G.J. Turvey

Effects of joint geometry and bolt torque on the structural performance of single bolt tension joints in pultruded GRP sheet material.

This paper contains the details of an experimental investigation into double lap single bolt tension joints made from 6.35 mm thick pultruded fibre reinforced plastic flat sheet. The joint geometry [edge distance to bolt diameter (E/D) and width to diameter (W/D) ratio] was varied and the effect of bolt clamping torque was investigated. Failure loads, critical end distances and critical widths were found to increase as the bolt clamping torque increased. After an initial bolt movement, the load vs bolt displacement plots are linear until the joints fail or the stiffness reduces significantly. The load at which the joint stiffness reduces has been called the damage load. This damage load is thought to be a useful quantity on which to base design. A simple statistical analysis has been carried out on the damage loads and damage load capacities for single bolt joints have been determined for prescribed confidence levels.

Effects of load position on the lateral buckling response of pultruded GRP cantilevers —Comparisons between theory and experiment

Details of a series of lateral buckling tests on a pultruded GRP I-section cantilever beam are described. The cantilever, which had spans ranging from 0.5 to 1.5 m, was subjected to point loads applied above, at and below the centroid of the free end cross-section. Vertical and horizontal deflections and the rotation of the free end cross-section were recorded as the beam was loaded and unloaded. Lateral buckling loads computed from modified simple closed form formulae and finite element eigenvalue analysis were compared with the maximum test loads. The computed buckling loads were generally significantly lower than the maximum test loads, though the differences between the loads appeared to be smallest for the longest span with the load applied just above the lower flange of the free end cross-section. The tests showed that significant vertical free end deflections develop before the cantilever buckles laterally and it is concluded that the effects of prebuckling deformations and geometric nonlinearity in addition to a more accurate evaluation of the in-plane shear modulus may have to be taken into account in order to achieve a closer correlation between the numerical analysis and the test results.

DR large deflection analysis of sector plates

Abstract An elastic large deflection analysis of uniformly loaded sector plates is presented. Numerical solutions are obtained by means of the Dynamic Relaxation (DR) algorithm coupled with an interlacing central finite-difference discretization scheme. Comprehensive verification of the DR results is provided via comparison with exact small deflection solutions and approximate large deflection solutions—the latter being derived from the ANSYS finite element program. Some new large deflection results, in the form of centre deflection vs pressure response curves, are presented for simply supported and clamped plates for a range of sector angles.

Lateral buckling tests on rectangular crosssection pultruded GRP cantilever beams

Results of a series of tests on rectangular cross-section pultruded GRP cantilever beams are presented. The beams are loaded in their stiffer plane of symmetry by means of a single point load acting through the centroid of the cross-section at the free end. Each beam was loaded well into the lateral postbuckling regime and then unloaded. Throughout the loading and unloading regimes end displacements, i.e. horizontal and vertical translations and the rotation of the cross-section, were recorded. Plots of support moment versus free end rotation are presented for all 16 beams tested and critical support moments (calculated using a modified formula for the critical moment of an isotropic cantilever) are compared with experimental maximum moments. The maximum support moments applied in the tests are also compared with theoretical critical support moments for span to depth ratios ranging from 4 to 25. It is shown that critical support moments provide reasonable lower bound estimates of the maximum support moments provided the span to depth ratio, l/d, exceeds 10.

Elastic large deflection analysis of isotropic rectangular Mindlin plates

Abstract Governing equations for the large deflection analysis of isotropic rectangular Mindlin plates are introduced and their solution using the DR algorithm is briefly outlined. Two computer programs, based respectively on interlacing and non-interlacing finite-differences, have been developed for the numerical solution of these equations. The programs have been verified by analysing a variety of thin and moderately thick plate problems for which alternative solutions are available. Sample results comparisons are presented in order to quantify the accuracy of the DR results. The non-interlacing finite-difference DR program is then used to compute new results for uniformly loaded square moderately thick plates with simply supported, clamped and combined simply supported and clamped edges.

Bolted connections in PFRP structures

A brief overview of some of the more noteworthy PFRP structures is presented. It is noted that, at the present stage of development, bolted connections are used extensively in fabricating structural frames from PFRP sections. Tests on bolted connections between PFRP sections, i.e., axially loaded and moment connections, and guidance for their design are reviewed. Some areas where further research and guidance are needed are mentioned and the paper is concluded with a few remarks on possible future developments.

Analysis of pultruded glass reinforced plastic beams with semi-rigid end connections

The influence coefficient method of analysis has been used to derive closed-form expressions for the mid-span deflection and end rotations of shear deformable uniform section beams with semi-rigid end connections. The formulae have been recast into performance indices which define the reduction in mid-span deflection, the increase in load carrying capacity and the increase in span relative to an otherwise identical simply supported beam for two practical load distributions: (1) a point load at mid-span and (2) a uniform load over the entire span. Expressions are also presented for the required rotation capacity of the semi-rigid end connections. Initial rotational stiffness data, derived from full-scale tests on web and web and flange cleat connections between two sizes of pultruded glass reinforced plastic (GRP) WF-section are used in the formulae to evaluate the performance indices for the practical range of span-to-depth ratios for load case (1). The values obtained quantify the benefits to be derived from exploiting semi-rigid end connection stiffness in the design of pultruded GRP beams with the current, very limited, range of section sizes.

Elastic small deflection analysis of annular sector Mindlin plates

An analytical method is developed for the bending response of annular sector Mindlin plates with two radial edges simply supported, and exact solutions are presented in the form of Levy-type series. Several different boundary conditions on the two circular edges are considered, viz. simply supported-simply supported, clamped-clamped and free-free. Numerical results for the case of uniform loading are presented to indicate the effect of shear deformation on the deflections and stress resultants at various points in the plate. Twisting stress couple and transverse shear stress resultant distributions along and near the edges of the plate are illustrated graphically, and the principal differences between the results predicted by Mindlins plate theory and classical thin plate theory are discussed in detail. Results obtained with the present exact analysis may serve as references for approximate solutions and, especially, as a ‘shear locking’ test for thick plate finite element analysis.

Torsion tests on pultruded GRP sheet.

Details of a series of simple torsion tests on rectangular cross-section strip specimens cut from 6·4 mm thick pultruded GRP sheet are described. Stiffness and strength data are presented for specimens with their torsion axes parallel with and transverse to the pultrusion direction. The differences in the development of failure in the two types of specimen are described. The stiffness data are analysed on the basis of simple torsion theory for orthotropic rectangular cross-section bars to determine both the in-plane and through-thickness shear moduli for the pultruded GRP sheet and it is shown that the average value of the former modulus is somewhat higher than (but nevertheless consistent with) values derived from shear tests.

Axisymmetric full-range analysis of transverse pressure-loaded circular plates

Incremental equations governing the axisymmetric full-range response of transverse pressure loaded, clamped and simply supported, circular plates are presented. The derivation and implementation of the full-section and layer constitutive equations is described in detail. The solution of the finite-difference approximations to the governing equations using the Dynamic Relaxation (DR) method is briefly outlined together with several refinements for improving computational efficiency. Both the full-section and layer analyses are used to compute plate deflections observed in several tests on uniformly loaded, clamped and simply supported, circular plates. It is observed that the layer analysis predicts the measured deflections more accurately than the full-section analysis. The analytical-experimental deflection correlation appears to be accurate for slender clamped plates and less accurate for stocky clamped and simply supported plates. It is suggested that various uncertainties about the plate test data may account, in part, for the lack of deflection correlation and that more carefully controlled plate tests should be undertaken in order to confirm this speculation.