R. M. Korol

Large displacement extension of consistent shell element for static and dynamic analysis

Abstract The superior performance of the consistent shell element in the small deflection range has encouraged the authors to extend the formulation to large displacement static and dynamic analyses. The nonlinear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear extension is based on a total Lagrangian approach. A detailed derivation of the non-linear stiffness matrix and the unbalanced load vector for the consistent shell element is presented in this study. Meanwhile, a simplified method for coding the nonlinear formulation is provided by relating the components for the nonlinear B-matrices to those of the linear B-matrix. The consistent mass matrix for the shell element is also derived and then incorporated with the stiffness matrix to perform large displacement dynamic and free vibration analyses of shell structures. Newmarks method is used for time integration and the Newton-Raphson method is employed for iterating within each increment until equilibrium is achieved. Numerical testing of the nonlinear model through static and dynamic analyses of different plate and shell problems indicates excellent performance of the consistent shell element in the nonlinear range.

Behaviour of extended end-plate connections under cyclic loading

Abstract The results of five tests on bolted end-plate beam-to-column connections are described. The specimens were subjected to cyclic loading simulating earthquake effects on a steel moment-resisting frame. The objective of the work is to determine the behaviour of this type of connection under cyclic loading well into the inelastic range and to ascertain the effect of design parameters such as end-plate thickness, column flange stiffener and bolt pre-tension force on the overall behaviour. Observations are made concerning the response of the connection and its elements. Informations and implications on the design of this type of connections to sustain simulated severe earthquake ground motion are presented. It is concluded that properly designed and detailed extended end-plate connection can provide excellent ductility as moment-resisting components in the seismic design of frames.

Extended End-Plate Connections Under Cyclic Loading: Behaviour and Design

Abstract Testing of seven full-scale extended end plate beam to-column connections under cyclic loading was undertaken. A detailed analysis of the connections and that of their individual elements is presented. The performance of the connections is evaluated in terms of strength, stiffness and energy dissipation. Observations are reported in the context of the current building code limits for steel construction. Recommendationsfor the seismic design of such connection types are proposed. It is concluded that sufficient energy dissipation capability without substantial loss of strength can be obtained by proper detailing of the connection.

Stability of elevated liquid-filled conical tanks under seismic loading, Part I—theory

Conical steel shells are widely used as water containments for elevated tanks. However, the current codes for design of water structures do not specify any procedure for handling the seismic design of such structures. In this paper, a numerical model is developed for studying the stability of liquid-filled conical tanks subjected to seismic loading. The model involves a previously formulated consistent shell element with geometric and material non-linearities included. A boundary element formulation is derived to obtain the hydrodynamic pressure resulting from both the horizontal and the vertical components of seismic motion acting on a conical tank which is prevented from rocking. The boundary element formulation leads to a fluid added-mass matrix which is incorporated with the shell element formulation to perform non-linear dynamic stability analysis of such tanks subjected to both horizontal and vertical components of ground motion. Although, the formulation was developed for conical vessels, it is general and can be easily modified to study the stability of any liquid-filled shell of revolution subjected to seismic loading. The accuracy of fluid added-mass formulation was verified by performing the free vibration analysis of liquid-filled cylindrical tanks and comparing the results to those available in the literature.

Stability of elevated liquid-filled conical tanks under seismic loading, Part II-Applications

In this paper, the numerical model developed in the previous paper is used to study the seismic performance of elevated liquid-filled steel conical tanks. A number of conical tanks which are classified as tall or broad tanks according to the ratio of the tank radius to its height are considered. The consistent shell element is used to model the tank surfaces, while the coupled boundary-shell element formulation is employed to obtain the fluid added-mass which simulates the dynamic pressure resulting from a seismic motion. Linear springs are used to model the supporting towers. The natural frequencies of the liquid-filled tanks due to both horizontal and vertical excitations are evaluated. This is followed by a non-linear dynamic analysis, using an appropriately scaled real input ground motion, and which includes the effect of both geometric and material non-linearities. Thin-walled structures of this kind may exhibit inelastic behaviour and a tendency to develop localized buckles, thus diminishing stiffness. The consequence could lead to overall instability of the structure. In general, time-history analyses indicate that liquid-filled conical tanks, often possessing apparently adequate safety factors under hydrostatic loading, are shown to be very sensitive to seismic loading when ground motion frequencies contain those of the fundamental frequencies of the vessels themselves.

Dynamic response of hollow section frames with bolted moment connections

The behaviour of moment-resisting steel frames under various types of loads is dependent on the type of beam-to-column connections and their flexibilities. The extended end-plate connection is a practical field bolted moment connection that can be adopted in moment-resisting steel frames with hollow structural steel (HSS) columns, by using high strength blind bolts. The objective of this work was to study the behaviour of blind bolted extended end-plate connections for HSS columns under cyclic loading. With proper detailing and modelling of such connections, it has been possible to investigate the effect of joint flexibility on the response of the frame when subjected to dynamic loading and then to compare its response to that of a rigid frame. It is concluded that the proposed bolted joint behaves in a predictable manner that can be modelled and analysed using standard frame analysis programmes. The study also showed that the inclusion of the connection flexibility in frame analysis is essential to obtain a more realistic frame behaviour.

Inelastic stability of conical tanks

The aim of this investigation is to study the effect of different imperfection shapes on the inelastic stability of liquid-filled conical tanks and to determine the critical imperfection shape that would lead to the minimum inelastic limit load. The study is carried out numerically using a self-developed shell element used to simulate a number of conical tanks having an imperfection shape in the form of Fourier series of equal coefficients. The Fourier analysis of the buckling modes indicates that the existence of axisymmetric imperfection will lead to the critical inelastic limit load for conical tanks.

Prediction of local buckling and rotation capacity at maximum moment

Abstract An approach which allows for the prediction of the initiation of local buckling in the design of W-shaped beams under steep moment gradient, is presented in this paper. The method described represents a refined moment-rotation model that includes the effects of strain hardening. This same approach helps define more accurately the slenderness limits of the plate elements in relation to the required rotation capacity, at maximum moment.

Critical buckling strains of round tubes in flexure

Abstract The results of a series of 11 tests on single and two span circular hollow tubular beams are used to compare with inelastic bending and axial compression theories of buckling. Predictions of critical strain from both analyses exceed the values obtained from the experimental results, the bending critical stress being somewhat higher than that for axial compression. Due to its simplicity, the latter case is used as a model to assess the form of the diameter-thickness ratio ( D t ) limitation for the various categories of design. For given D t , the critical buckling strain is found to be inversely related to yield stress to a power exponent n which generally lies between 0·5 and 1. Since n tends to unity for steels possessing nearly flat yield plateaus and high D t , the CSA-S16.1 (1974) prescriptions for D t limitations for compact and non-compact sections are reasonable. A slightly lower value of n for plastic design sections may, however, be appropriate.

Modelling of double chord rectangular hollow section T-joints by finite element method

Abstract A linear elastic T-joint comprised of double chord RHS has been modelled by treating the mated flanges as thin plates supported by coupled linear springs thus simulating the action of the side walls and connecting bottom flanges. A rigid rectangular inclusion is presumed for the branch member. Two loading conditions are analyzed—branch member axial force and branch member bending moment. The finite element formulation that is proposed incorporates rectangular plate and edge boundary spring elements. The model is then used to determine the punching shear and rotational stiffnesses of both double chord T-joints and single chord T-joints, thus demonstrating its versatility. The numerical values obtained are in good agreement with the experimental results available in the literature.