External Bending Moment Research Articles

Closed-form solutions for axially non-uniform Timoshenko beams and frames under static loading

This paper presents the Green’s Functions Stiffness Method (GFSM) for solving linear elastic static problems in arbitrary axially non-uniform Timoshenko beams and frames subjected to general external loads and bending moments. The GFSM is a mesh reduction method that seamlessly integrates elements from the Stiffness Method (SM), Finite Element Method (FEM), and Green’s Functions (GFs), resulting in a highly versatile methodology for structural analysis. It incorporates fundamental concepts such as stiffness matrices, shape functions, and fixed-end forces, in line with SM and FEM frameworks. Leveraging the capabilities of GFs, the method facilitates the derivation of closed-form solutions, addressing a gap in existing methods for analyzing non-uniform reticular structures which are typically limited to simple cases like single-span beams with specific axial variations and loading scenarios. The effectiveness of the GFSM is demonstrated through three practical examples, showcasing its applicability in analyzing non-uniform beams and plane frames, thereby broadening the scope of closed-form solutions for axially non-uniform Timoshenko structures.

Mechanical Behavior Monitoring and Load Inversion Analysis of Large-Diameter Underwater Shield Tunnel during Construction.

The construction of large-diameter shield tunnels underwater involves complex variations in water and earth load outside the tunnel segment, as well as intricate mechanical responses. This study analyzes the variation laws of external loads, axial forces, and bending moments acting on the segment ring during the shield assembly and removal from the shield tail. It accomplishes this through the establishment of an on-site monitoring system based on the Internet of Things (IoT) and proposes a Bayesian-genetic algorithm model to estimate the water and earth pressure. The fluctuation section exhibits a peak load twice as high as that in the stable section. These variations are influenced by Jack thrust, shield shell force, and grouting pressure. The peak load observed in the fluctuation section is twice as high as the load observed in the stable section. During the shield tail removal process, the internal forces undergo significant fluctuations due to changes in both load and boundary conditions, and the peak value of the axial force during the fluctuation section is eight times higher than that during the stable section, while the peak value of the bending moment during the fluctuation section is five times higher than that during the stable section. The earth and water pressure calculated using the inversion analysis method, which relies on the measured internal forces, closely matches the actual measured values. The results demonstrate that the accuracy of the water and earth pressure obtained through inversion analysis is twice as high as that obtained using the full coverage pressure method. These results can serve as a valuable reference for similar projects.

Analytical frequency-domain solution for Euler-Bernoulli frames with semi-rigid connections

This paper presents a novel method for analyzing the dynamic response of plane Euler-Bernoulli frames with semi-rigid connections subjected to arbitrary external loads and bending moments. The proposed solution methodology is the Green’s Functions Stiffness Method (GFSM) in the frequency domain. The GFSM is a mesh reduction method closely related with the Finite Element Method (FEM) sharing with it key components such as shape functions, fixed end forces, and stiffness matrices. By capitalizing on the strengths of both FEM and Green’s Functions, the GFSM facilitates the derivation of closed-form solutions for structural analysis. The formulation is initially established in the frequency domain and is later transformed into the time domain using the fast Fourier transform algorithm. To illustrate the applicability of the method, an example involving a one-bay, one-storey plane frame with semi-rigid connections is presented.

Modeling the joint rotational stiffness of a radial-type flight intersection joint: An analytical approach, numerical simulation, and experimental validation

Joint rotational stiffness (JRS) of a flight intersection joint (FIJ) and its accurate quantification play an essential role in studying the dynamic modal characteristics of a flight vehicle. This JRS of a FIJ is mostly determined through elaborate experiments due to the non-availability of a reliable predictive model. Therefore, in this paper, an analytical model is proposed to evaluate JRS of a radial type FIJ when subjected to external bending moment. In this model, at first, the tensile and compressive part of the FIJ section is identified by determining the neutral axis position. The respective part's contributing stiffness is then estimated by employing a spring-mass model. Later, the JRS expression is derived from the moment equilibrium condition and expressed as a function of the stiffness of the tensile and compressive part and neutral axis position. Subsequently, finite element analysis (FEA) is conducted with different numbers of screws, followed by detailed experimental investigations. The proposed analytical model is validated with the results from FEA and experiments for different screw configurations of FIJ. Further, the proposed model is extended to account for the effect of joint clearances on the JRS and the corresponding moment-rotation characteristics of the FIJ.

Shear stress migration in a tapered girder with trapezoidal corrugated steel webs

This study conducted a comprehensive investigation into the shear stress migration of a tapered prestressed concrete (PC) continuous box girder bridge with trapezoidal corrugated steel webs (TCSWs) throughout the entire construction process, including cantilever construction, structural system transformation and external prestressing tendon tensioning. The results revealed that the basic assumptions, which state that TCSWs bear all the shear force and that only the vertical component of the external prestressing contributes to shear stress when considering its contribution, are not valid for the shear design of tapered PC girder bridges with TCSWs. The horizontal component of the external prestressing and bending moments can cause additional shear forces via the Resal effect, which results in the migration of the shear stresses between the curved bottom concrete slabs and TCSWs. This study investigated the mechanism through which the Resal effect and external prestressing influence the migration of shear stress in the entire construction process. The results revealed that within continuous girders, the Resal effect exhibits both positive and negative implications. Specifically, the negative Resal effect exerts an unfavorable influence, resulting in an increase in the shear stress experienced by the TCSWs. Moreover, this study introduced a modified shear method that that takes into account the influence of bending moments and the horizontal component of external prestressing. In contrast to basic shear methods, this approach provides notably heightened accuracy.

Thin-walled cylindrical shells in engineering designs and critical infrastructures: A systematic review based on the loading response

Abstract Cylindrical shell structures are ubiquitous and essential supporting structures in various engineering applications. The aim of this research work is to provide a comprehensive overview of the behavior of cylindrical shell structures under different loading conditions, including external pressure, axial compression, and bending moment. The study found that the behavior of cylindrical shells was affected by their geometry, including diameter, length, thickness, and imperfections. These factors should be carefully considered in the design and analysis of cylindrical shells. Additionally, stiffeners and sandwich structures can be applied to improve the structural performance of cylindrical shells under different loading conditions. The work also highlighted the latest research trends in the field, such as the use of advanced materials, and numerical simulations to improve the understanding and design of cylindrical shell structures. Overall, this study has provided a valuable resource for engineers and researchers working on cylindrical shell structures, helping them to design and analyze the cylindrical shell structures more efficiently and effectively.

МОДЕЛЮВАННЯ РОБОТИ ПІДСИЛЕНОГО ПОПЕРЕДНЬО НАПРУЖЕНОГО ЗГИНАЛЬНОГО ДЕРЕВ’ЯНОГО ЕЛЕМЕНТУ

An undeniable disadvantage of wood when using it in construction is its excessive flexibility. One of the ways to increase the stiffness of wooden elements is to use prestressing and reinforcement with stiffer elements. The manufacturing process of pre-stressed bending elements proposed by us is simple. However, determining the necessary effort, the necessary bending of the beam to ensure reliable operation, preventing the destruction of the element is quite difficult. One of the methods of prestressing is described, namely, the method by which the beam receives internal stresses due to the release of the bending element after the action of the external load by gluing reinforced elements. The principle of such tension can be described in the following sequence: 1. We create a bend in the bending element by applying an external load to the element. 2. We reinforce the lower zone of the bending element. At the same time, we need to know under which stress-strained state the reinforced element was installed, so that its operation can be predicted. 3. We remove the applied force with which we created the bend in the flexible wooden element, while the element wants to acquire its original shape, but this will be prevented by the armature, which will absorb part of the load and leave a small bend. It was established that the level of prestressing, namely the curvature acquired by the bending element after prestressing, depends on the initial curvature of the wooden element, as well as on the area and physical and mechanical characteristics of the materials reinforcing the beam zones. To determine the prestress, it is necessary to establish the stress-deformed states of the bending element, which occur after gluing and release of the external force. At the same time, 3 levels of the stress-strain state can be distinguished. 1. At the first stage, the compressed zone is more than the stretched zone. The relative deformations of the compressed lower zone, where the material is to be attached, is the initial start for the work of the reinforced element. 2. At the second stage, the external bending moment decreases, the internal redistribution of forces takes place, in addition to the moment perceived by the compressed and stretched zone, a moment also occurs in the stretched reinforced element. 3. The third stage is characterized by the absence of an external load, and this causes a balance between the internal forces of the bending prestressed element. The equilibrium equation for three stages was obtained. When using the element as a load-bearing structure, the cross-section in the element can be with both positive and negative curvature. The peculiarities of these two stress-strain states are manifested in the change in the position of the compressed and stretched zones. In the first case, the compressed zone is located in the lower part of the element and the upper part is occupied by the stretched zone. After the curvature changes its sign from negative to positive, the upper part becomes compressed, and the lower part becomes stretched. As a result of the simulation, it is possible to conclude that the cross-section of a bending wooden element undergoes 3 main stress-deformed states during prestressing and two during its operation

Closed-form solution for non-uniform Euler–Bernoulli beams and frames

Non-uniform elements, such as non-prismatic and those made from composite materials, are commonly used in structures. This is because the variation in their internal forces makes uniform elements less effective to withstand the external loads. This paper presents the formulation of the Green’s Functions Stiffness Method (GFSM) for the static analysis of non-uniform Euler–Bernoulli frames subjected to arbitrary external loads and bending moments. The GFSM is a mesh reduction method that combines the strengths of the Stiffness Method (SM) and the Finite Element Method (FEM) with those of Green’s functions, resulting in an analytic method for obtaining closed-form solutions of reticular structures. As a particular case, the GFSM is closely related to the Transcendental Finite Element Method (TFEM), which allows to obtain closed-form solutions from an implementation of the latter by only making changes at the post-processing stage. Two examples are provided with the analysis of a beam and a plane frame. Additionally, two appendices are included with the particularization of the GFSM for some specific non-uniform elements, and general stepped elements.

Closed-form solution of Timoshenko frames using the Green’s Function Stiffness Method

This paper presents the formulation of the Green’s Function Stiffness Method (GFSM) for the static analysis of Timoshenko frames subjected to arbitrary external loads and bending moments. The GFSM is a novel analytic method that provides closed-form solutions of structures by combining the strengths of the Stiffness Method (SM) (exact relation between forces and displacements at the element ends) and Green’s functions (GF) (analytical closed-form structural response to any arbitrary external load). The GFSM is based on the classical idea of decomposing the solution of differential equations into homogeneous and particular (fixed) solutions, with the latter computed through superposition integrals using Green’s functions of fixed elements as kernels. Its principal aim is the computation of the displacements fields, while the internal forces are calculated directly from their derivatives. The GFSM is directly related to the SM and the Finite Element Method (FEM), making its numerical implementation easily performed from either of them. Additionally, the basic ideas behind the GFSM can be easily extended to other physical fields. An example is presented to show the advantages of the proposed method.

Closed-form solution of Timoshenko frames with semi-rigid connections

The response of steel frame structures is highly influenced by the degree of rotational stiffness of the connections between beams and columns, which are characterized by nonlinear moment–rotation (M−θr) curves. Design codes such as the ANSI/AISC 360-16 and the Eurocode 3 specify that the effect of the joints rotational stiffness should be included in the linear and/or nonlinear structural models used in the steel design process. To model the effect of the degree of rigidity between structural elements, it is a common practice to use zero-length semi-rigid connections. This paper presents the static formulation of the Green’s Functions Stiffness Method (GFSM) for prismatic Timoshenko frames with zero-length elastic semi-rigid connections subjected to arbitrary external loads and bending moments. The GFSM is a novel analytical method based on the classical Stiffness Method (SM), and the Green’s Functions (GFs), for the computation of closed-form solutions of the response of structures. This method is formulated from the decomposition of the structural response into two complementary parts: a homogeneous response (related to the stiffness matrix and the shape functions) and a particular or fixed response (associated with the load vector and the fixed displacement field), the latter computed using GFs of fixed elements. An example of a one-bay one-storey two-dimensional frame is presented.

Simulation Research on Continuous Concrete Beams Reinforced with External Prestressed CFRP Tendons.

This paper examines the effects of different loading patterns on the static characteristics of continuous concrete beams reinforced with external prestressed carbon fiber-reinforced polymer tendons (EPCFRPT) and qualitatively analyzes the results for two continuous concrete beams: SB-1 under symmetrical loading, and SB-2 under asymmetrical loading. Then, a finite element analysis model is introduced and calibrated by tests conducted at Southeast University and data collected from a literature review. Based on the FEA model, the initial prestress, cross-section area, and eccentricity of CFRP tendons as well as the steel reinforcement configuration were selected by a parametric study. The results indicated that the initial prestress and tendon cross-section area had the most influence on the tendon stress increment and the secondary bending moment of the middle support, while the reinforcement distribution and eccentricity of the tendons had little effect. The secondary bending moment had a linear positive correlation with the stress increment of tendons. These results allow a simplified equation for calculating the external load bending moment amplitude coefficient at ultimate to be proposed.

Modification of SDOF model for reinforced concrete beams under close-in explosion

In this paper, a modified single-degree-of-freedom (SDOF) model of reinforced concrete (RC) beams under close-in explosion is proposed by developing the specific impulse equivalent method and flexural resistance calculation method. The equivalent uniform specific impulse was obtained based on the local conservation of momentum and global conservation of kinetic energy. Additionally, the influence of load uniformity, boundary condition and complex material behaviors (e.g. strain rate effect, hardening/softening and hoop-confined effect) was considered in the resistance calculation process by establishing a novel relationship between external force, bending moment, curvature and deflection successively. The accuracy of the proposed model was verified by carrying out field explosion tests on four RC beams with the scaled distances of 0.5 m/kg1/3 and 0.75 m/kg1/3. The test data in other literatures were also used for validation. As a result, the equivalent load implies that the blast load near the mid-span of beams would contribute more to the maximum displacement, which was also observed in the tests. Moreover, both the resistance model and test results declare that when the blast load becomes more concentrated, the ultimate resistance would become lower, and the compressive concrete would be more prone to softening and crushing. Finally, based on the modified SDOF model, the calculated maximum displacements agreed well with the test data in this paper and other literatures. This work fully proves the rationality of the modified SDOF method, which will contribute to a more accurate damage assessment of RC structures under close-in explosion.

Study on the cell configurations and mechanical strength of planar-type solid oxide fuel cells

For solid oxide fuel cells, the following cell configurations have been developed: electrolyte-supported cell (ESC), anode-supported cell (ASC), and metal-supported cell (MSC). In this study, to compare the mechanical load tolerance corresponding to each of the abovementioned cell configurations, the curvature and residual stress were calculated using the Euler–Bernoulli beam theory. The results indicated that when the cells were flattened under the application of an external bending moment, the stress gradient in each layer of the cell disappeared, and the maximum stress in the cell was shown to decrease. Eventually, the failure probability of the cell substrate was demonstrated to take the smallest value. The allowable bending moments for the cell substrates were as follows: −0.17 to 0.08 Nm for ESC, −0.18 to 0.11 Nm for ASC, and −0.29 to 0.40 Nm for MSC at room temperature. Thus, MSC was found to possess the highest bending moment tolerance.

Study on the characteristics of pipe buckling strength under pure bending and external stress using nonlinear finite element analysis

Buckling and collapse are important failure modes for laying and operating conditions in a subsea position. The pipe will be subjected to various kinds of loads, i.e., bending moment, external pressure, and tension. Nonlinear finite element analysis was used to analyze the buckling strength of the pipe under pure bending and external pressure. The buckling of elastic and elasto-plastic materials was also studied in this work. The buckling strength due to external pressure had decreased and become constant on the long pipe when the length-to-diameter ratio (L/D) was increased. The non-dimensional parameter (β), which is proportionate to (D/t) (σy/E), is used to study the yielding influence on the buckling strength of pipe under combined bending and external pressure loading. The interaction curves of the buckling strength of pipe were obtained, with various the diameter-to-thickness ratio (D/t) under combination loads of external pressure and bending moment. For straight pipes L/D = 2.5 to 40, D = 1000 to 4000 mm, and D/t = 50 to 200 were set. The curved pipes D/t = 200, L/D =2.5 to 30 have been investigated by changing the radius of curvature-to-diameter ratio (R/D) from 50 to ∞, for each one. With decreasing R/D, the buckling strength under external pressure decreases slightly. This is in contrast to the bending of a curved pipe. When the value of R/D was decreased, the flexibility of the pipe was increased. However, the buckling strength of the pipe during bending was decreased due to the oval deformation at the cross-section.

Influence of number of studs on compliance of a flight intersection joint

Flight intersection joints are temporary joints used to integrate one airframe section with another. They are characterized by their capacity to resist the rotational flexibility when subjected to an external bending moment, commonly termed as the joint rotational compliance (JRC). Currently, JRC is quantified mostly by extensive experiments on the flight intersection joints. The influence of number of studs in a stud-pocket type intersection joint on JRC is not yet well understood in literature which is addressed in this paper through numerical simulations. The variation in joint compliance and its dependence on number of studs are brought out through the analysis of circumferential distribution of joint displacement, JRC and joint rotational stiffness.

Numerical Analysis of Initially Imperfect Pretensioned Bolted Connections

Bolted steel end-plate rigid connections are used to transfer straining actions between different parts of steel structures. However, during structural assembly some of these connections are erected with initial imperfections in form of gap between connected parts. This paper investigates numerically initially imperfect end plate connections subjected to major external bending moment and major shearing force. A finite element model (FEM) is developed to represent the behavior of these initially imperfect connections. The presented FEM is verified against experimental testing presented by the authors in previous work. The effect of the gap angle between connected parts on the connection bending strength and moment-curvature relationship is investigated by varying its value from 1.5° to 6°. The results of initially imperfect connections are compared to those of perfect ones and it is concluded that the loss in bending strength of imperfect connections varies from 11.5 % to 22 % for gap angles from 1.5° to 6° respectively.

Improvement and validation of residual stress measurement in composite laminates using the incremental hole-drilling method

In this paper, the incremental hole-drilling (IHD) method has been improved by attaching strain gauge rosettes on both top and bottom surfaces, and changing the calculation algorithm for solving the ill-conditioned problem. In order to assess the feasibility and accuracy of the improved IHD method, an experiment of measuring the in-plane stress distribution in a composite laminate under bending was proposed. The composite laminate, which is bended by an external pure bending moment and fixed in a stable state, contains an in-plane stress distribution with obvious gradients in thickness direction, which is essentially similar to residual stresses. A plain woven T800H/803 specimen was tested in the proposed experiment with the improved IHD method. The results calculated using both top-surface and bottom-surface measured strains, and by iteration algorithm, showed good agreement with the finite element method (FEM) simulation and high calculation efficiency.

Research on Fatigue Mechanical Properties of Austenitic Stainless Steel for Marine Environment

Jiang, Z.; Wang, J., and Cao, D., 2020. Research on fatigue mechanical properties of Austenitic stainless steel for marine environment. In: Wan, Z. (ed.), Coordinated Sustainable Development in Coastal Areas: Environment and Economy. Journal of Coastal Research, Special Issue No. 109, pp. 191–196. Coconut Creek (Florida), ISSN 0749-0208.Austenitic stainless steel is widely used in the marine environment because of its good strength, corrosion resistance, and weldability. However, the environment in the ocean is extremely complex and changeable, and the equipment may bear the combined action of static loads such as axial force, internal and external pressure, bending moment, and extreme temperature conditions. At the same time, it also bears the action of dynamic loads such as alternating external pressure, wave force, current force, which easily leads to fatigue damage of components. This study introduced the deformation behavior of austenitic stainless steel for the marine environment. In addition, the effects of oxidation damage and creep damage during fatigue deformation are summarized, and the dynamic strain aging effect in the process of fatigue deformation is described. It is very important to study fatigue behavior in a complex service environment.

Application and Performance Analysis of Intelligent Soft Materials in Oil and Gas Exploitation

In deep-sea oil and gas development, the problem faced by traditional materials is to consider the driving force of new material application. Soft matter science involves many fields such as mechanics, physics, biology, materials, chemistry and so on. It is regarded as a science in the 21st century and has received widespread attention in the world in recent years. The composition of soft matter is complex, and its motion does not depend on the atomic or molecular scale quantum mechanical action in the constituent units. During installation and service of deep water oil and gas transmission pipelines, the stress conditions are complicated, which not only meet the conditions of single load such as external hydrostatic pressure and bending moment, but also meet the conditions of combined action of external hydrostatic pressure and bending moment. The research and large-scale application of the physical mechanism of intelligent materials will lead to a major revolution in the development of material physics science. This paper analyzes the application and performance of intelligent soft materials in oil and gas exploitation.

Incorporating subject-specific geometry to compare metatarsal stress during running with different foot strike patterns

Stress fracture of the second metatarsal is a common and problematic injury for runners. The choice of foot strike pattern is known to affect external kinetics and kinematics but its effect on internal loading of the metatarsals is not well understood. Subject-specific models of the second metatarsal can be used to investigate internal loading in a non-invasive manner. This study aimed to compare second metatarsal stress between habitual rearfoot and non-rearfoot strikers during barefoot running, using a novel subject-specific mathematical model, including accurate metatarsal geometry. Synchronised force and kinematic data were collected during barefoot overground running from 20 participants (12 rearfoot strikers). Stresses were calculated at the plantar and dorsal periphery of the midshaft of the metatarsal using a subject-specific beam theory model. Non-rearfoot strikers demonstrated greater external loading, bending moments and compressive forces than rearfoot strikers, but there were no differences in peak stresses between groups. Statistical parametric analysis revealed that non-rearfoot strikers had greater second metatarsal stresses during early stance but that there was no difference in peak stresses. This emphasises the importance of bone geometry when estimating bone stress and supports the suggestion that external forces should not be assumed to be representative of internal loading.