R. Kitching

A theoretical and experimental study of hemispherical shells subjected to axial loads between flat plates

Abstract The quasi-static loading of an open hemispherical shell along its axis of symmetry through a rigid flat plate is considered with particular reference to large deformations and buckling. Deformation patterns which are symmetric and non-symmetric about the axis are studied analytically and experimentally for models of different materials and radius to thickness ratios varying between 36 and 460.

The effects of radial stresses on the strength of thin-walled filament wound GRP composite pressure cylinders

Abstract Filament wound glass fibre reinforced epoxy cylinders with thickness : internal diameter ratios of approximately 0.01, and winding angle ± 85° have been tested to failure under different combinations of axial load and internal pressure. The effect of the interaction coefficients in the Tsai—Wu failure criterion equation are considered. Results for the 17 specimens tested and published results for other winding angles have been used to assess some commonly used forms of failure criteria. It was shown that inclusion of the radial stress terms had no significant effect on the experimental results considered. The geometries and hoop to axial stress ratios for which radial stresses are likely to be important are stated.

Lower bound to limit pressure for cylindrical shell with part-through slot

Abstract A lower bound to the limit pressure of a cylindrical shell with a rectangular slot part through the thickness at mid-length is computed using a linear optimization technique. The sides of the slot are axial and circumferential. The analysis has been carried out for internal pressure applied to the cylinder such that the longitudinal pressure end force is (a) not taken by the cylindrical shell, (b) wholly taken by the cylindrical shell. Different proportions of rectangular slot and different radius to thickness ratios of the cylinder have been considered. Results are presented for a range of parameters.

Limit moment for a smooth pipe bend under in-plane bending

Abstract A lower bound for the limit moment of a smooth circular pipe bend of uniform thickness is calculated with no restrictions on the geometry except those of thin shell theory, though the bend angle and the effect of any straight length attachments are not considered. Results of the analyses suggest that the ( bend radius ) ( pipe radius ) ratio is of importance as well as the pipe factor ( bend radius x thickness ) ( pipe radius ) 2 , which is usually assumed to be the only important geometric parameter.

Behaviour of GRP smooth pipe bends with tangent pipes under flexure or pressure loads: A comparison of analyses by conventional and finite element techniques

Abstract A detailed finite element analysis has been carried out for a smooth pipe bend with straight pipe attachments made from glass reinforced polyester. The shell was modelled as a composite laminate made up of discrete isotropic laminae. The inside pipe diameter was 250 mm, the thickness was 9.52 mm and the bend radius was 250 mm. For in-plane flexural loading the deformation patterns were studied, especially in the vicinity of the smooth bend/straight pipe discontinuity. Warping of sections is reported, together with its influence on pipe bend flexibility for various bend angles. Comparisons of flexibilities and strain distributions are made with those calculated by making the frequently used assumption that the flattening of sections along the entire pipe bend is uniform. The discontinuity effects for out-of-plane flexure and internal pressure loadings, treated separately, are also considered.

Multi-mitred and single-mitred bends subjected to internal pressure

Abstract The stress analysis of a discontinuous pipe bend (a multi-mitred pipe bend) has been carried out for internal pressure loading. It is based on a previous analysis for in-plane bending of the same structure. Results of the analysis are compared with available experimental results. A modification of the analysis has been used to estimate pressure stresses in the vicinity of a single unreinforced mitred pipe joint and the results compared well with a recent more rigorous analysis except for very large mitre angles.

Pressurised eggshell analysis

Abstract A mathematical shape representative of the shell of the egg of a domestic fowl is proposed and a stress analysis is carried out for the shell when it is subjected to internal pressure. Algebraic expressions for the membrane solution are seen to give a close approximation to the complete analysis.

Flexibility of rectangular beams with abrupt changes of section

Abstract The usual strength of materials approach to the calculation of deflexions of stepped beams can incur errors if applied to stepped beams with large and abrupt changes of section. After initial comparison with experimental results, the finite element displacement method was used in an investigation into the properties of such beams, particular attention being paid to the relationships between the geometry and the centre line deflexion curves. Data are presented so that for a beam of any geometry and any loading condition, the centre line deflexion curve can be calculated by using simple bending relationships in conjunction with an equivalent variable second moment of area.

Experimental and theoretical stress analysis of multi-mitred lined glass reinforced plastic pipe bends

Abstract Strain distributions in five right angled multi-mitred composite pipe bends have been measured while subjected to in-plane flexure, out-of-plane flexure and internal pressure, each type of loading being applied separately. Strains were restricted to the linear regime and were less than 0.2%. Each bend and associated straight tangent pipes consisted of a PVC lining wrapped with E-glass chopped strand mat layers impregnanted with polyester resin. Results were compared with theoretical estimates using existing conventional and finite element analyses. The pipes had a nominal inside diameter and an equivalent bend radius of 250 mm

Flexibility of shafts with abrupt changes of section

Abstract The calculation of deflections of shafts by simple bending theory can incur errors if it is applied where the shafts are stepped with large and abrupt changes of section. Following an experimental check, the finite element displacement method was used for an investigation into the flexural properties of such shafts, particular attention being paid to the relationship between the step geometry and the centre line deflection curves. It is shown that centre line deflections of a stepped shaft may be calculated by using simple bending theory in conjunction with an appropriate equivalent variable second moment of area for sections of shaft in the region of the step. Graphical data on the equivalent second moment of area is provided for a wide range of step length / basic shaft diameter and step diameter / basic shaft diameter ratios.