Biezeno Pressure Vessel Heads

1956 ◽  
Vol 23 (4) ◽  
pp. 642-645
Author(s):  
R. A. Struble
Keyword(s):  
Shear Stress ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
Maximum Shear Stress ◽  
Head Shape ◽  
Thin Walled ◽  
Constant Maximum

Abstract The equation of thin-walled pressure vessel heads with constant maximum shear stress throughout is derived. Such heads, used on cylindrical vessels with uniform internal pressure, were first conceived by Biezeno in 1922 who gave a semigraphical prescription for determining the head shape.

Elastic-Plastic Stress Analysis of Pressure Vessels

2012 ◽  
Author(s):  
Yang-chun Deng ◽  
Gang Chen
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Strain Hardening ◽  
Pressure Vessel ◽  
Plastic Instability ◽  
Pressure Vessels ◽  
Structural Deformation ◽  
Elastic Plastic ◽  
Thin Walled ◽  
Plastic Stress

To save material, the safety factor of pressure vessel design standards is gradually decreased from 5.0 to 2.4 in ASME Boiler and Pressure Vessel Codes. So the design methods of pressure vessel should be more rationalized. Considering effects of material strain hardening and non-linear structural deformation, the elastic-plastic stress analysis is the most suitable for pressure vessels design at present. This paper is based on elastic-plastic theory and considers material strain hardening and structural deformation effects. Elastic-plastic stress analyses of pressure vessels are summarized. Firstly, expressions of load and structural deformation relationship were introduced for thin-walled cylindrical and spherical vessels under internal pressure. Secondly, the plastic instability for thin-walled cylindrical and spherical vessels under internal pressure were analysed. Thirdly, to prevent pressure vessels from local failure, the ductile fracture strain of materials was discussed.

Expressions of Load and Structural Deformation Relationship for Cylindrical and Spherical Vessels Under Internal Pressure

2010 ◽  
Author(s):  
Yang-chun Deng ◽  
Gang Chen
Keyword(s):  
Internal Pressure ◽  
Large Deformation ◽  
Pressure Vessel ◽  
Small Deformation ◽  
Plastic Instability ◽  
Structural Deformation ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Thin Walled ◽  
Deformation Relationship

Large deformation analysis for pressure vessel is much more complex than small deformation analysis, therefore, right now, there is no common recognized direct solution for load bearing capacity of pressure vessel yet, and this restrict the application of large deformation analysis in pressure vessel design. This paper based on elastic-plastic theory and considered material strain hardening and structural deformation effects, expressions of load and structural deformation relationship were the first time being derived for cylindrical and spherical vessels under internal pressure. And its practical value is equivalent to principal stress equations of thin-walled cylindrical and spherical vessels with considering non-linear structural deformation effect. Based on the study above and by introducing true stress-strain relationship of materials, analytical solutions of plastic instability pressure for thin-walled cylindrical and spherical vessels were derived.

Influence of Ductility on Creep Rupture Under Multiaxial Stresses

1962 ◽  
Vol 84 (2) ◽  
pp. 228-232 ◽  
Author(s):  
W. Sawert ◽  
H. R. Voorhees
Keyword(s):  
Shear Stress ◽  
Internal Pressure ◽  
Maximum Principal Stress ◽  
Creep Rupture ◽  
Principal Stresses ◽  
Relative Response ◽  
Combined Stresses ◽  
Thin Walled ◽  
Tubular Specimens ◽  
Stress Invariant

Creep-rupture times at 1200 and 1400 deg F were compared for notched versus unnotched bars and for thin-walled tubes in uniaxial tension versus combined tension and internal pressure to give a 1:1 ratio of longitudinal and transverse principal stresses. Relative response to multiaxial stresses of cast DCM alloy with low ductility was not essentially different from that of Rene´ 41 alloy with higher ductility. Creep rupture times of the tubular specimens under combined stresses correlated better in terms of the shear stress invariant than of maximum principal stress.

The Stresses in Thick-Walled Cylinders of Mild Steel Overstrained by Internal Pressure

1934 ◽  
Vol 126 (1) ◽  
pp. 407-455 ◽  
Author(s):  
Gilbert Cook
Keyword(s):  
Shear Stress ◽  
Mild Steel ◽  
Internal Pressure ◽  
Wall Thickness ◽  
Maximum Shear Stress ◽  
Internal Surface ◽  
Principal Stresses ◽  
Constant Shear Stress ◽  
Axial Compressive Stress ◽  
Set Up

The paper describes a theoretical and experimental investigation of the stress distribution across the walls of thick cylinders of mild steel when the internal pressure is such that the elastic limit of the material is exceeded and a certain amount of overstrain occurs. The main conclusions are:— (1) That in the cylinders in which it was possible to produce overstrain over the whole wall thickness the observed pressure is in close agreement with that calculated on the assumption of constant shear stress equal to the shear stress observed during plastic yield in tension. (2) That in partially overstrained cylinders the maximum shear stress in the elastic region varies as overstrain proceeds. (3) That at the internal surface the effect of overstrain is to reduce the circumferential tensile stress, and to set up an axial compressive stress. With sufficient wall thickness all three principal stresses at the internal surface become compressive for pressures which still permit of the external portions remaining elastic.

Three “Neutral” Loading Tests

1956 ◽  
Vol 23 (4) ◽  
pp. 497-502
Author(s):  
S. S. Gill
Keyword(s):  
Shear Stress ◽  
Plastic Strain ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Maximum Shear Stress ◽  
Loading Path ◽  
Plastic Strain Increment ◽  
Octahedral Shear Stress ◽  
Loading Tests ◽  
Von Mises

Abstract Three tests have been carried out using hollow tubes of alpha brass subjected to combined torsion and internal pressure. An initial torque was applied sufficient to cause plastic deformation, and then the torque was decreased and the internal pressure increased to keep the octahedral shear stress constant in two tests and the maximum shear stress constant in the third test. These loading paths were chosen because they would be neutral loading if the material obeyed the von Mises-Hencky or Guest yield criterion, respectively. Shear strain, axial, and circumferential strain were measured. All three tests gave some plastic strain during the “neutral” loading, but the constant maximum shear-stress loading gave much larger plastic strains than the constant octahedral stress loading. The plastic-strain increment vectors have been plotted to illustrate their direction relative to the loading path.

Elastic-Plastic Analysis of Some Pressure Vessel Heads

1970 ◽  
Vol 92 (2) ◽  
pp. 309-316 ◽  
Author(s):  
E. P. Popov ◽  
M. Khojasteh-Bakht ◽  
P. Sharifi
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
Good Accuracy ◽  
Yield Condition ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Thin Walled ◽  
Associated Flow Rule

Sixteen ASME standard torispherical heads attached to cylinders and subjected to internal pressure are analyzed as elastic and/or elastic-plastic shells using a new finite element. As basic elements, thin-walled frusta with curved meridians having common tangents and radii at the nodal circles are employed assuring good accuracy of the results. In the plastic analysis each wall-thickness was subdivided into concentric lamina in order to monitor the behavior of the material. The incremental law of plasticity in conjunction with the Mises yield condition and the associated flow rule were used in the inelastic range. The results of the analysis are presented in detail and are compared with the provisions of the ASME Pressure Vessel Code.

Asymptotic Stress Fields for Stationary Cracks Along the Gradient in Functionally Graded Materials

2002 ◽  
Vol 69 (3) ◽  
pp. 240-243 ◽  
Author(s):  
V. Parameswaran ◽  
A. Shukla
Keyword(s):  
Shear Stress ◽  
Stress Field ◽  
Functionally Graded Materials ◽  
Maximum Shear Stress ◽  
Functionally Graded ◽  
Stress Fields ◽  
Shear Mode ◽  
Graded Materials ◽  
Opening Mode ◽  
Constant Maximum

Stress field for stationary cracks, aligned along the gradient, in functionally graded materials is obtained through an asymptotic analysis coupled with Westergaard’s stress function approach. The first six terms of the stress field are obtained for both opening mode and shear mode loading. It is observed that the structure of the terms other than r−1/2 and r0 are influenced by the nonhomogeneity. Using this stress field, contours of constant maximum shear stress are generated and the effect of nonhomogeneity on these contours is discussed.

scholarly journals Studying the performance of fully encapsulated rock bolts with modified structural elements

2021 ◽  
Author(s):  
Jianhang Chen ◽  
Hongbao Zhao ◽  
Fulian He ◽  
Junwen Zhang ◽  
Kangming Tao
Keyword(s):  
Shear Stress ◽  
Load Transfer ◽  
Maximum Shear Stress ◽  
Coupling Model ◽  
Numerical Approach ◽  
Rock Bolt ◽  
Structural Elements ◽  
Rock Bolts ◽  
Two Stage ◽  
Bolt Diameter

AbstractNumerical simulation is a useful tool in investigating the loading performance of rock bolts. The cable structural elements (cableSELs) in FLAC3D are commonly adopted to simulate rock bolts to solve geotechnical issues. In this study, the bonding performance of the interface between the rock bolt and the grout material was simulated with a two-stage shearing coupling model. Furthermore, the FISH language was used to incorporate this two-stage shear coupling model into FLAC3D to modify the current cableSELs. Comparison was performed between numerical and experimental results to confirm that the numerical approach can properly simulate the loading performance of rock bolts. Based on the modified cableSELs, the influence of the bolt diameter on the performance of rock bolts and the shear stress propagation along the interface between the bolt and the grout were studied. The simulation results indicated that the load transfer capacity of rock bolts rose with the rock bolt diameter apparently. With the bolt diameter increasing, the performance of the rock bolting system was likely to change from the ductile behaviour to the brittle behaviour. Moreover, after the rock bolt was loaded, the position where the maximum shear stress occurred was variable. Specifically, with the continuous loading, it shifted from the rock bolt loaded end to the other end.

Flow and Thermal Fields in a Pendant Droplet Moving on Lyophobic Surface

2010 ◽  
Author(s):  
Basant Singh Sikarwar ◽  
K. Muralidhar ◽  
Sameer Khandekar
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Reynolds Number ◽  
Shear Stress ◽  
Heat Transfer Coefficient ◽  
Wall Shear Stress ◽  
Transfer Coefficient ◽  
Maximum Shear Stress ◽  
Computational Domain ◽  
Wall Shear

Clusters of liquid drops growing and moving on physically or chemically textured lyophobic surfaces are encountered in drop-wise mode of vapor condensation. As opposed to film-wise condensation, drops permit a large heat transfer coefficient and are hence attractive. However, the temporal sustainability of drop formation on a surface is a challenging task, primarily because the sliding drops eventually leach away the lyophobicity promoter layer. Assuming that there is no chemical reaction between the promoter and the condensing liquid, the wall shear stress (viscous resistance) is the prime parameter for controlling physical leaching. The dynamic shape of individual droplets, as they form and roll/slide on such surfaces, determines the effective shear interaction at the wall. Given a shear stress distribution of an individual droplet, the net effect of droplet ensemble can be determined using the time averaged population density during condensation. In this paper, we solve the Navier-Stokes and the energy equation in three-dimensions on an unstructured tetrahedral grid representing the computational domain corresponding to an isolated pendant droplet sliding on a lyophobic substrate. We correlate the droplet Reynolds number (Re = 10–500, based on droplet hydraulic diameter), contact angle and shape of droplet with wall shear stress and heat transfer coefficient. The simulations presented here are for Prandtl Number (Pr) = 5.8. We see that, both Poiseuille number (Po) and Nusselt number (Nu), increase with increasing the droplet Reynolds number. The maximum shear stress as well as heat transfer occurs at the droplet corners. For a given droplet volume, increasing contact angle decreases the transport coefficients.

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