The Journal of Strain Analysis for Engineering Design

As part of an extensive experimental study into the influence of semi-rigid connections on the behaviour of steel columns, a measurement device has been developed which permits the six individual components of three-dimensional deformation to be monitored. The theory used to process the measured deformations and the subsequent testing of a prototype device is described. A comparison between the deformations measured using the device, and those predicted using a column sub-assemblage finite element model is also presented.

A simple procedure for estimating the stress intensity factor of a continuous crack at the root of a circumferential notch in a round bar is presented. Numerical solutions for equivalent notched and un-notched geometries are compared. The resulting correction term for notches is formulated as a polynomial equation using only notch geometric parameters and is used in conjunction with the conventional stress intensity calibration for the un-notched configuration.

The finite element method has been used to obtain elastic stress data for simply-supported short beams with uniformly distributed loading and short built-in beams subjected to shear displacement (referred to as ‘sinking beams’). Length-to-depth ratios in the range 0.5–2.0 have been considered. In the case of the simply-supported beam, some results are compared with published data, while additional information on section warping and stress contours is presented. Similar results are presented for the sinking beam, for which alternative solutions are not currently published. Predictions are compared with estimates using simple theory for slender beams and modified theories which include transverse shear effects. It is apparent that these estimates can be significantly in error when length-to-depth ratios are less than 2.0.

A technique is described for manipulating strain gauge data obtained from tests on structural steel ‘H’ sections such that individual force components may be identified. The technique recognises the different structural actions present when open sections deform in a full three-dimensional fashion (compression, major and minor axis bending, and warping) covering both elastic and elastic–plastic behaviour. The results obtained from experimental tests on beam columns exhibited excellent agreement with the corresponding predictions of a sophisticated non-linear finite element analysis.

A series solution method is presented for analysing sharp asymmetric dry contact problems. It provides an exact representation for the pressure inside the contact, the contact width and also the displacement outside the contact for the frictionless two-dimensional problem of a rigid indentor acting on an elastic half-plane. The first part of the paper describes how the method can be used for symmetric and asymmetric punches without slope discontinuities. In the second part the method is modified to overcome the Gibbs phenomenon so that it can be applied to any punch, symmetric or asymmetric, with or without slope discontinuities. Finally, two analytic approaches are described and compared with the present solution method.

By means of combining Drucker's yield function with Hill's quadratic yield function, the anisotropic yield function of the sixth degree is proposed. It is able to include the effects of the third deviatoric stress invariant and initial anisotropy. The experimental evaluation is made on thin-walled cylindrical specimens of mild steel (in the fully annealed condition and the stress-relief annealed condition after a tensile pre-strain) and 2024 aluminum alloy (in the -0 and -T₆ tempered conditions). By applying proportional combined loadings of axial load, internal pressure, and torsion to the specimens, a change of yield stress with a rotation of the principal stress axes and a difference between the directions of the principal stress and principal strain increment are examined Under tension–internal pressure and tension–torsion, the yield surfaces and strain behaviour are determined. The fully annealed steel is almost isotropic for yielding although it reveals the effect of the third deviatoric stress invariant. The stress-relief annealed steel and the 2024–0 and -T₆ aluminum alloys exhibit axi-symmetric anisotropy. All of the yield surfaces can be expressed precisely by the proposed yield function. In addition, the normality rule is obeyed in strain behaviour.

An effective method is developed for determining the individual stresses from the trace of the stress tensor (isopachics) in a region adjacent to an arbitrarily-shaped traction-free boundary of a loaded component. The approach is facilitated by the fact that the stresses throughout such a region can be described completely in terms of only one complex potential. Equilibrium and compatibility prevail within the region, and the traction-free boundary conditions are satisfied. The concept is expected to be particularly useful for thermoelastic stress analysis.

This work arose from a design exercise which required a less constrained treatment of annular plates than is available from standard formulae. The transfer matrix method gives freedom for the thickness of the plate, and the pressure across it, to be any functions of radius, and for the plate to be supported at any radius, or at any radii, in whatever manner is relevant. Natural frequencies and mode shapes may be calculated by including the inertia terms in the matrices. Its limitation is that only axially symmetrical deformation and modes are covered by the method.