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CONTENTS
Volume 5, Number 3, May 1997
 

Abstract
This paper presents a new uniaxial material model for rate-sensitive analysis addressing both the transient and steady-state responses. The new model adopts visco-plastic theory for the rate-sensitive response, and employs a three-parameter representation of the overstress as a function of the strain-rate. The third parameter is introduced in the new model to control its transient response characteristics, and to provide flexibility in fitting test data on the variation of overstress with strain-rate. Since the governing visco-plastic differential equation cannot be integrated analytically due to its inherent nonlinearity, a new single-step numerical integration procedure is proposed, which leads to high levels of accuracy almost independent of the size of the integration time-step. The new model is implemented within the nonlinear analysis program ADAPTIC, which is used to provide several verification examples and comparison with other experimental and numerical results. The companion paper extends the three-parameter model to trilinear static stress-strain relationships for steel and concrete, and presents application examples of the proposed models.

Key Words
strain-rate effect, material model, nonlinear structural response

Address
Izzuddin BA, UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED,DEPT CIVIL ENGN,LONDON SW7 2BU,ENGLAND

Abstract
The companion paper presents a new three-parameter model for the uniaxial rate-sensitive material response, which is based on a bilinear static stress-strain relationship with kinematic strain-hardening. This paper extends the proposed model to trilinear static stress-strain relationships for steel and concrete, and discusses the implementation of the new models within an incremental-iterative solution procedure. For steel, the three-parameter rate-function is employed with a trilinear static stress-strain relationship, which allows the utilisation of different levels of rate-sensitivity for the plastic plateau and strain-hardening ranges. For concrete, on the other hand, two trilinear stress-strain relationships are used for tension and compression, where rate-sensitivity is accounted for in the strain-softening range. Both models have been implemented within the nonlinear analysis program ADAPTIC, which is used herein to provide verification for the models, and to demonstrate their applicability to the rate-sensitive analysis of steel and reinforced concrete structures.

Key Words
strain-rate effect, steel structures, reinforced concrete structures

Address
Fang Q, UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED,DEPT CIVIL ENGN,LONDON SW7 2BU,ENGLAND

Abstract
The elastic deflections and Euler buckling loads are investigated for a class of tapered and initially curved cantilevered beams subjected to loading at the tip. The beam\'s width increases linearly and its depth decreases linearly with the distance from the fixed end to the tip. Unloaded, the beam forms a circular are perpendicular to the axis of bending. The beam\'s deflection responses, obtained by solving the differential equations in closed form, are presented in terms of four nondimensional system parameters: taper ratio kappa, initial shape ratio Delta(0), end load ratio f, and load angle theta. Laboratory measurements of the Euler buckling loads for scale models of tapered initially straight, corrugated beams compared favorably with those computed from the present analysis. The results are applicable to future designs of the end structures of highway guardrails, which can be designed to give the appropriate balance between the capacity to deflect a nearly head-on vehicle back to its right-of-way and the capacity to buckle sufficiently that penetration of the vehicle may be averted.

Key Words
elastic buckling, Euler load, cantilevered beam, corrugated cross section, curved beam, guardrail, initial curvature, tapered beam, variable cross section

Address
Wilson JF, DUKE UNIV,DEPT CIVIL & ENVIRONM ENGN,DURHAM,NC 27708
N CAROLINA DEPT TRANSPORTAT,RALEIGH,NC

Abstract
The overall buckling mode in a composite steel-concrete beam over an internal support is necessarily lateral-distortional, in which the bottom compressive range displaces laterally and twists, since the top flange is restrained by the nearly rigid concrete slab. An efficient finite element method is used to study elastic lateral-distortional buckling in composite beams whose steel portion is tapered. The simplified model for a continuous beam that is presented herein is a fixed ended cantilever whose steel portion is tapered, and is subjected to moment gradient, This is intended to give an insight into distortion in a continuous beam that occurs in the negative bending region, and the differences between the cantilever representation and the continuous beam are highlighted. An eigenproblem is established, and the buckling modes and loads are determined in the elastic range of structural response. It is found from the finite element study that the buckling moment may be enhanced significantly by using a vertical stiffener in the region where the lateral movement of the bottom range is greatest. This enhancement is quantified in the paper.

Key Words
buckling, composite beams, distortion, elasticity, tapering

Address
Bradford MA, UNIV NEW S WALES,SCH CIVIL ENGN,DEPT STRUCT ENGN,SYDNEY,NSW 2052,AUSTRALIA

Abstract
This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using 2(N) algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

Key Words
dynamic structures, holonomic constraints, matrix exponential, algebraic and differential equations, numerical integration

Address
Liu XJ, UNIV PORTSMOUTH,DEPT CIVIL ENGN,BURNABY BLDG,BURNABY RD,PORTSMOUTH PO1 3QL,HANTS,ENGLAND
DALIAN UNIV TECHNOL,DALIAN 116024,PEOPLES R CHINA

Abstract
The bouncing of a cantilever with the free end pressed against a stop can create high-frequency vibration that the Bernoulli-Euler beam theory is inadequate to solve. An analytic procedure is presented using Timoshenko beam theory to obtain the non-linear response of a cantilever supported by an elastic stop with clearance at the free end. Through a numerical example, the bouncing behavior of the Timoshenko and Bernoulli-Euler beam models are compared and discussed.


Key Words
Timoshenko beam, impact, gap, nonlinear vibration

Address
Tsai HC, NATL TAIWAN INST TECHNOL,DEPT CONSTRUCT ENGN,POB 90-130,TAIPEI 10772,TAIWAN

Abstract
This paper is concerned with the time dependent service load behaviour of prestressed composite tee beams. The effects of creep and shrinkage of the concrete slab are modelled using the age adjusted effective modulus method and a relaxation approach. The tendon strain is determined considering compatibility of deformations and equilibrium of forces between the tendon and the composite tee beam. A parametric study is undertaken to study the influence of various aspects on the stress, strain and deformations of the concrete slab, steel beam and prestressing tendon. The effect of loading type and tendon relaxation has also been considered for various types of prestressing tendon materials. Recommendations are then made in relation to adequate span to depth ratios for varying levels of prestressing force.

Key Words
beams, composite construction, creep, prestressing, shrinkage, time effects

Address
Uy B, UNIV WOLLONGONG,DEPT CIVIL & MIN ENGN,WOLLONGONG,NSW 2500,AUSTRALIA

Abstract
In this paper a general analytical approach is proposed to analyse the nonlinear response of elastic cable under complex loads. The effect of temperature change on the cable is also considered. From the vertical equilibrium equations of cable, the general analytical formula of vertical displacement is derived. Based on the vertical displacement formula and on the compatibility condition of the cable, the dimensionless equation with respect to cable tension is established. By means of such analytical procedures, the exact solutions of various cable problems can be obtained quickly. The example given in this paper shows that the new procedure is efficient for practical analysis and can be easily implemented by a general computer program without the superposition problem which there has always been in traditional analytical methods.

Key Words
cable (ropes), tension

Address
HONG KONG POLYTECH UNIV,DEPT CIVIL & STRUCT ENGN,HONG KONG,HONG KONG
NANJING ARCHITECTURAL & CIVIL ENGN INST,NANJING 210008,PEOPLES R CHINA


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