Analysis of composite beams with partial shear interaction using available modelling techniques: A comparative study

This paper presents a modelling technique based on the direct stiffness method (DSM) to describe the behaviour in time of composite beams with partial shear interaction accounting for creep and shrinkage of the slab. The time‐dependent behaviour of the concrete is modelled using algebraic representations, such as the age‐adjusted effective modulus method and the mean stress method, while the steel joist, the reinforcement and the shear connection are assumed to behave in a linear‐elastic manner. Only one discretization (i.e. in the time domain) is required by the proposed stiffness formulations to perform a time analysis, while two discretizations (i.e. one in the time domain and the other in the spatial domain along the beam axis) are required by other modelling techniques available in the literature. The ability of the derived elements to overcome curvature locking problems observed to occur in some conventional displacement formulations is also highlighted. The proposed DSM approach is then validated against analytical solutions derived by the authors for simple structural systems. The applicability of this method for the time analysis of continuous composite beams is also illustrated. Copyright © 2008 John Wiley & Sons, Ltd.

A numerical formulation for the nonlinear quasi-viscoelastic (creep and shrinkage) analysis of steel-concrete composite beams that are curved in their plan is developed. The creep behavior of the concrete is considered by using the viscoelastic Maxwell-Weichert model, in which the aging effect of the concrete is taken into account. Geometric nonlinearities and the partial shear interaction that exist at the deck-girder interface in the tangential (or longitudinal) direction and in the radial (or horizontal) direction owing to the flexibility of the shear connectors are considered in the strain-displacement relationship. The modeling based on the developed formulation is validated by comparisons with available results reported in the literature. The effects of initial curvature, partial interaction, and geometric nonlinearity on the time-dependent behavior of curved composite beams are illustrated in selected examples.

Time-dependent analysis of composite beams with continuous shear connection based on a space-exact stiffness matrix

A steel-concrete composite beam element with material nonlinearities and partial shear interaction

Presented in the paper is the formulation of a governing second-order differential equation for the moment distribution along the length of a beam having two interfaces with partial shear interaction where two flange and two web components join to form the box shaped section. For practical applications such a closed-section beam of Fiber Reinforced Polymer (FRP) can be assembled from individual pultruded profiles using mechanical fasteners. This assembly approach can be used to construct deeper section sizes than can be achieved with a single pultrusion, and which can be transported in flat-pack units. In developing the governing equation for flexural response account is made of the finite connection stiffness at the web/flange interfaces by applying conventional elastic beam theory. The differential equation for the partial interaction problem is solved to formulate closed form equations for the flange force and the maximum deflection of a simply supported beam under four-point bending. A numerical parametric study is presented to show changes in beam performance indicators with the degree of shear interaction between the upper and lower bounds of full- and non-interaction. Results from a series of load tests using a three-layered prototype FRP beam are shown to be in good agreement. The theoretical predictions for maximum deflection are however found to be directly linked to the appropriateness of the measured connection stiffness entered into the closed-form equation.

Numerical evaluation for the effective slab width of continuous composite beams

Nonlinear flexural analysis of composite beam with Inverted-T steel girder and UHPC slab considering partial interaction

Nonlinear finite difference analysis of composite beams with partial interaction

The composite slim beam has become popular throughout Europe in recent years and has also been used on some projects in China. With its steel section encased in a concrete slab, the steel-concrete composite slim beam can provide the floor construction with minimum depth and high fire resistance. However, the design method of the T-shape steel-concrete composite beam is no longer applicable to the composite slim beam with deep deck for its special construction, of which the present design models are not available but mainly depend on experiences. The elevation of the flexural stiffness and bending capacity of composite slim beams with deep deck is rather complicated, because the influences of many factors should be taken into account, such as the variable section dimensions, development of cracks and non-linear characteristics of concrete, etc. In this paper, experimental investigations have been conducted into the flexural behavior of two specimens of simply supported composite slim beam with deep deck. The emphases were laid on the bonding force on the interface between steel beam and concrete, the stress distribution of beam section, the flexural stiffness and bending capacity of the composite beams. Based on the experimental results, the reduction factor of equivalent stress distribution in concrete flange is suggested, and the calculation method of flexural stiffness and bending capacity of simply supported slim beams are proposed.

Derivation of the exact stiffness matrix for a two-layer Timoshenko beam element with partial interaction

A comprehensive experimental programme was designed and executed with the aim of investigating the out-of-plane bending behaviour and capacity of cold-formed steel (CFS) stud walls sheathed with wood-based boards. The influence of key design variables, including the screw spacing, the board material and thickness, the stud and track thicknesses, the board configuration (single-sheathed, double-sheathed and unsheathed) and the presence/absence of longitudinal seams, noggins and track sections, was investigated and quantified. A total of 15 stud walls sheathed with either Oriented Strand Board (OSB) or plywood were tested under four-point bending. Ancillary material tests, and push-out and pull-out connector tests were also performed. The results revealed a surprising richness in failure modes, given the initial geometric simplicity of the system. Simultaneous crushing of the OSB and distortional buckling failure of the studs, with either full or partial shear interaction, was a commonly observed failure mode. However, rotational and lateral–distortional deformations of the studs, often accompanied by longitudinal cracking of the boards, were also observed as a cause of failure.

This paper presents an experimental investigation of the shear connection between outer layers of lightweight precast concrete sandwich panels (PCSP) made of high-performance concrete (HPC). The shear-transfer mechanism is based on reinforcing ribs composed of rigid polymer-based thermal insulation combined with carbon-fibre-reinforced polymer (CFRP) shear reinforcement. A total of seven full-scale sandwich panels were tested in four-point bending. This study compares three types of rigid thermal insulation used in the shear ribs—Purenit, Compacfoam CF400, and Foamglass F—and investigates the influence of the amount of CFRP shear reinforcement on the structural behavior of the panels. Additional specimens were used to evaluate the effect of reinforcing ribs and of polymer-based thermal insulation placed between the ribs. The experimental results show that panels with shear ribs made of Purenit and Compacfoam CF400 achieved significantly higher load-bearing capacities compared to Foamglass F, which proved unsuitable due to its brittle behavior. Increasing the amount of CFRP shear reinforcement increased the load-bearing capacity but had a limited effect on panel stiffness. The experimentally determined composite interaction coefficient ranged around α ≈ 0.03, indicating partial shear interaction between the outer concrete layers. A simplified strut-and-tie model was applied to predict the load-bearing capacity and showed conservative agreement with experimental results. The findings demonstrate that polymer-based materials, particularly CFRP reinforcement combined with rigid polymer insulation, enable efficient shear transfer without thermal bridging, making them suitable for lightweight and thermally efficient precast concrete sandwich panels.

IntroductionIn recent years, SMPMSM is quietly famous compared with other conventional motors in industrial applications due to higher efficiency, higher reliability, low cost, and smooth torque [1]–[3]. In general, several objective optimizations need to be consider, which required an optimization technique for an electrical motor. This paper deals with an optimal design of a surface-mounted permanent magnet synchronous machine (SMPMSM) with an exact analytical subdomain model by using a genetic algorithm method. To analyze the characteristic of permanent magnet (PM) motors, the classical optimization method, such as the finite element method (FEM), is intensively used. However, FEM has several time problems that require a longer computational time to evaluate the performance of PM motors. This problem can be overcome by using a genetic algorithm (GA) method combined with a subdomain model (SD), which developed an improved performance of SMPMSM, for instance, total harmonic distortion (THDv) and phase back-EMF. In this design, a three-phase 12-slot/8-pole PM motor is established with an exact SD model with radial magnetization patterns. Then, the GA ensemble with SD model to search the optimality of SMPMSM machine design. In the final analysis, the optimal new design of SMPMSM demonstrated by comparing with the initial design that is investigated by FEM. The result of induced back-EMF, and magnetic flux density of optimal design is compared with the initial design to show the advantages of GA optimization method.Analytical Model, Genetic Algorithm and Parameter of optimizationThe purpose of this analysis is to investigate the optimization design of a three-phase 12-slot/8-pole SMPMSM with a radial magnetization pattern. This optimization problem has been solved by obtains the minimum THDv as a fitness function. In order to process the optimization design of SMPMSM, several parameters need to be optimized i.e magnet pole-pitch, αp and slot-opening angle, boa. The roulette method is used to select the objective function of optimization with 50 maximum generations per iteration. The cross and mutation probability need to be set which requires linear and uniform recombination which is 0.89 and 0.025 respectively. The parameters of 12-slot/8-pole SMPM motor as follows: radius of the rotor, Rr = 23mm, the radius of PM surface Rm = 26mm, the inner radius of the stator Rsb = 42.5mm, axial length, la = 50mm, air-gap length, lg = 1mm, remanence of the magnet, Br, 1.12T, relative coil permeability, µr = 1.05 with the number of pole pairs, Np is 8 and number of stator slots, Ns is 12.The result, Discussion and ConclusionThe phase back electromotive force has a significant relationship with flux-linkage because phase back electromotive force is derived from the rate of change of flux-linkage. In Fig. 1. show the waveform of phase back electromotive force against rotor position of initial and optimal design in radial magnetization patterns. The initial design of phase back electromotive force waveform shows more trapezoidal compare with the optimal design which has a sinusoidal waveform. The comparison of total harmonic distortion between the initial and optimal design of SMPMSM are demonstrated in Fig. 2 below. The result from Fig.2. shows the highest total harmonic distortion of 12-slot/8-pole motor is an initial design which is 11.34% compared with the optimal design where 1.3%. The magnitude of harmonic in phase back electromotive force |En| of initial design shows 22.24 V compare to optimal design which is 17.4 V. This shows a good agreement that the optimal motor design gives lowest total harmonic distortion compare with the initial design. The optimizes of SMPMSM motor with the following parameters are given in Table 1. **

In a steel-concrete composite beam (hereafter referred to as a composite beam), partial interaction between the concrete slab and the steel beam results in an appreciable increase in the beam deflections relative to full interaction behavior. Moreover, the distribution type of the shear connectors has a great impact on the degree of the composite action between the two components of the beam. To reveal the effect of shear connector layout in the performance of composite beams, on the basis of a developed one-dimensional composite beam element validated by the closed-form precision solutions and experimental results, this paper optimizes the layout of shear connectors in composite beams with partial interaction by adopting a stepwise uniform distribution of shear connectors to approximate the triangular distribution of the shear connector density without increasing the total number of shear connectors. Based on a comparison of all the different types of stepped rectangles distribution, this paper finally suggests the 3-stepped rectangles distribution of shear connectors as a reasonable and applicable optimal method.

Modeling composite beams with partial interaction