Improving the shear capacities of lipped channel beams with web openings using plate stiffeners

Cold-formed steel lipped channel beams (LCB) are used extensively in residential, industrial and commercial buildings as load bearing structural elements. Their shear capacities are considerably reduced when web openings are included for the purpose of locating building services. Past research has shown that the shear capacities of LCBs were reduced by up to 70% due to the inclusion of these web openings. Hence there is a need to improve the shear capacities of LCBs with web openings. A cost effective way of eliminating the detrimental effects of large web openings is to attach suitable stiffeners around the web openings and restore the original shear strength and stiffness of LCBs. Hence detailed experimental studies were undertaken to investigate the behaviour and strength of LCBs with stiffened web openings subject to shear, and combined bending and shear actions. Both plate and stud stiffeners with varying sizes and thicknesses were attached to the web elements of LCBs using different screw-fastening arrangements. Simply supported test specimens of LCBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. Numerical studies were also undertaken to investigate the strength of LCBs with stiffened web openings. Finite element models of LCBs with stiffened web openings under shear, combined bending and shear actions were developed to simulate the behaviour of tested LCBs. The developed models were then validated by comparing their results with experimental results and used in further studies. Both experimental and finite element analysis results showed that the stiffening arrangements recommended by past research and available design guidelines are not adequate to restore the original shear strengths of LCBs. Therefore new stiffener arrangements were proposed based on screw fastened plate stiffeners. This paper presents the details of this research study and the results.

Can we safely deform a plate to fit every bone? Population-based fit assessment and finite element deformation of a distal tibial plate

Anatomically precontoured plates are commonly used to treat periarticular fractures. A well-fitting plate can be used as a tool for anatomical reduction of the fractured bone. Recent studies highlighted that some plates fit poorly for many patients due to considerable shape variations between bones of the same anatomical site. While it is impossible to design one shape that fits all, it is also burdensome for the manufacturers and hospitals to produce, store and manage multiple plate shapes without the certainty of utilization by a patient population. In this study, we investigated the number of shapes required for maximum fit within a given dataset, and if they could be obtained by manually deforming the original plate. A distal medial tibial plate was automatically positioned on 45 individual tibiae, and the optimal deformation was determined iteratively using finite element analysis simulation. Within the studied dataset, we found that: (i) 89% fit could be achieved with four shapes, (ii) 100% fit was impossible through mechanical deformation, and (iii) the deformations required to obtain the four plate shapes were safe for the stainless steel plate for further clinical use. The proposed framework is easily transferable to other orthopaedic plates.

Fracture analysis of stiffened panels under combined tensile, bending, and shear loads

The objective is to present the formulation of numerically integrated modified virtual crack closure integral technique for concentrically and eccentrically stiffened panels for computation of strain-energy release rate and stress intensity factor based on linear elastic fracture mechanics principles. Fracture analysis of cracked stiffened panels under combined tensile, bending, and shear loads has been conducted by employing the stiffened plate/shell finite element model, MQL9S2. This model can be used to analyze plates with arbitrarily located concentric/eccentric stiffeners, without increasing the total number of degrees of freedom, of the plate element. Parametric studies on fracture analysis of stiffened plates under combined tensile and moment loads have been conducted. Based on the results of parametric,studies, polynomial curve fitting has been carried out to get best-fit equations corresponding to each of the stiffener positions. These equations can be used for computation of stress intensity factor for cracked stiffened plates subjected to tensile and moment loads for a given plate size, stiffener configuration, and stiffener position without conducting finite element analysis.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

Lamination-dependent shear deformation models for bending of angle-ply laminated plates

Lamination-dependent shear corrective terms in the analysis of bending of laminated plates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses by using CLPT inplane stresses in the two in-plane equilibrium equations of elasticity in each ply. In the development of a general model for angle-ply laminated plates, special cases like cylindrical bending of laminates in either direction, symmetric laminates, cross-ply laminates, antisymmetric angle-ply laminates, homogeneous plates are taken into consideration. Adding these corrective terms to the assumed displacements in (i) Classical Laminate Plate Theory (CLPT) and (ii) Classical Laminate Shear Deformation Theory (CLSDT), two new refined lamination-dependent shear deformation models are developed. Closed form solutions from these models are obtained for antisymmetric angle-ply laminates under sinusoidal load for a type of simply supported boundary conditions. Results obtained from the present models and also from Ren's model (1987) are compared with each other.

Lamination-dependent shear deformation models for cylindrical bending of angle-ply laminates

Lamination-dependent shear corrective terms in the analysis of flexure of laminates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses and using them in the two in-plane equilibrium equations of elasticity in each ply. Adding these corrective terms to (i) Classical Laminate Plate Theory (CLPT) displacements and (ii) Classical Laminate Shear Deformation Theory (CLSDT) displacements, four new refined lamination-dependent shear deformation models for angle-ply laminates are developed. Performance of these models is evaluated by comparing the results from these models with those from exact elasticity solutions for antisymmetric 2-ply laminates and for 4-ply [15/-15](s) laminates. In general, the model with shear corrective terms based on CLPT and added to CLSDT displacements is sufficient and predicts good estimates, both qualitatively and quantitatively, for all displacements and stresses.

A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

Dynamics of a flexible splitter plate in the wake of a circular cylinder

Rigid splitter plates in the wake of bluff bodies are known to suppress the primary vortex shedding. In the present work, we experimentally study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate is free to continuously deform along its length due to the fluid forces acting on it; the flexural rigidity (EI) of the plate being an important parameter. Direct visualizations of the splitter plate motions, for very low values of flexural rigidity (EI), indicate periodic traveling wave type deformations of the splitter plate with maximum tip amplitudes of the order of I cylinder diameter. As the Reynolds number based on cylinder diameter is varied, two regimes of periodic splitter plate motions are found that are referred to as mode I and mode II, with a regime of aperiodic motions between them. The frequency of plate motions in both periodic modes is found to be close to the plane cylinder Strouhal number of about 0.2, while the average frequencies in the non-periodic regime are substantially lower. The measured normalized phase speed of the traveling wave for both periodic modes is also close to the convection speed of vortices in the plane cylinder wake. As the flexural rigidity of the plate (EI) is increased, the response of the plate was found to shift to the right when plotted with flow speed or Re. To better capture the effect of varying EI, we define and use a non-dimensional bending stiffness, K*, similar to the ones used in the flag flutter problem, K*=EI/(0.5 rho(UL3)-L-2), where U is the free-stream velocity and L is the splitter plate length. Amplitude data for different EI cases when plotted against this parameter appear to collapse on to a single curve for a given splitter plate length. Measurements of the splitter plate motions for varying splitter plate lengths indicate that plates that are substantially larger than the formation length of the plane cylinder wake have similar responses, while shorter plates show significant differences.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Composite laminates are prone to delamination. Implementation of delamination in the Carrera Unified Formulation frame work using nine noded quadrilateral MITC9 element is discussed in this article. MITC9 element is devoid of shear locking and membrane locking. Delaminated as well as healthy structure is analyzed for free mode vibration. The results from the present work are compared with the available experimental or/and research article or/and the three dimensional finite element simulations. The effect of different kinds and different percentages of area of delamination on the first three natural frequencies of the structure is discussed. The presence of open-mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of places between the second bending mode, with that of the first torsional mode frequency is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layerwise theories as compared to equivalent single layer theories for very large delaminations is stated. The effect of different kinds of delamination and their effect on the second bending and first torsional mode shape is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory

In the present research, the discrete dislocation theory is used to analyze the size effect phenomena for the MEMS devices undergoing micro-bending load. A consistent result with the experimental one in literature is obtained. In order to check the effectiveness to use the discrete dislocation theory in predicting the size effect, both the basic version theory and the updated one are adopted simultaneously. The normalized stress-strain relations of the material are obtained for different plate thickness or for different obstacle density. The prediction results are compared with experimental results.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Self-instability and bending behaviors of nano plates

This paper aims at investigating the size-dependent self-buckling and bending behaviors of nano plates through incorporating surface elasticity into the elasticity with residual stress fields. In the absence of external loading, positive surface tension induces a compressive residual stress field in the bulk of the nano plate and there may be self-equilibrium states corresponding to the plate self-buckling. The self-instability of nano plates is investigated and the critical self-instability size of simply supported rectangular nano plates is determined. In addition, the residual stress field in the bulk of the nano plate is usually neglected in the existing literatures, where the elastic response of the bulk is often described by the classical Hooke’s law. The present paper considered the effect of the residual stress in the bulk induced by surface tension and adopted the elasticity with residual stress fields to study the bending behaviors of nano plates without buckling. The present results show that the surface effects only modify the coefficients in corresponding equations of the classical Kirchhoff plate theory.

Improved Equivalent Frame Analysis Method for Flat Plate Structures in Vicinity of Edge Columns

This paper proposes a modification to the ACI 318-02 equivalent frame method of analysis of reinforced concrete flat plate exterior panels. Two existing code methods were examined: ACI 318 and BS 8110. The derivation of the torsional stiffness of the edge strip as proposed by ACI 318 is examined and a more accurate estimate of this value is proposed, based on both theoretical analysis and experimental results. A series of 1/3-scale models of flat plate exterior panels have been tested. Unique experimental results were obtained by measuring strains in reinforcing bars at approximately 200 selected locations in the plate panel throughout the entire loading history. The measured strains were used to calculate curvature and, hence, bending moments; these were used along with moments in the columns to assess the accuracy of the equivalent frame methods. The proposed method leads to a more accurate prediction of the moments in the plate at the column front face, at the panel midspan, and in the edge column. Registered Subscribers: View the full article. This document is available as a free download to qualified members. An electronic (PDF) version is available for purchase and download. Click on the Order Now button to continue with the download.

Repair Welding Effects on the Bending Fatigue Strength of AISI 4130 Aeronautical Steel used in a Critical to the Flight-Safety Structure

The aim of this study was to analyze the effect of successive TIG (tungsten inert gas) welding repairs on the reverse bending fatigue strength of AISI 4130 steel, which is widely used in components critical to the flight-safety. In order to simulate the abrupt maneuvers, wind bursts, motor vibration and helixes efforts, which generate cyclic bending loadings at the welded joints of a specific aircraft component called motor cradle, experimental reverse bending fatigue tests were carried out on specimens made from hot-rolled steel plate, 1.10 mm (0.043 in) thick, by mean of a SCHENK PWS equipment, with load ratio R = -1, under constant amplitude, at 30 Hz frequency and room temperature. It was observed that the bending fatigue strength decreases after the TIG (Tungsten Inert Gas) welding process application on AISI 4130 steel, with subsequent decrease due to re-welding sequence as well. Microstructural analyses and microhardness measurements on the base material, heat-affected zone (HAZ) and weld metal, as well as the effects of the weld bead geometry on the obtained results, have complemented this study.