Dynamic Bending Moment Research Articles

Seismic response of permafrost slopes supported by the thermal anchor pipe frame: Theoretical analysis and shaking table test verification

To study the seismic response of the thermal anchor pipe frame supporting permafrost slope system, the coupled dynamic interaction model of the permafrost slope with the thermal anchor pipe frame in thawing and freezing periods was established by taking into account the stratification characteristics of the permafrost slope in different typical seasons, respectively. Based on D'Alembert's principle and Dirac's function, the coupled vibration equilibrium differential equations are given and the seismic response of the system is analyzed for different periods. The reliability of the proposed model was further verified through shaking table tests. The results show that the acceleration response at different positions during both freezing and thawing periods is similar to the initial loading seismic wave shape. The peak acceleration and velocity during the thawing period is greater than that during the freezing period. The shear force and bending moment of the frame column are distributed alternately positive and negative along its height. The incremental dynamic shear force and bending moment are greater during the thawing period. However, the peak bending moments and shear forces are greater during the freezing period when the combined effects of frost and earthquakes. The peak bending moment occurs at the position of the first layer of the thermal anchor pipe, and the shear force suddenly changes near the thermal anchor pipe. In seismic design, attention should be paid to checking the internal force of the frame column during the freezing period to prevent plastic bending failure. The results contribute to further understanding the dynamic interaction mechanism of the thermal anchor pipe frame permafrost slope system, which has important practical significance for its seismic resistance.

An optimised equivalent modelling approach for LMRP/BOPs in the global dynamic analysis of deepwater risers

ABSTRACT Lower marine riser package/blowout preventers (LMRP/BOPs) play a crucial role in transferring the dynamic loads from the slim drilling risers to the subsea wellhead (SW). Generally, the LMRP/BOPs are usually modelled as the combination of pipe and mass elements in the finite element analysis. In this paper, an optimised equivalent modelling approach for LMRP/BOPs was proposed to improve the calculation accuracy of dynamic cyclic bending moment of SW. In the proposed methodology, the equivalent model of LMRP/BOPs was established based on the deformation analysis of the local fine model of LMRP/BOPs. Using the Newton–Raphson method, the equivalent model was optimised to acquire the optimal equivalent model of LMRP/BOPs. A case study indicated the modelling accuracy of LMRP/BOPs was improved by 14.6% compared to the conventional approach by using the proposed approach, thus the calculation accuracy of the dynamic cyclic bending moment of SW was improved accordingly.

Influence of the anchor angle on the seismic response of anchored stabilizing piles: Centrifuge modeling tests

Anchored stabilizing piles (ASPs) are widely used as excavation support systems in slope anti-seismic reinforcement engineering. In this study, a set of centrifuge contrast tests were designed and used to explore the influence of the anchor angle on the seismic response of the system to further deepen the research on the seismic response of ASPs. To this end, the effects of two anchor cable arrangement angles on the slope seismic response, lateral dynamic earth pressure, anchor cable axial force, and pile dynamic moment were compared and analyzed. The results show that changing the angle of anchor cable arrangement can reduce the degree of seismic damage to the slope and the settlement of the slope top (up to a maximum reduction of 77%) and, to some extent, reduce the amplification of acceleration inside the slope. Under seismic action, the different angles of anchor cables do not change the distribution of seismic earth pressure and peak dynamic bending moment but can significantly affect their magnitude and growth rate. The appropriate arrangement angle of the anchor cable can effectively slow the growth of the internal force of the anchor cable and reduce the risk of anchor cable failure. The anchor cable is not the main load-bearing component in an ASP but the primary component that limits pile displacement. Overall, this study can provide a detailed data foundation for subsequent centrifuge comparative tests and parameter analysis.

Comparison of Dynamic Amplification Factor of Deflection and Bending Moment of Highway Continuous Box-Girder Bridges by Mode Superposition.

There are differences between the dynamic deflection and bending moment (strain) in the same section of continuous girder bridges. However, the selection of the response for calculating dynamic amplification factors (DAFs), which are essential for bridge health monitoring and safety assessment, remains controversial. Modes may play a role in the relationship between the deflection DAF and the bending moment DAF in both numerical analysis and field tests. To investigate the distinctions between the DAFs of the deflection and bending moment in a continuous girder bridge, functional expressions of the DAFs were derived, taking into account multi-factor coupling under concentrated forces. The interaction effects of the mode and road surface condition (RSC), vehicle speed, bridge span length, and span number on the deflection DAF, the bending moment DAF, and the ratio of the deflection DAF to the bending moment DAF (RDM) of precast continuous box-girder bridges were analyzed using vehicle-bridge interaction. To ensure the accuracy of the DAF in numerical computations and experimental tests, two types of accuracy indexes and the corresponding cut-off modes were provided. Validation was conducted by performing dynamic load tests on two field bridges. The results indicate that different modes have a significant effect on the RDM of the mid-span section of a bridge. When considering multiple factors, the deflection DAF and bending moment DAF of the mid-span section increased rapidly with the considered modes and then stabilized. Statistically, the RDM of all nine bridges ranged from 1.00 to 1.12, indicating that the deflection DAF was greater than the bending moment DAF. The suggested cut-off modes can be utilized for efficient and accurate calculation of the DAF and response signal fidelity.

Probabilistic models of dynamic increase factor (DIF) for reinforced concrete structures: A Bayesian approach

The response of structures under rapidly varying loads can be affected by strain rate sensitivity generally expressed using Dynamic Increase Factor (DIF). Current models for estimating the DIF in Reinforced Concrete (RC) structures are generally deterministic and have restricted applicability due to their dependence on limited experimental data resulting in bias. This paper overcomes these limitations by proposing three probabilistic models that quantify compressive and tensile concrete and steel DIF, accounting for the relevant uncertainties. The proposed models are based on existing deterministic models with the addition of probabilistic correction terms. Bayesian updating is employed to estimate the unknown model parameters using observational data from a large collection of experimental observations. The models incorporate model uncertainties stemming from assumed model form and (potential) missing variables through a model error term. The proposed probabilistic models are used to evaluate the reliability of RC structures under dynamic loads. As an illustration, the proposed probabilistic models are used to estimate the reliability of an example RC column under combined dynamic axial force and moment, and a RC column or beam under dynamic bending moments resulting in cracking. In the two examples, we consider the ACI 318-19 requirements for Ultimate Limit State (ULS) and Serviceability Limit States (SLS). In comparison to deterministic DIF models, the proposed probabilistic models yield enhanced predictive accuracy, presenting a practical and robust approach to assess the structural reliability under impact and blast loads.

A new seismic input method for layered soil and its application in dynamic response analysis of underground structure

With the acceleration of urbanization, the seismic problem of underground engineering is getting more and more attention. In actual projects, foundation soils often show a complex layered distribution. In terms of layered ground motion input, this study propose a new layered ground motion input method based on infinite element boundary, which avoids the application of spring and damping elements on the boundary nodes of layered soil, simplifies the ground motion input process and has high accuracy at the same time. To reasonably simulate the nonlinear seismic response of layered soil, the equivalent linear model of soil is nested to Mohr-Coulomb (MC) model to establish the viscoelastic-plastic model. The seismic response analysis procedure of the soil-structure monolithic model considering the nonlinearity of the layered soil is given. On this basis, the soil-structure nonlinear seismic response analysis is carried out to study the effect of burial depth on the seismic performance of underground structures, taking a project as an example. The results show that with the increase of the burial depth of the structure, the top–bottom displacement difference shows a change law of first increasing and then decreasing under the action of earthquake; From the internal force response, the most unfavorable burial depth exists due to the joint influence of the burial depth of the structure and the characteristics of the layered soil; For the same burial depth condition, the dynamic bending moment caused by the seismic load action is larger compared to the shear response.

Lateral Dynamic Response of Helical Pile in Viscoelastic Foundation Considering Shear Deformation

Helical piles are a new type of pile that has good application prospects, and researchers have carried out an in-depth investigation into their vertical uplift and compressive bearing capacity. However, there is relatively little research on the dynamic bearing characteristics of helical piles. Therefore, the lateral vibration of a helical pile embedded in the viscoelastic foundation is systematically studied in this article. Utilizing the equivalent stiffness method to transform a helical pile into a cylindrical pile of special diameter, the lateral vibration model of the helical pile considering shear deformation is established based on the Winkler foundation model and the Timoshenko beam theory. The analytical solutions for the lateral dynamic displacement, bending moment, and shear force of the helical pile are strictly derived, and the rationality of the present solutions is also verified by comparing them with existing solutions. Based on the present solutions, a parametric study is carried out to investigate the influence of the pile and soil properties on the lateral dynamic response of the helical pile. It is found that the load excitation frequency and pile–soil stiffness ratio have a significant influence on the lateral dynamic displacement, bending moment, and shear force of the helical pile with space and time response.

Numerical investigations on the dynamic responses of metro tunnel-soil-ground building under oblique incidence of seismic wave

With the development of urban rail transits, the metro tunnels frequently underpass the above-ground buildings, and understanding the dynamic responses of metro tunnel-soil-ground buildings experiencing oblique incidence of seismic waves is of crucial importance. Considering that the seismic waves in the near-field seismic area are mostly obliquely incident to the ground at a certain angle, a two-dimensional numerical model for tunnel-soil interaction system and tunnel-soil-above ground structure was established by Abaqus software, in which the viscoelastic boundary and equivalent nodal forces were adopted to simulate the ground motion. The effects of tunnel burial depth, tunnel spacing, and tunnel frame spacing on the seismic responses of metro tunnel-soil and metro tunnel-soil-above ground building were analyzed under oblique incidence of SV wave with different incident angles. It was found that the tunnel depth has a significant effect on the lining dynamic bending moment and axial force peak, and its influence is closely related to the site category. The tunnel spacing has a minor impact on the dynamic response of the lining structure. The incident angle has a significant effect on the peak value of the dynamic shaft force of the lining. The application of the frame on the ground has a significant impact on the tunnel. The influence of above-ground buildings and tunnel burial depth should be considered when tunnel design is carried out.

Influence of Auxiliary Pipelines of the Deepwater Drilling Riser on the Dynamic Characteristics of the Subsea Wellhead

During deepwater drilling, the subsea wellhead will be subjected to dynamic loads transmitted from the marine environment, floating drilling platform, riser, and blowout preventer (BOP). Therefore, complex dynamic responses will be induced, which will seriously affect the safety of the subsea wellhead. In this paper, considering the effect of auxiliary pipelines on the riser, a novel entire mechanical model of the floating platform–riser–BOP–subsea wellhead is established. By using the finite-difference method, the governing equations are solved. Finally, the dynamic bending moment and stress distribution of the subsea wellhead are obtained. Moreover, the model is verified by numerical simulation in Orcaflex. On this basis, the influence of the wave height, wave period, sludge height of the subsea wellhead, rotational stiffness of the lower flexible joint, and wall thickness of the conductor on the dynamic characteristics of the subsea wellhead is discussed. Analysis results show that the theoretical analysis results are in good agreement with the numerical simulation. The auxiliary pipelines have important influence on the dynamic characteristics of the subsea wellhead. Wave period is the most important factor affecting the mechanical behavior of the subsea wellhead. Wave height, wall thickness of the conductor, and sludge height are secondary factors affecting the mechanical behavior of the subsea wellhead. The rotational stiffness of the lower flexible joint has little influence on the mechanical behavior of the subsea wellhead. By solving the optimized mechanical model proposed in this paper, the dynamic characteristic of the subsea wellhead conforms more to the actual deepwater drilling conditions. This study has reference significance for the design and mechanical control of the subsea wellhead in deepwater drilling.

Transverse seismic responses of a shield tunnel considering the influence of segment joints

The segment joints of a shield tunnel are generally the weak components of the structure, and they can be considerably damaged under strong seismic loading, thus influencing the overall seismic behavior. In this study, Finite Element simulation analyses of centrifuge shaking table tests and a shield tunnel project are carried out to investigate the influences of the segment joints on the seismic responses and the associated mechanisms. First, the reliability of the numerical procedure is validated by using the centrifuge shaking table test results. The numerical procedure is then used, together with the refined simulation approach for segment joints, to carry out extensive numerical analyses of the seismic responses of a shield tunnel project under different horizontal earthquake loadings. The research results show that due to the influence of the segment joints, the peak value of the dynamic bending moment of each segment tends to be more uniform. When the stiffness reduction method is used to consider the influence of the segment joints, the peak values of the dynamic bending moments can be too large, while the peak values of the dynamic axial forces may be too small. In addition, the tunnel segment rotates during an earthquake, resulting in relatively large relative displacements of the segment joints.

Dynamic analysis of a single Pile embedded in SM soil using 1-g shaking table tests

The soil-structure interaction on a single pile in dense SM soil was investigated by using 1-g shaking-table tests and an analytical study. The emphasis was on analyzing the dynamic behavior of a mass mounted on a single pile embedded in different soil conditions. The cases of a single pile embedded in dried and saturated SM soils were tested under input acceleration, and subsequently, the analytical study was also performed. It is shown that the natural frequency is much lower for saturated soil than in dry soil conditions. It was found that the natural frequency of a pile-soil system embedded in SM soil is much less than the natural frequency of a single pile embedded in SP soil condition. It was also found that the dynamic bending moment and lateral displacement of a single pile in SM soil were much lower than those in SP soil. Analysis of the p–y curves in this study revealed that SM soil exhibits higher initial stiffness than SP soil but lower ultimate soil resistance than SP soil. Calculating the dynamic behavior of a pile in SM soil can be a safe-side result due to its higher lateral stiffness compared to the pile in SP soil.

Performance of CFST members internally strengthened with I-shaped CFRP under impact load

This study presents experimental and numerical research on the dynamic behaviors and resistances of square concrete-filled steel tubular members internally strengthened by I-shaped CFRP profile (SCFST-CFRP) with fixed boundary conditions subjected to lateral impact loads. Dynamic impact tests were conducted on five SCFST-CFRP specimens and a traditional concrete-filled steel tubular (SCFST) specimen, examining their dynamic responses with respect to deformation modes, impact force, displacement, and strain distribution at different levels of impact energies and impact momentums. The test results indicated that the deformation of the specimens was concentrated in the impact region, approximately 0.38 L above the base, due to the transient localized characteristics of the lateral impact load. In terms of displacement and impact force, the SCFST-CFRP member exhibited better impact resistance compared to the SCFST member. Finite element models of the SCFST-CFRP members were created using LS-DYNA and validated against the impact tests. These validated models were then utilized to explore the damage patterns, dynamic bending moment, and load transfer mechanism of the SCFST-CFRP member under lateral impact loading. Additionally, a parametric study was conducted to evaluate the effects of load and structural parameters, including CFRP profile, impact energy, and impact momentum, on the impact resistance and dynamic flexural capacity of the SCFST-CFRP member. The results demonstrate that the enhancement in impact resistance caused by the inner CFRP profile was more significant under higher impact energy. Based on the parametric analysis results, empirical equations were proposed to predict the dynamic flexural capacity of lateral impact-loaded SCFST-CFRP members.

Seismic performance of U-shaped spillway retaining wall from shake table tests

A series of large-scale shake table tests were performed to evaluate the seismic behavior of a U-shaped spillway retaining wall. Three test model configurations were employed using different backfill conditions in terms of in-place soil density. Two earthquake records were employed as input motion and scaled in terms of time duration and acceleration amplitude to assess various aspects of seismic response. The test results showed that dynamic wall deflection and wall bending moment generally increased with Peak Ground Acceleration (PGA) amplitude. At peak wall deflection, the seismic earth pressure increment coefficient (ΔKAE) was back-calculated from the measured bending moment along each wall. In addition, the location of ΔKAE along the wall height and the resulting base moment were evaluated and discussed. The results suggested that seismic demands were generally lower up to a PGA of about 0.8 g, compared to the classic Seed and Whitman recommendation for seismic lateral earth pressure and seismic bending moment of retaining walls. Beyond PGA of 0.8 g, test results were in general agreement with the Seed and Whitman solution. Finally, two-dimensional finite element analyses were performed, and the computational results showed overall reasonable agreement with the experimental data.

Artificial neural network-based multiple-input multiple-output metamodel for prediction of design parameters for a high-speed rail viaduct

The prediction of the design parameters of short to medium-span supported bridges in critical locations (such as canal/road crossings) under the action of high-speed trains has been investigated in this article. An artificial neural network (ANN)-based MIMO (multiple-input multiple-output) metamodels is proposed in conjunction with the semi-analytical framework of simply-supported bridges. Three cases, namely single moving load, series of moving loads at equal spacing (HSLM-B), and as per conventional train configuration (HSLM-A) recommended in Eurocode1: EN 1991-2 (2003), are considered. The prime novelty of the article is to develop a dimensionless semi-analytical framework to train and validate a MIMO metamodel implementing ANN for predicting the multiple dynamic responses of bridges under high-speed loads. The dependency of the maximum dynamic responses, that is, displacement, shear force, and bending moment, on the governing parameters (structural and loading) have been elucidated using Pearson's correlation matrix for the three different train configurations. Further, the robustness and efficiency of the best-fitted metamodels have been compared, and a user interface has been developed for ease of implementation. This platform evaluates the responses such as displacement, shear force, bending moment, and structural safety confirming the standards of Eurocode EN 1990:2002 + A1:2005 (E).

Study on hybrid fibre reinforced UHPC beams under single and repeated lateral impact loading

This paper investigates the dynamic response of hybrid fibre reinforced ultra-high performance concrete (UHPC) beams against single and repeated low-velocity impact loads. A brief description of the drop weight impact tests on the UHPC beams was presented first followed by the development of the material and structural model in finite element analysis. A plasticity-based concrete material model with validated compressive and tensile strength surface and damage algorithm was adopted for hybrid fibre reinforced UHPC material. Based on the test results, the bond-slip behaviour between steel rebar and UHPC matrix was developed in an empirical form and incorporated in the model. Compared to the model with the bond-slip definition, the model with perfect bonding was found to underestimate the maximum mid-span deflection, which highlighted the necessity of considering the bond-slip behaviour in dynamic analysis where large deflection occurs. The repeated impact tests were performed numerically, and the results were validated with experimental data. A parametric study was then performed to investigate the effect of key parameters, including different impact energy and the same impact energy but different impact numbers. The results indicated when the total energy increased, the repeated impact loads became more hazardous than the single impact load. With the validated model, the dynamic shear force and bending moment distribution diagrams were compared to study the failure mechanism in single and repeated impact loads.

Experimental and numerical study on the impact resistance of ultra-high performance concrete strengthened RC beams

To enhance the impact resistance of built reinforced concrete (RC) members, the effectiveness of using ultra-high performance concrete (UHPC) for strengthening RC structures was investigated in this study. The mechanical properties of UHPC were evaluated by the uniaxial compression, tension and flexural bending tests. Drop weights with hemispherical and wedge-shaped indenter were adopted to impact the beam specimens with and without UHPC strengthening. A total of six beams, including three control RC beams and three UHPC jacketed RC (RC-UHPC) beams, were tested. The beams were prestressed in the axial direction with a 200 kN force. The test results revealed that the UHPC jackets improved the structural impact resistance. With an impact mass of 411 kg and an impact velocity of 4.95 m/s, the maximum and residual deflection of the RC-UHPC specimen decreased by 15.3 % and 21.1 % as compared to the RC control specimen, and the failure mode shifted from diagonal shear failure to flexural failure. To further investigate the dynamic responses of the beams, a detailed finite element model was established and validated with the test results in terms of the impact force, structural deflection and damage profile. The dynamic shear force and bending moment distribution diagrams were numerically derived to examine the failure mechanism of the test specimens. Finally, a parametric study was conducted to evaluate the effect of different impact locations and UHPC jacket length on the impact resistance of strengthened RC beams.

Dynamic and monotonic response of Monopile Foundations for Offshore wind turbines using centrifuge testing

The seismic response of monopile foundations is a growing area of research as the offshore wind industry expands worldwide, including in earthquake prone regions of the world. This paper presents dynamic centrifuge tests aimed at investigating the dynamic response of monopiles in both dry and saturated sandy soils. The latter case includes soil liquefaction under strong input motions, with measured excess pore pressures indicating liquefaction. The natural frequency of the monopile-soil system is experimentally determined by measuring the response to a sine sweep motion. Strong earthquakes are then applied at this frequency and its harmonics. This paper discusses the response of the monopile in terms of the peak accelerations observed in the dry and saturated tests, as well as using response spectra and amplification ratios. The dynamic bending moments along the pile are also measured to infer the bending moment profile with depth. Finally, two identical monopiles are pushed-over in each of the centrifuge tests to establish the pre and post-earthquake monotonic response, including the lateral stiffness and capacity, which are compared for the dry model tests and the saturated case.

Predicting the Response of RC Beam from a Drop-Weight Using Gene Expression Programming.

For structures and load-bearing beams under extreme impact loading, the prediction of the transmitted peak impact force is the most challenging task. Available numerical and soft computing-based methods for finding peak impact force are not very accurate. Therefore, a simple and user-friendly predictive model is constructed from a database containing 126 impact force experiments of the simply supported RC beams. The proposed model is developed using gene expression programming (GEP) that includes the effect of the impact velocity and the impactor weight. Also identified are other influencing factors that have been overlooked in the existing soft computing models, such as concrete compressive strength, the shear span to depth ratio, and the tensile reinforcement quantity and strength. This allows the proposed model to overcome several inconsistencies and difficulties residing in the existing models. A statistical study has been conducted to examine the adequacy of the proposed model compared to existing models. Additionally, a numerical confirmation of the empirical model of the peak impact force is obtained by reference to 3D finite element simulation in ABAQUS. Finally, the proposed model is employed to predict the dynamic shear force and bending moment diagrams, thus rendering it ideal for practical application.

Establishing the True Dynamic Bending Moment of Propeller Shaft Using a Single Bridge of Strain Gauge

The measurement of shaft bending (whirling) moment can be performed via a telemetry system including strain gauges which can obtain the bending stress. By using a single bridge of strain gauge, it was possible to obtain only the nominal bending moment. However, in case of the propeller shaft vibration measurement, the true dynamic bending moment is needed to evaluate the effect of propeller forces on the stability of the bearings. To deal with this, typically two bridges of strain gauge at 90 degrees are needed. This research presents a novel reliability assessment method in establishing the true dynamic bending moment using only one bridge of strain gauge. This is achieved by using the actual bending stress measured by strain gauge combined with its own phase lag stress at an angle of 90 degrees. To validate this technique, the experiments were performed under the rapid turning transient states during a sea trial of a 50,000 DWT oil/chemical tanker. As a result, great fluctuations in propeller force were detected, resulting in a non-uniform oil film in the bearings. The displacement sensor was also installed and confirmed the established true dynamic bending moment.

On the auto-oscillation effect of Kaplan rotors during load rejection

High vibrations due to auto-oscillation effects can occur at power units with Kaplan type runner during load rejection. These vibrations may be present in the turbine braking mode when the wicket gates are almost closed, and the rotating runner pushes the water towards the draft tube resulting in higher pressure below the runner blades. The upward leakage flow between runner blades and discharge ring is suspected to cause the vibration phenomenon.Within this contribution, a fluid-structure-interaction (FSI) technique is applied to identify the mechanism of self-excitation. The investigation is carried out on a disk that represents the simplified geometry of a Kaplan runner. Computational fluid dynamics (CFD) simulations are used in order to obtain parameters in terms of stiffness, damping and inertia of the fluid to be applied in the following shaft line analysis. Damped modal analyses of the shaft line allow for evaluation of the stability of natural frequencies and corresponding mode shapes of the shaft line. A resulting negative damping indicates the occurrence of auto-oscillation behavior of the shaft line. For the operating condition under investigation, mode shapes with negative damping are obtained with this approach and a dynamic bending moment on the runner due to lateral movement in combination with a tilting at the runner in these mode shapes is identified as source of instability.Based on these findings, an analytical approach for modeling the relevant effect is derived and compared to CFD result as well as results from acoustic finite element modelling. Finally, conclusions for avoidance of self-excited vibrations at Kaplan runners are proposed.