Internal Stress Resultants Research Articles

Structural performance of steel plates

In general, plates are classified as thick plates when the minimum dimension to thickness ratio (b/h) is less than 10, thin plates when the b/h ratio ranges from 10 to about 100, provided that the plate maximum deflection to thickness ratio (w/h) is less than 0.2, and membranes when the b/h ratio approaches 100 and w/h ≥ 0.2. Thick plates develop internal stress resultants governed by three-dimensional elasticity similar to that of a solid body. Thin plates behave as plane stress members governed by two-dimensional elasticity. Membranes can only develop internal tensile stress within the plate’s neutral plane. Few studies have adopted b/h ratios between 90 and 110 to investigate the feasibility of the utilization of such plates in their various available forms. The current study with the b/h ratio of 100 aims to fill the gap. Steel Plates are available in different forms such as intact plates, stiffened, perforated, and stiffened perforated plates. They are used in buildings, bridges, ships, as well as aerospace structures. In this study, the investigated steel plate has a square shape and is subjected to uniaxial loading. The plate edges are simply supported. The plate is 200 mm wide and 2 mm thick. In this case, the critical buckling strength is, in general, less than the plate maximum strength. With further loading, the plate would experience an undesirable sudden mode of failure owing to buckling instability. This study aims at investigating the performance of the different forms of square steel plates, such as intact, stiffened, perforated, and perforated stiffened, when the minimum dimension to thickness ratio is 100. A pushover finite element linear elastic buckling analysis as well as a nonlinear large deflection buckling analysis have been carried out. The study indicated that the increase in the plate maximum strength in single, double, and triple stiffener plates was 75.6%, 174%, and 196%, respectively, compared to that of the intact plate. Based on the obtained results, it is concluded that the utilization of plates having the b/h ratio of 100 is feasible provided that the appropriate plate form is adopted.

A three‐phase laminated anisotropic elliptical inhomogeneity with internal uniform stress resultants

AbstractWe use the Stroh octet formalism for the coupled stretching and bending deformations of Kirchhoff laminated anisotropic thin plates together with the complex variable formulations of the decoupled stretching and bending deformations of Kirchhoff homogeneous isotropic thin plates to study the internal stress resultants inside a laminated anisotropic elliptical inhomogeneity bonded to a surrounding infinite laminated anisotropic matrix through a confocal interphase layer composed of a homogeneous isotropic plate when the matrix is subjected to uniform remote membrane stress resultants and bending moments. We prove that for given geometric and material parameters of the composite, the internal stress resultants inside the elliptical inhomogeneity are uniform when four specific conditions on the remote loading are satisfied. Furthermore, the internal uniform elastic field is determined in real‐form in terms of the two 8 × 8 fundamental elastic plate matrices for both the inhomogeneity and the matrix and the three 4 × 4 real matrices S, H, and L for the matrix.

Elzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions

In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified to a fourth order ordinary differential equation (ODE). The general solution for the Airy stress potential function in the Elzaki transform space was obtained by solving the ODE. By inversion, the general solution for the Airy stress potential function was obtained in the physical domain space variables in terms of four unknown integration constants. Normal stresses and shear stress fields were also determined for the general case of 2D elasticity problems. The Flamant problem was solved as a particular illustration of 2D elasticity problems. The stress boundary conditions and the requirement of equilibrium of the internal stress resultants and the external forces were used simultaneously to determine the four constants of integration. The Airy stress potential function and the normal and shear stress fields were thus completely determined. The principle of superposition was used to obtain the elasticity solutions for the stress fields in the elastic half plane due to strip load of infinite extent, and solutions for horizontal stresses on smooth rigid retaining walls due to strip loads and parallel line load of infinite extent acting on the elastic half plane.

Structural modelling of textile-reinforced concrete elements under uniaxial tensile loading

The paper presents a non-linear structural model for evaluating the macro-structural response as well as the distribution of the internal stress resultants of textile reinforced concrete composites under uniaxial static loading. The equilibrium equations and the appropriate boundary conditions are derived on the basis of the variational principle of the minimum potential energy approach. Various aspects related to the unique micro-structural behavior associated to the bonding mechanism of the yarns and the concrete matrix, as well as the nonlinearity of both materials, are taken into consideration and implemented in the variational principle. The obtained set of nonlinear equilibrium equations is formulated according to the mixed formulation which yields a set of first order nonlinear ordinary differential equations. The solution procedure is conducted by the mixed-half-station interlacing-grid finite-difference scheme and by Newton–Raphson method. Results provided by the proposed model are compared to experimental tests from the literature and demonstrate its generality, accuracy, simplicity, and its easy implementation in various experimental setups. It is further demonstrated that the presented structural model can successfully capture the macro-structural response and gives an insight into the micro-structural mechanism involved in the load carrying capacity of the TRC composite element.

Research on Long-distance Non-contact Surface Defect and Crack Detection System in Civil Engineering Structures

Cracks are the result of excessive internal stress released by concrete materials. Cracks reduce the peak stress of the section. Therefore, the deformation energy stored in the structure is lower than a certain limit. Reducing the internal deformation energy by cracking is the inherent characteristic of concrete materials. Many concrete structures will have different degrees and forms of cracks, which is a quite common phenomenon. Cracks have become a common disease of concrete structures, which has long been a technical problem for construction engineers. Traditional crack detection methods of concrete bridges can not meet the needs of modern bridge detection. Based on this, this paper presents a long-distance non-contact surface defect and crack detection system, which is an economical and effective new method for bridge disease detection. This paper analyses the working principle and workflow of the detection system.

Experimental study of moment sharing in multi-joist timber-concrete composite floors from zero load up to failure

The critical T-sections of multi-joist timber-concrete composite (TCC) floors must be designed at ultimate for support shear force and midspan moment, both of which are influenced by transverse sharing, but to different extents. Prior experimental work has investigated only support reaction sharing and only up to serviceability loads. The present experimental study builds on that status quo by quantifying also moment sharing, via strain gauge layouts at quarter-span and midspan, along with reaction sharing via load cells at the supports of a multi-joist TCC specimen, over the entire load range up to failure. Use of steel mesh connectors bonded into hardwood laminated veneer lumber joists, and near geometric resemblance to a real building TCC floor recently built in London, were novel features of the specimen. The results show that midspan moment and reaction sharing both vary nonlinearly with load, but in distinctly different ways from each other (with up to almost 20% difference observed between them), in the progression between the uncracked, cracked and connection ductility regimes. In this approach reliable assessment of moment sharing depends on the quality of the recorded strains. Accordingly, the strain data were shown to be of high quality by converting these data to internal stress resultants that were then found to satisfy longitudinal equilibrium. It is concluded that this strain gauge layout is useful for future work aimed at building a database of transverse sharing of moments in TCCs.

Coated inhomogeneities of arbitrary shape with internal uniform hydrostatic stress resultants in isotropic laminated plates

We study the internal stress resultants inside an elastic inhomogeneity of arbitrary shape embedded in an infinite Kirchhoff plate (matrix) via an intermediate coating. Each material phase is considered an isotropic laminated plate and the surrounding matrix is subjected to uniform remote membrane stress resultants and bending moments. We find that internal uniform hydrostatic stress resultants within the inhomogeneity can be achieved when (i) the mapping function characterizing the shape of the inhomogeneity is identified and specialized accordingly; (ii) the relative coating thickness should satisfy a higher-order algebraic equation; (iii) several restrictions on the remote loading should be satisfied for given material and geometric parameters of the composite plate. When all these conditions are met, the hoop membrane stress resultant and hoop bending moment on the coating side are uniform along the entire inhomogeneity–coating interface.

State-of-Charge Dependence of Mechanical Response of Lithium-Ion Batteries: A Result of Internal Stress

Effect of state-of-charge on the mechanical response of lithium-ion batteries subjected to mechanical abuse loading are studied. Indentation tests are performed on a cylindrical cell and a pouch cell at different states-of-charge. The test results evidence that the mechanical behavior of the cylindrical cell is significantly state-of-charge dependent, while for the pouch cell it is almost state-of-charge independent. To clarify the cause of such a difference in state-of-charge dependence, two control tests are designed and executed. Based on the control test results, we conclude that the internal stress to resist the charging-induced volume expansion of jellyroll is the major reason for state-of-charge dependence of the mechanical behavior. We also conclude that the difference in state-of-charge dependence between the two types of cells is closely associated with the casing stiffness (stiff metallic casing vs. soft pouch) and the construction method of jellyroll (winding versus stacking), which together create different conditions of resisting the volume expansion and retaining the internal stress. A supplementary test is carried out on the pouch cells under a normal cyclic charging-discharging condition to measure the volume expansion and the reaction force of the unconstrained and constrained pouch cell respectively.

10.13: Bending resistance evaluation of shallow floor beams exposed to fire

ABSTRACTFor the moment, the Eurocode 4 standards give detailed analysis rules merely for the standard or ordinary composite beams where the concrete section rests on the top flange of a steel beam. In contrast to shallow floor beams (abbreviated as SF‐beams), where only the bottom flange is directly exposed to fire, the ordinary composite beams do not have any inborn fire protection. Although the SF‐beams are not excluded from the scope, no special design rules are given for them, and they only appear in one schematic figure in EN 1994‐1‐2. The basic method for evaluating the bending resistance of fire exposed composite beams is based on the employment of rigid‐plastic stress blocks in steel and concrete. However, it is also possible to utilize elasto‐plastic analysis, where the flexural strain distribution and the corresponding stresses are taken into account, and the maximum compressive strain of the concrete could be set to control the straining. The analysis results between the rigid‐plastic and elasto‐plastic sagging bending resistances of fire exposed SF‐ beams are compared and the additional useful information obtained from the latter analysis is illustrated. For any strain distribution that fulfils the equilibrium of internal stress resultants of the composite section, there is a well‐defined bending moment, curvature and bending stiffness. The data following from the elasto‐plastic stress analysis can further be utilized for evaluating nominal deflections that cannot be associated with the rigid‐plastic resistance analysis.

Quenching residual stresses in T-section 7050 aluminum alloy forging

Distribution of quenching residual stresses in T-section 7050 aluminum alloy forging was obtained using a combination method of finite element method (FEM), contour method, layer removal method and X-ray diffraction. The results show that, experimental results and FEM result of internal residual stresses are in good agreement. While surface stresses obtained by layer removal method and contour method are slightly different with X-ray diffraction and FEM results, thus X-ray diffraction measurement of surface stresses must be taken into consideration to fully understand the distribution of quenching stresses in the T-section 7050 aluminum alloy forging. Moreover, surface residual stresses are compressive of about -150MPa, while residual stresses in the core are tensile with a maximum up to 210MPa, which is very harmful for the subsequent machining.DOI: http://dx.doi.org/10.5755/j01.mech.23.3.14259

Incremental-iterative model for time-variant analysis of SFRC subjected to flexural fatigue

Fatigue behaviour of plain (PC) and steel fibre reinforced concrete (SFRC) is of growing interest in concrete engineering since structural reliability often depends on the concrete’s damage state. The current paper deals with its investigation. Starting from a new and universal SN-approach for PC and SFRC based on stress- and material-dependent ductility and a cycle-dependent strain evolution under centric pulsating loads an isotropic and time-dependent material damage parameter is derived. In the framework of the elasto-plastic damage theory, wherein PC and SFRC are idealized homogeneously on macroscopic level, this damage parameter in conjunction with the established envelope concept enables to compute time-dependent stiffness and strength degradations as well as increasing plastic strains. Additionally, an assessment of the total number of cycles to failure of specimens subjected to multi-staged cyclic loading is permitted by a specific damage accumulation procedure. Decisive parameters like fibre type, length, orientation, dosages and bond on the axial static and cyclic material response are covered. To compute numbers of cycles to failure, deflections and stress redistributions of members exposed to flexural fatigue, the findings are integrated into a plastic hinge model. This accounts for localization of damage after cracking in a discontinuity region typical for both, PC and SFRC. Cycle- and crack-width-dependent deflections are obtained for valid states of equilibriums between external loads and internal stress resultants. To assess macroscopic cracking a strain criterion serves. In the numerical simulation, time-increments are performed according to Lemaitre’s jump-in-cycles procedure. For verification test results from literature are recalculated. Theoretical and experimental data are in good accordance on average proving a comparable fatigue behaviour of PC and SFRC in principle. However, fibre’s impact on fatigue life and deformation capacities of concrete is ambivalent, depending on specific material and load characteristics.

Shear buckling of sandwich plates – Incompressible and compressible cores

Abstract Shear buckling behavior of sandwich panels with an incompressible and a compressible core is presented. The mathematical formulation includes various formulations for layered sandwich panel such as: Ordinary Sandwich Panel Theory (OSPT), High-Order Sandwich panel Theory (HSAPT) without in-plane core rigidity and with in-plane rigidity (HSAPT-A) Theory. The various models are based on a variational approach that yields the non-linear field equations and the appropriate boundary conditions. The high-order model that takes into account the in-plane rigidity through the depth of the core, denoted as HSAPT-A, uses the accurate solution of the 3D elasticity problem involved. Linearization is achieved using a perturbation technique which yields equations for the pre-buckling and buckling stages along with the appropriate boundary conditions. A Galerkin solution type is adopted for all models and a closed-form solution through the depth of the core is used for the high-order case where the core rigidity is considered. A numerical study of a simply-supported panel with various layouts and dimensions and subjected to in-plane shear load is conducted. The results include bifurcation loads and mode shapes (3D or contour plots) of the displacements, internal stress resultants and interfacial stresses at face–core interfaces.

Non-linear soil–structure interaction in disconnected piled raft foundations

Disconnected piled raft foundations are characterised by no structural connection between the upper raft and the underlying piles, mostly playing the role of settlement-reducers. The resulting raft–pile gap is usually filled with a granular interlayer, through which the loads from the superstructure are transferred to the piles.In this paper, the complex interaction mechanisms involving the foundational components (raft, piles and soil) are numerically investigated by means of 3D finite elements analyses, accounting for soil non-linearity. The main features of the soil–structure interaction mechanisms under purely vertical external loads are explored over a realistic range of raft–soil gaps for different pile configurations, in which the number of piles – i.e. their spacing – is varied. Special attention is also devoted to the structural response of the piles in terms of axial and bending internal stress resultants. In particular, while disconnection beneficially affects the structural pile response, increasing the raft–pile gap tends to reduce the overall settlement/stiffness efficiencies.The numerical results being presented are in substantial agreement with the outcomes from literature small-scale experiments and suggest a number of relevant theoretical inferences.

Three-phase elliptical inclusions with internal uniform hydrostatic stress resultants in isotropic laminated plates

Within the framework of the Kirchhoff-Love isotropic and laminated plate theory, we study the internal stress resultants of a three-phase elliptical inclusion which is bonded to an infinite matrix through an interphase layer. The interfaces of the three-phase inclusion are two confocal ellipses. Two conditions are found to ensure that the internal stress resultants within the elliptical inclusion are uniform and hydrostatic. For given material and geometric parameters of the composite system, the two conditions can be interpreted as restrictions on the remote uniform membrane stress resultants and bending moments. When these two conditions are met, the hoop membrane stress resultant and hoop bending moment in the interphase layer are found to be uniform along the entire interphase/inclusion interface.

The Mechanism of Moisture Transport in a Gel Cylinder

In drying of gels, the analysis of the process must encompass both heat and mass transfer aspects as well as deformation, usually very strong, of the material in the process. Deformation is almost always assumed to be linearly dependent on moisture content without considering an internal stress or pressure build-up. Since there is a great commercial interest in production of non-deformed dry gels by convective ambient pressure drying, it was interesting to investigate the behavior of such materials in drying. Convective drying would eliminate the expensive supercritical. In this work several types of gels were synthesized and dried convectively in a lab scale. Since drying induces the internal stress formation responsible for shrinkage and cracking, great care was taken to measure deformation and internal pressure development in gel during drying. Cylindrical gel samples 35 mm in diameter were dried convectively in air at 30, 40, and 50 °C. The hydrogels were made of PVP, agar-agar, and silica. Different types of behavior of the gels during drying was observed: almost uniform deformation in the case of PVP, case-hardening for agar-agar gels, and cracking for silica hydrogels. This behavior directly results from different mechanical properties of the investigated gels. It was also observed that the internal pressure changes from initially overpressure to underpressure in the course of drying which is also a result of internal stress build up. The experimental data may be used for validation of mechanical models of drying of non-linear visco-elastic solids.

Transient Side-Load Analysis of Out-of-Round Film-Cooled Nozzle Extensions

Understanding the impact of out-of-round nozzle extension on the nozzle side load during engine transient startup operations has garnered special interest from design engineers of late. The out-of-round nozzle extension could be the result of asymmetric internal stresses, deformation induced by previous tests, and asymmetric loads induced by hardware attached to the nozzle. The objective of this study was to computationally investigate the effect of out-of-round nozzle extension on the nozzle side loads during an engine startup transient. The rocket engine studied encompasses a regeneratively cooled chamber and nozzle, along with a film-cooled nozzle extension. The computational methodology is based on an unstructured-grid pressure-based computational fluid dynamics formulation, and on transient inlet boundary flow properties derived from an engine system simulation. Six three-dimensional cases were performed, with the out of roundness achieved by three different degrees of ovalization, elongated on lateral and axes: one slightly ovalized, one more ovalized, and one significantly ovalized. The results show that the separation line jump was the primary peak side-load physics. Compared with the peak side load of the perfectly round nozzle, the peak side loads increased most for the slightly ovalized nozzle extensions. The peak side loads then reduced moderately from the slightly ovalized nozzle extensions to the more ovalized nozzle extensions. For the significantly ovalized nozzle extensions, the peak side loads dropped substantially from those of the slightly ovalized nozzle extensions, due to increased flow directionality.

Nondestructive damage detection in Euler-Bernoulli beams using nodal curvatures-Part I: Theory and numerical verification

SUMMARY This paper deals with the problem of nondestructively detecting, locating, and quantifying damage in beam-type structures. To achieve this objective, structural responses collected prior and subsequent to damage are related to the changes in physical properties of the structure. The proposed methodology is based on the moment–curvature relations of the Euler–Bernoulli beam theory and the assumption that internal stress resultants are invariant before and after damage. Damage is expressed in terms of local decreases in the flexural stiffness of structural members. These decreases are shown to cause singularities in the curvature profile of the beam. Utilizing fundamental equations of solid mechanics, we relate discontinuities in the flexural stiffness distribution to the pre-damage and post-damage nodal curvatures. The resulting system of linear equations can be solved to obtain specific element damage indices. The performance of the proposed methodology is evaluated using numerically generated experiments. It is shown that the location, the extent, and the severity of damage in beams may be successfully identified with the proposed technique provided that the structure conforms to the deformations dictated by the Euler–Bernoulli beam theory. The practicality of the methodology under field conditions is demonstrated in the accompanying paper Nondestructive damage detection in Euler-Bernoulli beams using nodal curvatures-Part II: Field measurements. Copyright © 2013 John Wiley & Sons, Ltd.

Evaluation of Rate of Deformation for Early-Age Concrete Shrinkage Analysis and Time Zero Determination

Early age cracking is usually the result of internal tensile stresses induced by self-desiccation shrinkage (SDS) rather than external loading. Hence, the prediction of early age cracking risk is strongly linked to autogenous shrinkage development. Both the ultimate magnitude of shrinkage and the time zero (TZ), at which shrinkage starts to develop an internal stress, could be decisive for high-performance concrete (HPC) durability. The moment TZ can be considered as the borderline between autoplastic shrinkage and effective shrinkage. Deformation rate curves might be used as a framework to identify the three main phases of hardening that occur in cement paste as hydration progresses, and the development rate of autogenous shrinkage (AS). The present study proposes starting shrinkage measurement (autogenous or total) from the moment when the rate of deformation reaches its maximum value (the first peak in the curve) and the shrinkage strain rate curve pattern changes sharply, or at the end of plastic-shri...

Static Strain Aging of Microstructural Constituents in Transformation-Induced-Plasticity Steel

A pronounced difference in static strain aging was observed between unstrained and prestrained low-alloy multiphase transformation-induced-plasticity (TRIP) steel. High bake-hardening (BH) values were obtained for prestrained TRIP steel. This aging behavior was shown to be directly related to the multiphase microstructure, by analyzing static strain aging in the ferrite and bainite separately. The ferrite in TRIP steel exhibits very limited strain aging, due to the Cottrell atmosphere formation. The bainite constituent, which contains retained austenite, has a pronounced static strain-aging response in the 2 pct prestrained condition. This is a result of internal stresses generated by the strain-induced martensite and the low-temperature aging of this phase. In the absence of strain-induced martensite, the BH values of TRIP steel are low and are due only to the Cottrell atmosphere formation. The TRIP steel exhibits an intermediate BH response, due to the composite effect of its ferrite and bainite constituents. The influence of the cross-sectional changes and volume changes during tensile tests carried out to determine the BH values is also reviewed.

Elastica of sandwich panels with a transversely flexible core—A high-order theory approach

The elastica behavior of an extensional sandwich panel with a “soft” core when subjected to in-plane compressive loads is presented and it is compared with the response of its extensional equivalent single layer (ESL) with shear deformations model. The field equations along with the appropriate boundary conditions for the sandwich and the ESL panels have been derived through a variational approach following the High-order SAndwich Panel Theory (HSAPT) approach that takes into account the vertical flexibility of the core. The governing equations include the effects of the extension of the mid-surfaces of the face sheets of the sandwich panel or the mid-plane of the ESL model which the classical elastica approach misses. The results of the elastica response of a clamped-simply-supported sandwich panel and its ESL counterpart are presented and compared. They include the response along the panel, deformed shapes and equilibrium curves of in-plane loads versus structural quantities such as displacements and internal stress resultants and stresses. These results reveal that the predicted buckling load of the ESL panel is larger than that of the sandwich panel and that deep in the non-linear range the upper face sheet wrinkles with increasing overall and edge displacements and a release of the load. Hence, the use of an equivalent single layer panel especially when a sandwich panel with a compliant core is considered may lead to unsafe and unreliable predictions when large displacements and large rotations are considered.