Hoop strain

Example 23 A cylindrical polypropylene tank with a mean diameter of 1 m is to be subjected to an internal pressure of 0.2 MN/m. If the maximum strain in the tank is not to exceed 2% in a period of 1 year, estimate a suitable value for its wall thickness. AVhat is the ratio of the hoop strain to the axial strain in the tank. The creep curves in Fig. 2.5 may be used. 

Solution The maximum strain in a cylinder which is subjected to an internal pressure, p, is the hoop strain and the classical elastic equation for this is... 

Hence the hoop strain, se, at the bore of the ring is given by... 

A filament wound composite cylindrical pressure vessel has a diameter of 1200 mm and a wall thickness of 3 mm. It is made up of 10 plies of continuous glass fibres in a polyester resin. The anangement of the plies is [O3/6O/ — 60],. Calculate the axial and hoop strain in the cylinder when an internal pressure of 3 MN/m is applied. The properties of the individual plies are... 

Note that is small compared to as or Oa and so it is often ignored. Hoop strain,... 

A simpler, although less accurate, method of evaluating these press fits is to assume that the shaft will not deform when pressed into the plastic. This is reasonably accurate when a metal shaft is used in a plastic hub. The hoop strain developed that is reasonably accurate in the hub is then given by the equation ... 

Figure 7. Strain amplification A plot of the strain amplification ratio er as a function of the load frequency for different load magnitudes. Strain amplification ratio is defined as the ratio of the hoop strain in the cell process membrane to the bone surface strain at the osteonal lumen, e is the strain on the whole bone s is the load on the whole bone. Previously published in You et al. (2001).

Finally, the matrix must be attached to the cell process and the canalicular wall in order for the drag force to be transmitted to the membrane and its underlying intracellular actin cytoskeleton. If such linker molecules are present, drag forces exerted on the matrix fibers will produce a tensile stress on these linker molecules that, in turn, will produce radial (hoop) strain in the intracellular actin cytoskeleton as schematically shown in Figure 6. Possible candidates for these attachment molecules are CD44, laminin, and various integrins. [64, 149],... 

Figure 4 shows the predicted hoop strain and axial strain according the increasing pressure. Due to the close-end effect, the axial deformation remains low and exhibits a backup once the liner plasticization started around 200 bars. Only a change of slope is observed for the hoop strain at the same point, even if some non linear phenomena occur. 

Axial and hoop strains according the inside pressure... 

Figure 4 Deformations from simulation, Eoo for the hoop strain and Ezz for the axial strain.

The stresses in a pressurised pipe, free to expand in length, were analysed in Section C.3 of Appendix C. However, buried gas pipe is connected at both ends to immovable objects such as houses, and the surrounding soil prevents the pipe moving laterally. Consequently, the longitudinal strain in the pipe is zero. In this elastic plane strain situation, the hoop strain is given by Eq. (C.21) as... 

Problem 3 When the pipe is placed under pressure, the hoop and longitudinal stresses in the wall are given by Eqs (C.19) and (C.21). The hoop strain for an elastic material is given using Eq. (C.18) as... 

Therefore, substituting v = 0.4, the creep hoop strain will be smaller than that in a tensile creep test by a factor (1 — v ), if the hoop and tensile stresses are equal. Examining Fig. 7.6, the tensile stress to cause a creep strain of 3/0.84 = 3.6% after 50 years is approximately 4 MPa. For a 4 bar pressure to cause a hoop stress of 4 MPa, the pipe SDR = 21 by Eq. (14.2). This is the maximum SDR allowed. 

Heating to 350 K increased the output of all three gauges near the cone apex. The hoop strain at the top (gauge 4) may have been very small due to the constraint of the test fixture. Comparison of gauges 1 and 2 indicates that there was a greater strain on the exterior than on the interior. 

An analytical relationship for adhesive effective modulus and bulk modulus can be given for the case where tubular bars are bonded together and loaded in their axial direction, (see references 5.17 and 5.19). It is assumed that the adherends are infinitely rigid i.e. the radial and hoop strains in the adhesive and adherends are zero. Then the... 

Despite the minimal ductdity and capabUity for flexure, snap fits and interference fits are possible with reinforced PPS compoimds, since their high modulus makes it possible to attain adequate holding strength with minimal interference. Snap-fit applications typically involve only onetime assembly, and press-fit components should not induce more than about 0.5% hoop strain. Considerable force is often required for assembly and must be applied with care to prevent part cracking. Molded-in inserts are preferred over press fitting for larger components such as hubs or bearings. 

To postpone the onset of splitting of deficiently lap-spliced reinforcements and to reduce the severity of the subsequent deterioration, a hoop strain of 1,000 E is appropriate for the design of the composite jacket for circular and rectangular columns. Also steel plates should be used in the wrapper region of rectangular columns. 

A pipe of external diameter wall thickness IF = 8 mm is produced from the polymer of Problem 4.1. It is internally pressurized with closed ends to a pressure of 0.4 MPa. Find the hoop strain and axial strain in the wall of the pipe 20 hours after the pressure is applied. Take Poisson s ratio to be constant at 0.4 for this material and hoop stress = P(4 —2IF)/2IF. 

The expression for Ng is derived from the axial and hoop strains. In referring to Big. 5. >, ihf axial strain is given by... 

Figure 11.4 Hoop strain at outside surface during autofrettage of a thick-walled cylinder (OD/ ID = 2.35 yield strength = 965 MPa).

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