Combined Load Cases Research Articles

An algorithm to simulate the nonlinear behavior of RC 1D structural members under monotonic or cyclic combined loading

Interaction of lateral loading, combined with axial force needs to be determined with care in reinforced concrete (RC) one-dimensional structural members (1D SMs) such as beam-columns (BCs) and columns. RC 1D SMs under heavy axial loading are known to fail by brittle mode and small lateral displacements. In this paper, a macro element-based algorithm is proposed to analyze the RC 1D SMs under monotonic or cyclic combined loading. The 1D SMs are discretized into macro-elements (MEs) located between the critical sections and the inflection points. The critical sections are discretized into fixed rectangular finite elements (FRFE). The nonlinear behavior of confined and unconfined concretes and steel elements are considered in the proposed algorithm. The proposed algorithm has been validated by the results of experimental tests carried out on full-scale RC structural members. The evolution of ultimate strain at extreme compression fiber of a rectangular RC section for different orientations of lateral loading shows that the ultimate strain decreases with increasing the axial force. In the examined cases, this ultimate strain ranges from 0.0024 to 0.0038. Therefore, the 0.003 value given by ACI-318 code for ultimate strain, is not conservative and valid for the combined load cases with significant values of axial force (i.e. for the axial forces heavier than 70% of the ultimate axial force).

Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints

This paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufacturing equipment and improve the inherent frequency response of the mechanism. Firstly, a vector-mapping isomorphism between the fully CPM and conventional isomorphic parallel mechanism was constructed with a kinematic differential Jacobian matrix. Then, the mathematical model of topology optimization was put forward considering the compromise programming on the static stiffness and mean vibration-inherent frequency of the mechanism as the design variable and the minimization of compliance as the objective function. A constraint of volume fraction was considered and multi-objective micro displacement mechanism topology optimization based on a prismatic-revolute-revolute (3-PRR) planar nano-positioning continuum structure was performed using the solid isotropic material with penalization (SIMP) technique, which combines the criteria of the optimization algorithm and the vector isomorphic mapping method. Multi-objective topology optimization of the continuum structure micro displacement mechanism was investigated and presented by optimizations with different initial rejection rates. The simulation results show that the stiffness and vibration suppression performance of the continuum structure were improved, whereas the positioning of differential kinematics characteristics of the 3-PRR micro displacement planar fully CPM and isomorphic prototype mechanism retain the same. The modal analysis also provides a rational configuration for the micro displacement mechanism dimensional design and its optimal modal parameters. The crossover oscillation in frequency response of the continuum structure was reduced and quickly converged in the optimization iterations. The performance of the optimized mechanism was verified by the experiments on a planar fully compliant micro displacement continuum structure based on Lead Zirconate Titanate (PZT) actuator.

Experimental & numerical study of the Tensile/Compression-Shear Arcan test under dynamic loading

The characterization of the adhesive of bonded assemblies under combined and dynamic loading cases appears to be crucial for the development of the future structures dedicated to the transport industry. To date, most of the tests on adhesive joints are dedicated to comparative studies and only a few ones to characterization. Among these, the stress concentration-free bonded Arcan Tensile/Compression-Shear test specimen (Arcan TCS) developed by Créac’hcadec et al. allows to characterize the adhesive of bonded joints under combined quasi-static loading cases while minimizing the edge effects. This paper deals with an extension of the use of this specimen under dynamic loadings.In a first part, an experimental study of the Arcan TCS device under drop weight conditions is made. The mechanical behaviour of the adhesive appears to be non-linear and clearly dependent of the strain rate. Also, stress-strain curves highlight a significant influence of tests conditions. In particular, the way the kinetic energy is transmitted by the falling mass to the testing device plays a significant role on the vibrational behaviour and the loading rate of the specimen.In a second part, a dedicated finite element model is built under the plane stress and elastic assumptions. Results extracted from this numerical study are in agreement with several experimental observations. Moreover, they allow a better understanding of the loading seen by the adhesive.

An Overall Interaction Concept for an alternative approach to steel members design

The present paper focuses on a new, alternative design philosophy: the Overall Interaction Concept (O.I.C.). This concept, based on the well-established resistance-instability interaction and the definition of a generalised relative slenderness, was thought and built to i) improve actual design practice, ii) increase accuracy, iii) advance simplicity and consistency, and iv) provide a sound framework for computer-assisted resistance predictions.This paper first details the bases and features of the O.I.C. approach, and provides mechanical interpretations of its application steps. Comprehensive sets of results at the cross-sectional level are then presented, for both H-shaped and hollow sections. Ayrton-Perry-based χ-λ design relationships for hollow structural shapes are proposed and shown to lead to more accurate, consistent and safe resistances when compared to Eurocode 3 rules, in addition to being significantly simpler in application. As for the behaviour and response of members, numerous F.E. results are reported, demonstrating the potential of a χ-λ approach to successfully apply to members under combined load cases. Also, the challenging case of coupled instabilities is investigated, and the O.I.C. approach is showed to be very efficient and appropriate. Further developments towards the derivation of full O.I.C. procedures to steel members are currently under way.

Application of the idealized structural unit method for ultimate strength analyses of stiffened plate structures

ABSTRACTTo assess the safety of ship structures, the determination of the ultimate hull girder strength is of essential importance. The idealized structural unit method (ISUM) is a simplified method to perform progressive collapse analyses of large structural systems with less computational efforts compared to non-linear finite element analyses (FEA). In this paper, the basic concept and the applicability of ISUM are demonstrated for a stiffened plate panel under lateral pressure and inplane thrust. Ship structures are subjected to global bending moments and lateral pressure loads. To simulate the collapse behaviour of such complex structural systems, a box-girder specimen in bending is investigated. Appropriate numerical models are presented and the corresponding ultimate strength values are validated against experimental results. To simulate combined load cases with lateral pressure loads acting on the bottom of the box-girder specimen, the corresponding ultimate strength values determined with ISUM are compared with non-linear FEA results.

Ant colony optimization for dynamic stability of laminated composite plates

This paper presents the dynamic stability study of laminated composite plates with different force combinations and aspect ratios. Optimum non-diverging stacking is obtained for certain loading combination and aspect ratio. In addition, the stability force is maximized for a definite operating frequency. A dynamic version of the principle of virtual work for laminated composites is used to obtain force-frequency relation. Since dynamic stiffness governs the divergence or flutter, an efficient optimization method is necessary for the response functional and the relevant constraints. In this way, a model based on the ant colony optimization (ACO) algorithm is proposed to search for the proper stacking. The ACO algorithm is used since it treats with large number of dynamic stability parameters. Governing equations are formulated using classic laminate theory (CLT) and von-Karman plate technique. Load-frequency relations are explicitly obtained for fundamental and secondary flutter modes of simply supported composite plate with arbitrary aspect ratio, stacking and boundary load, which are used in optimization process. Obtained results are compared with the finite element method results for validity and accuracy convince. Results revealed that the optimum stacking with stable dynamic response and maximum critical load is in angle-ply mode with almost near-unidirectional fiber orientations for fundamental flutter mode. In addition, short plates behave better than long plates in combined axial-shear load case regarding stable oscillation. The interaction of uniaxial and shear forces intensifies the instability in long plates than short ones which needs low-angle layup orientations to provide required dynamic stiffness. However, a combination of angle-ply and cross-ply stacking with a near-square aspect ratio is appropriate for the composite plate regarding secondary flutter mode.

Experimental study of a new multi-column tension leg-type floating wind turbine concept

Offshore deep-water region is rich in high-quality wind energy. Currently offshore floating wind turbine is the most potential equipment to exploit it. The relevant scaling laws need to be considered during the offshore floating wind turbine model test were analysed and a proper scaling methodology was established according to the loading conditions. The wave tank model test was conducted for the proposed new multi-column tension leg-type floating wind turbine concept in SKLOE’s wave basin with the geometric scaling factor of 50 according to the main dimensions and environmental conditions. By using a modified blade design based on the same wind turbine thrust coefficient, the aerodynamic Reynolds number scaling effect was dissimilated during the model test. Still water tests, white noise wave tests and combined wind wave and current tests were carried out. During the combined wind, wave and current tests, both the turbine operating (DLC01-05) and parked conditions (DLC06, DLC07) were investigated. To identify the dominate load of the dynamic responses, each design load case was further separated into four different sub-load cases: wind only case, wave only case, current only case and combined load case. Global response variables including platform motion, tendon tension, rotor thrust, and nacelle accelerations were examined. In summary, the proposed WindStar TLP system showed relatively small dynamic motion responses to environmental loads due to its natural frequencies are well kept away from the dominant wave periods and the tendons still holds a sufficient safety factor, and the minimum tendon tensions remain positive under all the selected DLCs. The model testing results could serve as a reference for the further research.

Strength and Design of Pin-Ended Circular Arches with Sinusoidal Corrugated Web under Combined In-Plane Loads

AbstractThis paper presents numerical and experimental investigations of the in-plane strength and design of pin-ended circular arches having a sinusoidal corrugated web under combined in-plane loads. Finite-element models are developed that account for the effects of the corrugated web, initial geometric global and local imperfections of the arch and its web and flanges, residual stresses, the included angle and curvature of the arch, and different combined load cases. These are validated by test results and used together with the experiments to investigate the failure modes and strengths of such arches. It is found that an I-section arch with a corrugated web may fail in a global mode or in a web shear buckling mode. There are two types of global failure modes for arches under combined loads. In most cases, corrugated arches may fail in an elastoplastic buckling mode. However, when wind load plays an important role in the combined loads, corrugated arches may fail in a plastic yielding mode. An interact...

Optimization design of tuned mass damper for vibration suppression of a barge-type offshore floating wind turbine

An efficient method for restraining the large vibration displacements and loads of offshore floating wind turbines under harsh marine environment is proposed by putting tuned mass dampers in the cabin. A dynamics model for a barge-type offshore floating wind turbine with a fore–aft tuned mass damper is established based on Lagrange’s equations; the nonlinear least squares Levenberg–Marquardt algorithm is employed to identify the parameters of the wind turbine; different parameter optimization methods are adopted to optimize tuned mass damper parameters by considering the standard deviation of the tower top longitudinal displacement as the objective function. Aiming at five typical combined wind and wave load cases under normal running state of the wind turbine, the dynamic responses of the wind turbine with/without tuned mass damper are simulated and the suppression effect of the tuned mass damper is investigated over the wide range of load cases. The results show that when the wind turbine vibrates in the state of damped free vibration, the standard deviation of the tower top longitudinal displacement is decreased approximately 60% in 100 s by the optimized tuned mass damper with the optimum tuned mass damper mass ratio 1.8%. The standard deviation suppression rates of the longitudinal displacements and loads in the tower and blades increase with the tuned mass damper mass ratio when the wind turbine vibrates under the combined wind and wave load cases. When the mass ratio changes from 0.5% to 2%, the maximum suppression rates vary from 20% to 50% correspondingly, which effectively reduce vibration responses of the offshore floating wind turbine. The results of this article preliminarily verify the feasibilities of using a tuned mass damper for restraining vibration of the barge-type offshore floating wind turbine.

Coupled dynamic response analysis of a multi-column tension-leg-type floating wind turbine

This paper presents a coupled dynamic response analysis of a multi-column tension-leg-type floating wind turbine (WindStar TLP system) under normal operation and parked conditions. Wind-only load cases, wave-only load cases and combined wind and wave load cases were analyzed separately for the WindStar TLP system to identify the dominant excitation loads. Comparisons between an NREL offshore 5-MW baseline wind turbine installed on land and the WindStar TLP system were performed. Statistics of selected response variables in specified design load cases (DLCs) were obtained and analyzed. It is found that the proposed WindStar TLP system has small dynamic responses to environmental loads and it thus has almost the same mean generator power output under operating conditions as the land-based system. The tension mooring system has a sufficient safety factor, and the minimum tendon tension is always positive in all selected DLCs. The ratio of ultimate load of the tower base fore-aft bending moment for the WindStar TLP system versus the land-based system can be as high as 1.9 in all of the DLCs considered. These results will help elucidate the dynamic characteristics of the proposed WindStar TLP system, identify the difference in load effect between it and land-based systems, and thus make relevant modifications to the initial design for the WindStar TLP system.

A constitutive hardening model of coupled plastic deformation and martensitic transformation in steels

The article presents a constitutive model aimed at simulation of martensitic transformation induced by stress and plastic strain coupled with the hardening process in austenitic steels. The yield and transformation conditions are assumed to depend on back stresses evolving during plastic deformation and transformation processes. Their interaction affects essentially the hardening rate of a material. The thermodynamic background is reviewed and applied with both free energy and dissipation functions used in derivation of the rules of flow, hardening and transformation kinetics. The constitutive model parameters are specified and next the simulation of strain hardening for monotonic and cyclic loading is presented for the cases of uniaxial tension-compression and for combined tension-torsion deformation programs. The effect of strain ratcheting is analyzed for the cases of uniaxial and combined loading. It is shown that the transformation process is shown to essentially reduce the ratcheting strain.

Structural Analysis for Design Improvement of Stainless 5,000ton Rectangular Water Tank Structures

The finite element analysis of large sized rectangular water tank structures made of stainless steel materials is carried out for various combined load cases. The combined load cases for a large size of 5,000ton are further determined using the specification(KS B 6283) established from the Korean Standards Association. For the better numerical efficiency, the rectangular panels are modelled using the ANSYS program. The numerical results obtained for different load cases show as follows. In order to resist the snow load, it takes the influence of the gap than the size of the column. Also, in order to resist the water pressure, it shall increase the thickness of the wall. But, increasing the thickness of the wall is considerably less economical. Therefore, the angle with big thickness should be placed right next to the wall.

Finite Element Stress Analysis of Large Sized Rectangular Water Tank Structures Made of Stainless Steel Materials

The finite element stress analysis of large sized rectangular water tank structures made of stainless steel materials is carried out for various combined load cases. The combined load cases for a large size of 5,000ton are further determined using the specification(KS B6283) established from the Korean Standards Association. The changed water capacity due to the size of reservoirs could be heavily dependent for evaluating seismic effects, especially for large reservoirs. For the better numerical efficiency, the rectangular panels are modelled using the ANSYS ADPL module. The numerical results obtained for different load cases mainly show the effect of the interactions between the different load combination and other various parameters, for example, the water capacity, and different stainless steel materials. The structural performance for various load combinations is also evaluated.

Behaviour of structural stainless steel cross-sections under combined loading – Part II: Numerical modelling and design approach

In parallel with the experimental study described in the companion paper (Zhao et al., submitted for publication), a numerical modelling programme has been carried out to investigate further the structural behaviour of stainless steel cross-sections under combined loading. The numerical models, which were developed using the finite element (FE) package ABAQUS, were initially validated against the experiments, showing the capability of the FE models to replicate the key test results, the full experimental load–deformation histories and the observed local buckling failure modes. Upon validation of the FE models, parametric studies were conducted to generate additional structural performance data over a wide range of cross-section slenderness and combinations of loading. The experimental and numerical results were then compared with the design capacity predictions from the current European Standard EN 1993-1-4 (2006) and American Specification SEI/ASCE-8 (2002) for stainless steel structures. The comparisons revealed that the current design standards can significantly under-estimate the resistance of stainless steel cross-sections subjected to combined loading; this under-prediction of capacity can be primarily attributed to the lack of consideration of strain hardening of the material under load. The Continuous Strength Method (CSM) is a deformation-based design approach that accounts for strain hardening and has been shown to provide accurate predictions of cross-sectional resistance under compression and bending, acting in isolation. In the present paper, proposals are made to extend the scope of the CSM to the case of combined loading. Comparisons between the CSM design proposals and the test and FE results indicated a high level of accuracy and consistency in the predictions. The reliability of the proposals was confirmed by means of statistical analyses according to EN 1990 (2002).

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined external pressure and axial compression in thermal environments

The buckling and postbuckling analysis for an anisotropic laminated thin cylindrical shell of finite length subjected to combined loading of external pressure and axial compression using the boundary layer theory is presented. The material of each layer in the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are obtained utilizing classical shell theory and von Kármán–Donnell strain displacement relations. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfection of the shell, is extended to the case of anisotropic laminated thin cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. Postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells with respect to the material and geometric properties and load-proportional parameters under different sets of thermal environmental conditions is numerically illustrated. The analytical model developed can be used as a versatile and accurate tool to study the buckling and postbuckling behavior of composite structures.

Postbuckling of Buried Geodesically Stiffened Pipelines under Combined External Pressure and Axial Compression

AbstractUnderground pipelines for transportation and commercial usage are in high demand for meeting both sustainable population and economic growth in well-established metropolitan areas. This study presents the postbuckling analysis of buried geodesically stiffened pipelines of finite length subjected to combined loading of external pressure and axial compression. The pipeline, treated as a shell structure, is embedded in soil, and the pipe–soil interactions are modeled as a Pasternak elastic foundation. The governing equations are based on Reddy’s higher order shear deformation shell theory with the von Karman-Donnell type of kinematic nonlinearity. Nonlinear prebuckling deformation and initial geometric imperfection of the liner are both taken into account to investigate the buckling and postbuckling behavior of geodesically stiffened cylindrical pipes under combined loading cases. The effect of stiffeners (e.g., geodesic, axial, and ring stiffeners) is evaluated by a smeared approach, and a singular ...

Finite element analysis of reinforced concrete spandrel beams under combined loading

A nonlinear, three-dimensional finite element analysis was conducted on six intermediate L-shaped spandrel beams using the "ANSYS Civil FEM" program. The beams were constructed and tested in the laboratory under eccentric concentrated load at mid-span to obtain a combined loading case: torsion, bending, and shear. The reinforcement case parameters were as follows: without reinforcement, with longitudinal reinforcement only, and reinforced with steel bars and stirrups. All beams were tested under two different combined loading conditions: T/V = 545 mm (high eccentricity) and T/V = 145 mm (low eccentricity). The failure of the plain beams was brittle, and the addition of longitudinal steel bars increased beam strength, particularly under low eccentricity. Transverse reinforcement significantly affected the strength at high eccentricities, that is, at high torque. A program can predict accurately the behavior of these beams under different reinforcement cases, as well as under different ratios of combined loadings. The ANSYS model accurately predicted the loads and deflections for various types of reinforcements in spandrel beams, and captured the critical crack regions of these beams.

Finding Maximum Moment: Determining HL-93 Truck Position on Simple Spans

In the days of the AASHTO standard bridge design specifications, engineers used simple equations for calculating the HS-20 live-load moment for a simple span bridge. Engineers computed and compared the lane load moments to the truck load moments. The larger moment controlled the design. The second axle of the design truck was not placed at midspan but rather at a 2 ft 4 in. (0.711 m) offset from midspan. The correct orientation of the offset required that the truck’s resultant force reside on the opposite side of the midspan from the second axle. As an example, for a 50 ft (15.240 m) span, this 2 ft 4 in. (0.711 m) offset yielded a 628 kip-ft/lane (851 kN-m/lane) truck moment compared with a 620 kip-ft/lane (841 kN-m/lane) truck moment without an offset. By the 1990s, a new AASHTO specification was introduced based on LRFD. The old HS-20 live-load model was modified to combine its component lane load and truck load cases into a single load case called HL-93. This combined load case impacted the traditional 2 ft 4 in. (0.711 m) offset and made it vary according to span length. This paper proposes to derive an equation for determining the correct truck offset to produce maximum moment using HL-93 loading on simple spans greater than 40 ft (12.192 m). The scope of this paper does not include the tandem vehicle, because it does not govern spans greater than 40 ft (12.192 m) in length.

Dimensioning of Punctiform Metal-Composite Joints: A Section-Force Related Failure Criterion

Reliable line production processes and simulation tools play a central role for the structural integration of thermoplastic composites in advanced lightweight constructions. Provided that material-adapted joining technologies are available, they can be applied in heavy-duty multi-material designs (MMD). A load-adapted approach was implemented into the new fully automatic and fault-tolerant thermo mechanical flow drill joining (FDJ) concept. With this method it is possible to manufacture reproducible high strength FRP/metal-joints within short cycle times and without use of extra joining elements for the first time. The analysis of FDJ joints requires a simplified model of the joint to enable efficient numerical simulations. The present work introduces a strategy in modeling a finite-element based analogous-approach for FDJ-joints with glass fiber reinforced polypropylene and high-strength steel. Combined with a newly developed section-force related failure criterion, it is possible to predict the fundamental failure behavior in multi-axial stress states. The functionality of the holistic approach is illustrated by a demonstrator that represents a part of a car body-in-white structure. The comparison of simulated and experimentally determined failure loads proves the applicability for several combined load cases.

Meso-scale finite element modeling of NomexTM honeycomb cores

NomexTM honeycomb core composite sandwich panels are widely used in aircraft structures. Detailed meso-scale finite element modeling of the honeycomb geometry can be used to analyze sandwich inserts, vibration response, and complex combined loading cases. The accuracy of a meso-scale honeycomb modeling technique for static load cases was evaluated. A rectangular honeycomb core was modeled with perfect hexagon honeycomb cells. Compression and shear tests simulations with linear and non-linear solutions were performed for four core densities. The simulated moduli and buckling strengths were recorded. These results were compared to property data published by honeycomb manufacturers. The simulated maximum honeycomb wall stresses at the manufacturer predicted core strengths were also recorded. The honeycomb walls’ first compression deformation mode shape was observed. Sinusoidal small imperfections were then introduced in the honeycomb geometry based on that deformation mode shape. These imperfections provided a better match to manufacturer compressive modulus data while having a limited impact on the shear moduli. The simulated properties did not exactly match manufacturers’ shear and compression data together for all the core densities. Modeling the honeycomb cells with rounded corners and with increased thickness at the cell junctions are potential strategies to improve the accuracy.