a compressive stress in the roof plates, wliich i.s transferred to the shell as hoop tension. A stiflfening angle should be ai ded to the top shell course at the junction of the roof and shell to al orb the stress as a tensile load. The forces acting on the ring are shown in Fig, 3.19. 

The key factor here is that unsymmetrical pressures are often damaging to cylindrical silo structures, whether constructed in metal or concrete, and this effect is more important than the possible peak pressure occurring at one point. In particular, if the peak pressure only occurs at one point around the circumference, then the pressures are necessarily unsymmetrical and the worst aspect of this load case is not the simple relationship between normal pressure and circumferential (hoop) tension of Figure 3.11. 

This is one of the most common causes of silo structural problems, since it is so often overlooked. It results when the withdrawal point from the hopper is not located on the vertical centerline of a circular silo [7,8], and is particularly common when using silos with multiple hoppers in which only one or two of the hopper outlets arc used at a lime. If the resulting flow channel intersects the silo wall, non-uniform pressures will develop around the circumference of the silo leading to horizontal and vertical bending moments. See Figure 1. Many silo designers incorrectly account for these non-uniform pressures by only increasing hoop tension. [9,10]... 

Hoop tension (splitting failure beyond hole)... 

HOOP TENSION—SPLITTING FAILURE BEYOND HOLE... 

The hoop tension phenomenon is perhaps the most Ukely mode of failure. This mode occurs when the lift force acts in tension in the hoop direction, as shown in Figure 7.5. This mode of failure is the tensile force acting on the area of the lug from the top of the lug hole to the lug edge in one plane, and the lug... 

FIGURE 7.5 Hoop tension forces splitting apart a lifting lug. 

Hoop tension is quite often the governing mode. 

OKHT 68771718.8 If this space is filled then Hoop Tension is acceptable... 

OK 91.6149579 If this space is filled than Hoop Tension stress is OK... 

The maximum actions (e.g., membrane forces and bending moments, circumferential or meridional) induced in the seismic design shall be less or equal to the resistance of the shell evaluated as in the persistent or transient design sitnaticHis. For the cylindrical steel shell buckling by vertical (meridional) compression with simultaneous action of hoop tension due to hydrostatic loading ( elephant s foot mode of failure ) is a critical simation. 

Section 8.5 and Aimex D of EN 1993-1-6 (European Committee for Standardization 2007), paragraphs D.1.2 and D.1.5, give a systematic methodology for the calculation of cylindrical shell resistance against meridional axial compression in the presence of hoop tension due to internal pressure. Moreover, paragraph A. 10 of EN 1998-4 (European Committee for Standardization 2006b) provides alternative rules for internally pressurized shell buckling, based on the work by Rotter (1990). 

R.E. Ely, Hoop Tension Strength of Composite Graphite-Aluminum Tubes , Army Missile Research Development and Engineering Lab Redstone Arsenal A1 Physical Sciences Directorate, AD0489900, 24 Aug (1966)... 

---