Moment Amplification Research Articles

Out-of-plane interactive behavior and design of novel T-hooked buckling-restrained steel plate shear walls

To eliminate the use of a large number of connecting bolts for the cover panels in conventional buckling-restrained steel plate shear walls (BRSPSWs), T-hooked BRSPSW was proposed by using T-sectional stiffeners for restraining the out-of-plane deformation of the cover panels. With larger-sized flexural cover panels that provide confinement effects to the infilled steel plate, the out-of-plane interactive behavior between the infilled steel plate and each cover panel is greatly concerned for safe designs of the T-hooked BRSPSW. In this paper, a refined finite element (FE) model was established for evaluating the out-of-plane restraining effects in the T-hooked BRSPSW. The key parameters affecting the high-order buckling modes of the infilled steel plate were analyzed. The average spacing between adjacent buckling half-waves varied from 0.15 to 0.7 times the height of the steel sub-plate across common parameter ranges. Furthermore, a formula that estimates the total extrusion force produced by the buckled steel plate was corrected. By simplifying the cover panels into one-way flexural plates under uniform force, a flexural moment amplification coefficient in the range of 1.11 − 9.74 was defined to consider the difference between the actual strip-shaped interaction forces and the simplified model. Finally, a formula to calculate the bending moment of cover panels was proposed to safely design the T-hooked BRSPSWs.

Computational study of lateral jet interaction in hypersonic thermochemical non-equilibrium flows using nonlinear coupled constitutive relations

The present study reports the numerical analyses of lateral jet interaction around a Terminal High Altitude Area Defense-type (THAAD-type) model in hypersonic rarefied flows, with the real gas effect incorporated. The computation approach employed is the recently developed thermochemical non-equilibrium nonlinear coupled constitutive relations (NCCR) model. Regarding the simulation conditions, the flight velocity and height are set to 20 Ma and 80 km, respectively. To disclose the flow mechanism of lateral jet interaction, the complex flowfield characteristics and surface pressure distributions are discussed at length. Additionally, the research explores the impact of two key factors, namely, the jet pressure ratio and the jet Mach number, on the control performance of an in-flight vehicle's reaction control system (RCS). The results demonstrate that the complicated flowfield structures in lateral jet interaction are successfully reproduced by the NCCR model. With an increase in either the jet pressure ratio or the jet Mach number, the force and moment amplification factors decrease, while the absolute value of the normal force coefficient increases. Notably, it is found that the rarefied gas effect captured by the NCCR model against the Navier–Stokes–Fourier solution affects the lateral jet interaction flowfield, e.g., weakening the compressibility of the barrel shock and the expansibility of the Prandtl–Meyer expansion fan, as well as strengthening the jet wraparound effect. Importantly, the rarefied gas effect also exerts a prominent influence on the performance of RCS, with the degree of influence diminishing as the jet Mach number or the jet pressure ratio increases.

Uncertainty and Sensitivity Study on Lateral Jet Interaction for Hypersonic Missile

The demanding working environment of hypersonic missiles imposes high requirements on the reliability and stability of the reaction control system. This work aims to investigate the impact of uncertainties in freestream and jet parameters on the flowfield and aerodynamic performance of a missile with a lateral jet. Initially, the influence of angle of attack and Mach number on aerodynamic characteristics is evaluated. The findings indicate that the lateral jet control effect is enhanced as the Mach number increases. Moreover, the interference force/moment does not vary linearly with the angle of attack, and there are notable differences in the flow characteristics when the jet is on the windward and leeward sides. Subsequently, six parameters are selected as input variables. The uncertainties of the output results are analyzed using a stochastic expansion based on the nonintrusive polynomial chaos method. Sensitivity analysis is performed using Sobol indices to estimate the relative contributions of each parameter to the overall uncertainty. Within the given uncertainty interval, the surface pressure of the missile exhibits significant variation, with a maximum uncertainty of approximately 480%. The uncertainty of the recirculation zone range is 50.14%, while the pitch moment amplification factor has an uncertainty of 52.44%. The freestream Mach number, angle of attack, and jet pressure ratio are identified as key factors affecting the aerodynamic performance, surface pressure coefficient, and jet penetration height. Conversely, the contribution of other parameters can be considered negligible.

Investigations into the Flexural-Torsional Buckling Behavior of Steel Open-Section Beam-Columns

This paper is in the field of elastic flexural-torsional buckling of steel beam-columns of bisymmetric narrow-flange and wide-flange I-section shape. Investigations are focused on the derivation of the strain components and the energy equation, based on the displacement-field formulation in the deflected configuration. At the same time, a review of analytical solutions based on the classical and refined energy-equations are summarized, presented and discussed. The relationship between the maximum in-plane bending moment and the compressive force of beam-columns is the main objective of this research investigation. Simple boundary conditions of end-sections free to deflect and to warp are considered, together with an arbitrary loading-pattern. The principle of superposition and the moment amplification rule for considering the second-order effects are widely used. The main conclusions are drawn in relation to the flexural-torsional resistance-evaluation design of steel beam-columns in modern design codes for steelwork.

Wave interaction with an elliptic disc submerged in a two-layer fluid

Wave interaction with a horizontal elliptic disc submerged in a two-layer fluid is studied here assuming linear theory. An elliptic coordinate system is used to solve the three-dimensional problem analytically. The fluid region is divided into a number of subregions and by means of separation of variables, velocity potential in each region is expressed in terms of series of Mathieu and modified Mathieu functions of real argument. Matching conditions along with the orthogonal properties of eigenfunctions provide solutions for the fluid velocity potentials. Numerical results are presented for the wave-induced forces and moments. The effect of variations in the depth of submergence of the disc, angle of incidence of the incoming wave, density ratio of the fluid and aspect ratio of the disc on these physical quantities have been analyzed. In particular, sudden amplification of forces and moments have been observed at certain frequencies when the disc is situated at close proximity to the interface. Various other behaviors of the solution are investigated in some detail.

Research on design and numerical simulation of self-centering prefabricated RC beam-column joint with pre-pressed disc spring devices

To improve the resilience performance of precast concrete frame structure, a novel self-centering prefabricated concrete beam-column joint with controllable plastic hinge (PJ-CPH) is proposed in this manuscript. Controllable plastic hinge is an innovative connection configuration composed by pin shaft, rotational friction damper and disc spring self-centering devices. The rotational friction damper is used for withstanding bending moment and dissipating seismic energy. The disc spring self-centering device is used for withstanding bending moment and providing restoring force, while the pin shaft is merely used for withstanding shear force. A detailed design procedure was presented by introducing self-centering ratio α and moment amplification factor β. A flag-shaped hysteretic model of PJ-CPH was proposed, simultaneously, a numerical model was developed based on the OpenSees computational platforms. The numerical simulation analysis was carried out for four PJ-CPH models with different parameters and one cast-in-situ beam-column joint model under low cyclic loading. Analysis results indicate that the hysteretic curve obtained by theoretical calculation are in good agreement with the numerical simulation results. Consequently, the effectiveness of the established hysteretic model was verified. Compared with the cast-in-situ beam-column joint, PJ-CPH achieves the damage-free connection and exhibits the superior resilience performance. The simulation results suggest that self-centering ratio α values should be assumed approximately in the range 1.00–1.30, moment amplification factor β values in 1.30–1.40, which can induce damage to concentrate in controllable plastic hinge, protect the main structure from damage and reduce repair costs.

Flexural design of restraining panels in buckling-restrained steel plate shear walls considering high-order buckling modes

Buckling-restrained steel plate shear wall (BRSPSW) is one kind of excellent energy dissipating member. The inner steel plate in BRSPSW usually works with high-order buckling modes to resist lateral force under the buckling restrained effect of outer restraining panels. However, current design of the restraining panels is commonly based on simplified uniform-loaded plates without considering the effect of the high-order buckling modes, which may result in unsafe designs. In this paper, the high-order buckling modes in BRSPSW and their influence on the flexural design of the restraining panels were studied. Finite element (FE) models that can accurately simulate the out-of-plane interaction behavior of BRSPSW were developed and verified by existing test results. The numerical results show that the high-order buckling of the steel plate leads to a series of inclined strip-shaped stress regions on restraining panels. When the parameters of BRSPSW are varied in common range, the positive and negative bending moments of the restraining panel under the strip-shaped force are 9.6 and 2.8 times those under the uniform force, respectively. The differences between the bending moment of the restraining panels under strip-shaped force and that under uniform force become larger as the spacings of the strip-shaped stress regions increase. Furthermore, the spacings of the strip-shaped stress regions increase with the decrease of the height-to-thickness ratio of the steel plate and the increase of the gap between the steel plate and the restraining panel. Two fitting formulas of the positive and negative moment amplification factors considering the effect of the high-order buckling modes are proposed to design the restraining panels safely. Additionally, a simplified model and bending moment equations of the restraining panels in BRSPSW are suggested. To avoid the excessive negative bending moments occurring at side supports of the restraining panel, the ratio of cantilever length to middle span is suggested to be not more than 0.4.

Solving the Moment Amplification Factor of a Lateral Jet by the Unsteady Motion Experimental Method

In this paper, unsteady motion tests of a lateral jet adjusting an air vehicle’s attitude are carried out. Curves of pitch moment amplification factors (KM) for a lateral jet versus angle of attack (α) are obtained using a wind tunnel free-flight test technique with a jet and data processing method. This new method overcomes the disadvantage of previous experiments that can study only one unsteady characteristic. The free-flight test technique in the proposed method ensures that the test model can be coupled in real-time with multiple parameters (unsteady flow caused by the jet, unsteady air vehicle aerodynamic force, and unsteady air vehicle motion). This approach simulates an actual air vehicle’s complete jet test process and ensures more authentic and reliable test results. In the new data processing method, continuous data curves are fitted to discrete data points, making it easier to convert the angular displacement versus time curve into the pitch moment versus α curve to obtain KM. The results show that when the pressure of the micro high-pressure gas cylinder is 2.0 MPa, KM is below 1, indicating that the lateral jet does not significantly promote the pitching moment. When the gas cylinder pressure is 4.0 MPa and the angle of attack is 5° < |α| < 16°, KM is greater than 1, and the lateral jet promotes the pitching moment. When 16° < |α| < 20°, KM is less than 1, and the lateral jet does not significantly contribute to the pitching moment. It was further found that KM decreases slowly with increasing α. When |α| > 30°, the influence of the jet on the pitching moment nearly disappears.

Método de reforçamento estrutural para avaliação do encamisamento em pilares com amplificação de momentos sob cargas sísmicas

Abstract Different reasons can make certain structures need reinforcement to achieve specific levels of safety and performance. The occurrence of events of significant magnitudes, such as earthquakes, are examples of this. Retrofitting vulnerable structures becomes a practice to mitigate the destructive effects of earthquakes, and the RC Jacketing becomes an alternative. The present work studies this type of reinforcement, proposing and applying an assessment methodology under vulnerable construction built in a high seismic risk zone. The diagnostic of the current situation was determined, and the structural suitability was evaluated using RC Jacketing. With the computational software S-Model, created in this research, the effectiveness of the proposed reinforcement was verified, based on the results of the analysis carried out with commercial software. The preload was considered, and the strength of the reinforced column section was verified against all load combinations. The S-Model program was able to verify the non-simultaneous occurrence of the amplification of moments with the most critical loading. Both conditions demand more significant stresses on the element, and therefore the calculation of the steel areas of the column may be underestimated if they are not considered.

A mechanical model for soil-rectangular tank interaction effects under seismic loading

In this paper, the dynamic behavior of concrete rectangular tanks subjected to motions caused by an earthquake considering the effects of soil-structure-fluid interaction is studied. An analytical mechanical model for a rectangular tank with flexible walls, taking into consideration the effects of rigid-base rocking motion and lateral translation, is developed. The model with a lumped-parameters idealization of foundation soil is used to evaluate the system's response to ground earthquake motions. Using this model, the soil-structure-fluid interaction effect can be taken into account in the seismic analysis of flexible rectangular tanks in a fast and practical manner. To verify the mechanical model, the numerical results of the fixed-base case are compared with the experimental results. The results show that dynamic soil-tank interaction under horizontal seismic excitations, depending on the type of soil, can cause a profound effect on the amplification of hydrodynamic forces and moments exerted on the tank structure.

Interaction of geometric and material nonlinearities in stainless steel frames

AbstractAdequate mechanical properties make stainless steel an excellent construction material for structures. The current stainless steel European structural code EN1993‐1‐4 (2015) is largely based on provisions given for carbon steel EN1993‐1‐1 (2005) and does not establish specific design rules for the global analysis of stainless steel structures. Thus, the same classification criterion applies in both codes for sway and non‐sway structures, as well as providing the same predicting expressions for the amplification of bending moments in basic structures, despite the considerable differences between the mechanical behaviour of these two materials. However, recent numerical research on stainless steel frames with H cross‐sections by Walport et al. (2019) showed that the degradation of stiffness due to material nonlinearities considerably affects the response of stainless steel frames, causing greater deformations and increasing second order effects.In order to contribute to the optimal design of stainless steel structures, this paper investigates the influence of the nonlinear material response of stainless steel alloys on frame‐type structures with Rectangular Hollow Sections based on the experimental results conducted by Arrayago et al. (2019), and the interaction of material and geometric nonlinearities.

Elastic-plastic stability of shear-deformable circular arches

Shear deformations affect the stability of arches. This paper investigates the in-plane elastic-plastic stability and design of pin-ended circular arches including shear deformations. The elastic buckling axial forces for symmetric and anti-symmetric buckling are first studied for radially compressed arches and arches uniformly loaded along the horizontal projection, formulas are proposed so that they are used to compute the normalized slenderness and the moment amplification factors respectively. The strength reduction factors of axially compressive arches are studied during which the effect of accompanying bending moments has been excluded, a formula for the strength reduction factors (SRF) of arches with uniform axial forces are proposed. This study verified that the effect of shear deformation can be fully included by the normalized slenderness. The SRF is also modified to make it applicable for real arches where axial forces are always varied along the arch centroid line. Then the moment amplification factor of arches subjected to uniformly distributed loads along the horizontal projection, are derived theoretically and validated by FE predictions. Finally, based on the modified SRF and the moment amplification factor, an interactive axial force-bending moment stability design equation is developed, which considers the effect of shear deformations and provides excellent predictions for the in-plane strength of shear-deformable pin-ended circular arches in bending and compression.

Effectiveness of multiple jets for a finned large slenderness ratio missile in supersonic crossflows

The reaction control system with multiple lateral jets shows great advantages in agility and maneuverability for supersonic air vehicles. Interactions among sonic jet plumes, X-shape fins, and supersonic crossflow at Mach 4.5 and Reynolds number 3.8 × 107 are numerically studied considering different number of jets for a large slenderness ratio missile with 7 jet exits. Three-dimensional Reynolds-averaged Navier–Stokes equations closed by Spalart–Allmaras turbulence model for the structured grid are validated and solved. The overall force and moment amplification factors of configurations with and without fins are analyzed and compared. Moreover, the force and moment amplification factors on fins and ratio of force and moment on fins are proposed and discussed to measure the jet effectiveness contributed from fins. The number of jet plumes is under consideration for all cases. Results show that the increment of effectiveness decreases as the number of jets increases for the finned configuration. Fins can significantly improve the jet effectiveness with more than 70% force and 50% moment increment, which shows great advantages to the jet effectiveness as well as the overall aerodynamic performance.

Buckling of stepped columns considering the interaction effect among columns

The effective length factors of stepped columns, as provided by the current design codes, are not suitable for certain situations, such as multi-bay frames and pitched-roof portal frames, because the interaction effect among the columns and the influence of the roof inclination angle are not considered. This paper proposes a simple but accurate hand calculation method to evaluate the effective length factors and second-order effects on framed stepped columns. In this approach, the expression of the negative lateral stiffness for stepped columns is first determined and then used to determine the effective length factors considering the interaction effects among columns. This is followed by a theoretical analysis to evaluate second-order effects, and expressions for calculating the deflection and moment amplification factors are developed. A practical method to account for the influence of the roof inclination angle for frames with stepped columns is also presented. The results of the performed eigenvalue and nonlinear static analyses demonstrate the validity of the proposed method. Based on the presented analysis, recommendations are made for the improvement of current design codes. Finally, the values of the key factors, αs0 and αsN, for some common cases are determined. The findings will assist in the development of reliable and cost-efficient designs of stepped columns in mill buildings.

Experimental Study on Loading Capacity of Glued‐Laminated Timber Arches Subjected to Vertical Concentrated Loads

Glued‐laminated timber arches are widely used in gymnasiums, bridges, and roof trusses. However, studies on their mechanical behaviours and design methods are still insufficient. This paper investigates the in‐plane loading capacity of circular glued‐laminated timber arches made of Douglas fir. Experiments were conducted on four timber‐arch models with different rise‐to‐span ratios under concentrated loads at mid‐span and quarter‐point locations. The structural responses, failure modes, and loading capacity of the timber arch specimens were obtained. The results show that the timber arches presented symmetric and antisymmetric deformation under mid‐point and quarter‐point loading conditions, respectively. The downward shifting of the neutral axis of the cross section was observed under mid‐point loading condition, which contributes to higher loading capacity compared to that under quarter‐point loading condition. The loading condition significantly affects the ultimate loads and the strain distribution in the cross section. Based on the design formula in current standards for timber structures, an equivalent beam‐column method was introduced to estimate the loading capacity of the laminated timber arches under vertical concentrated loads. The moment amplification factor in the formula was compared and discussed, and the value provided in the National Design Specification for Wood Construction was recommended with acceptable accuracy.

Design and Analysis of an Origami-structured Actuator for Backdriveability and Power Amplification

An origami-structured compliant actuator (OSCA) is developed for human–robot interaction, in which adequate power output, as well as safety, is emphasized under a limited power supply. The OSCA inherits the safety feature from soft actuators, while, at the same time, it ensures that expansion in off-axis directions is converted to on-axis moment. The kinematic singularity originating from its actuator design gives rise to a significant mechanical advantage over certain ranges of motion. The compressibility of airflow within the actuator essentially provides both backdriveability and elasticity, the latter contributing to increasing the actuator's power output in the same way as does a series elastic actuator. In this study, the design of an actuator structured based on origami is presented, and analyses on benefits in moment amplification and power amplification from the OSCA design and air compressibility are examined. These efforts provide an insight into producing high power by the OSCA in unison with a low driving-point impedance.

Future Inversion of the Magnetic Field and Possible Changes in the Structure of the Magnetosphere

IGRF-12 model data have been used to analyze the change in the global structure of internal sources of the Earth’s magnetic field. A decrease in the dipole magnetic moment is accompanied by a rapid growth of multipole moments. This justifies the theoretical model of the magnetic field inversion as a gradual decrease in the dipole field with general conservation of its direction and amplification of multipole moments. Paleo- and archeomagnetic data indicate that this process has already been taking place for almost 2.5 thousand years and has occurred repeatedly many times in the past. A decrease in the dipole magnetic moment leads the magnetopause to approach the Earth to disappear completely in almost 1.5 thousand years.

Spatial variation of seismic ground motion effects on nonlinear responses of cable stayed bridges considering different soil types

The main objective of this study is providing comparative results of cable stayed bridges under non-uniform and uniform excitations and identifying the key parameters and elements for seismic design purposes. For this purpose, three cable stayed bridges were modeled in SAP2000 software and imposed to uniform and non-uniform displacement time series. Four different soil types were considered for generating sixteen different load cases. Twenty displacement time series, generated using spectral representation method, were considered in each load case for obtaining the statistical characteristics of responses. Bridge responses were obtained in terms of girder, pylon and the cable's internal forces. Results of this research indicate that depending on the soil type beneath each support, the response of bridge may vary significantly. Deck and pylon stiffness are important parameters for describing the amount of girder moment or cable's axial force amplification. Girder moment, cables axial force, pylons shear and pylons drifts are amplified up to 1.8, 1.4, 1.48 and 3.1 respectively in the worst load case.

EFFECTS OF THE INITIAL DEFLECTION SHAPE ON THE MOMENT AMPLIFICATION FACTOR OF BEAM-COLUMNS

In the design of slender steel beam-columns, the moment amplification factor is used to estimate the maximum moment along with the longitudinal direction. While formulas for evaluating the factor have been presented on the basis of elastic or elastic-plastic analysis, the initial deflection of the column is not considered. The effect that the initial deflection on the strength and behavior of the column has been shown only when the initial deflection shape is half sine wave. This paper discusses the effect of the initial deflection shape on the value of the moment amplification factor by performing the analytical work. The analytical model is the hinged-end beam-column subjected to constant axial compressive force and end moments. First of all, the equilibrium differential equation which governs the problem is solved and the formula for calculating the bending moment is presented. In the parametric study, magnitude of initial deflection, initial deflection shape, axial load ratio, slenderness ratio and end moment ratio are selected as the parameters. In this paper, we discuss the effects of the amount of the initial deflection and the initial deflection shape.

Extension of Direct Displacement-Based Design to Include Higher-Mode Effects in Planar Reinforced Concrete Frame Buildings

Now that problems with force-based seismic design have been clearly identified, design is inclined toward displacement-based methods. One such widely used method is Direct-Displacement-Based Design (DDBD). Yet, one of the shortcomings of DDBD is considering higher-mode amplification of story shear, moments, and displacements using equations obtained from limited parametric studies of regular planar frames. In this paper, a different approach to account for higher-mode effects is proposed. This approach determines the lateral secant stiffness of the building frames that fulfill the allowable inter-story drift without exceeding the desired story displacements. Using the stiffness, an elastic response spectrum analysis is carried out to determine elastic higher-mode force effects. These force effects are then combined with DDBD-obtained first-mode force effects using the appropriate modal superposition method so that design can be performed. The proposed design procedure is verified using Nonlinear Time History Analysis (NTHA) of twelve planar frames in four categories accounting for mass and stiffness irregularity along the height. In general, the NTHA response outputs compared well with the allowable limits of the performance objective. Thus, it fulfills the aim of minimizing the use of NTHA for planar frame buildings, thereby saving computational resources and effort.