Combined Effects Of Bending Research Articles

Constitutive behavior of asymmetric multi-material honeycombs with bi-level variably-thickened composite architecture

Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties.

Comparison Between the Behavior of Reinforced Concrete Beams and RPC Beams Under Bending and Torsion Moments

Abstract Typically, the beams were subjected to bending and torsion moments especially at building edge. However, most of the studies focus on the flexural or torsional behavior of the beams independently, and few studies investigated these two combined effects. The research intends to explore the structural behavior of eight 1500mm x 200 mm x 150 mm rectangular beams that were tested under the combined effects of bending and torsional moments, with four main values of (T/M) ratio: pure bending, pure torsion, and two combined cases. The research investigates the effect of using reactive powder concrete (RPC) on beam behavior compared to normal concrete (NC). The outcome demonstrates that using RPC in beams instead of NC beams will significantly increases the cracking capacity by 136.4% in the case of pure bending and significantly increases the ultimate capacity by 118% in the case of combined moments with (T/M = 1). Also, using RPC leads to significant reduction in deflection and rotation values especially after beam cracking. RPC reduces compressive concrete strain and values of strains in longitudinal and transverse reinforcement especially in advanced loading stages.

Structural behavior of RPC beams subjected to flexural and torsional effects

This research is concerned with the behavior of reactive powder concrete beams (RPC) under the combined effects of bending and torsion moments, with three main parameters: torsional to bending moments ratio (T/M), longitudinal reinforcement ratio ( ), and transverse reinforcement ratio ( ). 12 rectangular reinforced RPC beams with dimensions of (1500 200 150) mm were tested. The outcome demonstrated that increasing the longitudinal reinforcement ratio from =0.009 to =0.016 improved the ultimate capacity significantly by 34.16%, and 35.54% in cases of (T/M) =0, and 0.5 respectively, also it significantly improved moment-deflection response in the case of (T/M) = 1, and well improved torque-rotation response in cases of (T/M)=0.5, and 1. Increasing the transverse reinforcement ratio from = 0.0042 to =0.0075 improved the ultimate capacity significantly by 49.22% in case of pure torsion and slightly improved it in other cases. Also it significantly improved moment- deflection response in case of (T/M) = 1 and improved torque -rotation response in cases of (T/M)=1and ꝏ.

Structural behavior of RPC beams subjected to flexural and torsional effects

This research is concerned with the behavior of reactive powder concrete beams (RPC) under the combined effects of bending and torsion moments, with three main parameters: torsional to bending moments ratio (T/M), longitudinal reinforcement ratio ( ), and transverse reinforcement ratio ( ). 12 rectangular reinforced RPC beams with dimensions of (1500 200 150) mm were tested. The outcome demonstrated that increasing the longitudinal reinforcement ratio from =0.009 to =0.016 improved the ultimate capacity significantly by 34.16%, and 35.54% in cases of (T/M) =0, and 0.5 respectively, also it significantly improved moment-deflection response in the case of (T/M) = 1, and well improved torque-rotation response in cases of (T/M)=0.5, and 1. Increasing the transverse reinforcement ratio from = 0.0042 to =0.0075 improved the ultimate capacity significantly by 49.22% in case of pure torsion and slightly improved it in other cases. Also it significantly improved moment- deflection response in case of (T/M) = 1 and improved torque -rotation response in cases of (T/M)=1and ꝏ.

Experimental and numerical investigation of flattened and bent miniature heat pipes with two heat sources for laptop computers

In this study, the combined effects of bending and flattening heat pipes with two heat sources on thermal resistance were numerically and experimentally studied. A composite wick of grooves and fibers was used in the heat pipe to prevent wick damage from the deformation of the heat pipe. The heat pipes were bent up to 90° and flattened to three final thicknesses of 2.5, 3.0 and 4.0 mm. Two discrete heat sources were supplied to the heat pipe, with a total heat load of 40 W. It was observed that not only damage to the composite wick was prevented but also the thermal performance of the heat pipe was slightly enhanced, particularly when a higher heat load was placed farther from the condenser. Bending the 3 mm final thickness heat pipe from 0° to 90° led to a 40.8% reduction in thermal resistance when supplying evaporator section 1 (located farthest from the condenser) at 30 W and a 25% reduction for another case when supplying 10 W at evaporator section 1. The mathematical models, generally used in previous studies, predicted the thermal resistance unsatisfactorily with a relative root mean square error of up to 70.74% compared with the experimental results. In this study, a novel mathematical model was developed to include the existence of liquid receding in the wick, a new concept of the contact factor at the heating surface, and the extension of an absorbable length in the fibrous wick. The proposed model provided a much better agreement with a relative root-mean-square error as low as 23.68%. Thus, the proposed mathematical model can provide better predictions of the thermal performance of the groove–fiber wick heat pipe.

A new perspective into torsional inelastic response of actively controlled irregular multistorey buildings

The nonlinear dynamics of irregular structures is influenced by both local and global torsional effects. In order to capture the inelastic structural response, the concept of plastic hinges is one of the most used tools due to its numerical efficiency. However, the combined effect of bending and torsion into the inelastic domain is scarcely illustrated in literature. In this paper, the recently developed 3D Force Analogy Method is augmented with an algorithm to consider axial force – biaxial bending moment –torque interaction. A structure having both plan and elevation irregularities is considered as a case study to illustrate the benefits of the proposed algorithm. The structural control concept is further implemented in the attempt to improve structural performance of irregular structures. A non-commercial Matlab/Simulink code is developed for the scopes of this paper.

Behavior of Steel Beams Subjected to Bending and Shear Loading Under Localized Fire Conditions

Civil structures were designed to carry a variety of loading during their service life, including fire hazards. As a result, providing fire safety to structural members is one of the most important tasks in civil infrastructure design. Steel structural members are subject to fire-induced damage or collapse due to their high heat conductivity and quick loss of strength and stiffness qualities. Furthermore, the failure in steel beams under the combined effects of bending, shear, and fire loading is poorly understood in the literature. A present study consists of experimental investigations on the fire response of steel beams under bending and shear dominant loading. The specimens have a constant length of 1250 mm. The total depth of the specimens was changed according to the section chosen: 4 in, 6 in, and 8 in (10 cm, 15 cm, and 20 cm). The results of tests show that beams can fail suddenly due to a high drop in yield and ultimate strength of the steel beam. the increase in temperature degree reduced greatly the yield and ultimate flexural strength of the steel beams with different sizes (for all groups). This reduction reached at some times to 50% for the ultimate strength capacity of the specimen. Shear strength is also affected greatly by fire exposure and the reduction reached to about 38%. Furthermore, the design strength capacity can only tolerate loads at low temperatures. This reduction in strength was noted under flexural and shear dominant loading. Moreover, the design strength capacity can withstand against loading at low-temperature degrees only.

Large-deformation mechanics of anti-curvature lattice materials for mode-dependent enhancement of non-linear shear modulus

Shear modulus assumes an important role in characterizing the applicability of different materials in various multi-functional systems and devices, such as deformation under shear and torsional modes and vibrational behavior involving torsion, wrinkling, and rippling effects. Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. In general, the lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt initially straight beams. While shear modulus and multiple other mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. In this article, we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the complementary deformed shapes of cell walls of honeycomb lattices under anti-clockwise or clockwise modes of shear stress as the initial beam-level elementary configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode of shear stress, leading to increased effective shear modulus. Within the framework of a unit cell based approach, initially curved lattice cell walls are modeled as programmed curved beams under large deformation. The combined effect of bending, stretching, and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame. Governing equation of the elementary beam problem is derived using variational energy principle based Ritz method. In addition to application-specific design and enhancement of shear modulus, unlike conventional materials, we demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress. The developed physically insightful semi-analytical model captures nonlinearity in shear modulus as a function of the degree of anti-curvature and applied shear stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattices would introduce novel exploitable dimensions in mode-dependent effective shear modulus modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.

Coupled bend–twist mechanics of biomimetic scale substrate

We develop the mechanics of combined bending and twisting deformation of a one-dimensional filamentous structure with protruding stiff fish-scale-like plates embedded at an angle on the surface. We develop a Cosserat kinematic formulation along with scale contact constraints. This geometrically exact model allows us to bypass the limitations of small deflection finite element computations, thereby preserving the accuracy of scale kinematics. The derived structure–property relationships reveal, for the first time, the combined effect of bending and twisting on a slender fish-scale inspired substrate. The model subsumes previous models on pure bending and pure twisting, but also shows previously unobserved phenomena that arise due to the coupled effects of these loads. These include a new interpretation of kinematic locking behavior, multiple contact regimes, asymmetric sensitivities of one curvature over the other, and discontinuous transitions in the nonlinear moment–curvature and torque–twist behaviors, reflecting the complex scale engagement patterns.

Investigations in twin-cell box girder bridges subjected to combined effects of bending and torsion

Investigations in twin-cell box girder bridges subjected to combined effects of bending and torsion

Analytical assessment of restraint forces and crack widths in end-restrained building slabs

This paper deals with the analytical assessment of restraint forces and crack widths in end-restrained building slabs. The analysis concentrates on the service limit state (SLS) and the challenge is hereby the appropriate consideration of the combined effect of axial restraint due to imposed deformations and bending cracking due to loading. As for the imposed deformations, the paper regards the drying shrinkage of concrete under indoor conditions, although any other temperature deformation or combination of shrinkage and temperature could be included accordingly.A deformation-based approach is presented, in which imposed deformations are made compatible with the released deformations of the slab due to opening of loading-induced bending cracks. The solution aims an appropriate inclusion of the most relevant effects while still providing a practicable and verifiable solution for the complex problem of assessing the restraint forces as well as the crack widths in end-restrained building slabs.The result of this approach is an analytical quantification of restraint forces to be transferred in the restraining members. In addition, the presented approach enables the determination of crack widths in the restrained conditions. An important asset of the analytical nature of this approach is the explicit correlation between individual system parameters, especially concrete properties and surrounding conditions, member dimensions and provided reinforcement, loading in the SLS and restraining condition.The paper includes the presentation of the general idea of a deformation-based assessment of end-restrained building slabs; the demonstration of this approach with an example from the literature; and the comparison of the analytical design solution with experimental results on the combined effect of bending and axial restraint in slab-like specimens.

Nonlinear numerical simulation for reinforced concrete elements with explicit time integration procedure

This study aims to assess numerically the behavior of a wide range of reinforced concrete (RC) components under bending or combined effect of bending and axial compression. Reference case studies of RC beams with different reinforcement ratios and beam-column joints are modeled using LS-DYNA software. When larger time step is used in modeling with implicit solvers, convergence problems may appear at higher degrees of nonlinearities, as the solution is reached through multiple iterations to reach equilibrium at every time step. To avoid these divergence issues, explicit time integration procedure is another alternative and can be used effectively in simulating dynamic problems. With minimizing inertia effects, this procedure can also be used to solve static and quasi static problems. In this study, explicit time integration procedure is utilized and the acting loads were applied slowly to minimize the inertia effects. Consequently, longer run time for the simulation process is needed with explicit time integration. Selective Mass Scaling (SMS) can be used to control the required run time by increasing the model critical time step by adding artificial mass to a limited number of stiff elements like, the transverse reinforcements. With this procedure, similar results to the reference experimental findings are obtained in terms of load-displacement curves, crack patterns and strains in the reinforcements. Models verification with different added masses are shown using grid convergence index (GCI) method. The main objective of this work, is to assess the accuracy of explicit solvers in modeling RC elements under quasi static loading. So that, they may be used with confidence for modelling different RC elements.

Theoretical and Experimental Free Vibration Analysis of a Loaded Curved Beam With Moving Boundaries

The present article theoretically and experimentally investigates free vibration characteristics of generalized curved beams with moving boundaries. The dynamic behavior is characterized about deformed configuration, attained under different concentrated loads, and rigidly connected to the midpoint of the beam. The coupled static and dynamic analysis of the geometric nonlinear problem is decomposed into two parts: the static problem dealing with large deformed configuration and the dynamic problem dealing with small amplitude free vibration of the deformed configuration beam. The analysis is carried out incrementally in embedded curvilinear coordinate frames using variational principle. The governing equation of the static problem is derived for a combined effect of bending and center line extension. The governing equation for free vibration is derived at the particular configuration of the updated beam geometry, using Hamilton's principle. The comparison between the numerical and experimental results successfully validates the proposed semi-analytical model and leads toward some meaningful observations.

A parametric study on geometrically nonlinear behavior of curved beams with single and double link rods, and supported on moving boundary

The paper presents a parametric study on effect of several geometric parameters on stress and deformation behavior of non-uniform curved beam with moving boundary. The parameters, considered in the present study, are height to span ratio of curved beam, ratio of radius of roller support to height of beam and types of support connection mechanisms. Effect of these parameters is observed for different curved profile shapes. Non-uniform initial curvature and combined effects of bending, stretching and warping of beam cross-section due to shear deformation are considered in the derivation of nonlinear strain-displacement relation in body fitted curvilinear frame. Based on the derived nonlinear kinematics and assumptions of large deformation but small strain and moderate initial curvature, nonlinear system governing equation is derived through variational principle based minimization of total potential energy method. An iterative numerical solution algorithm is developed and implemented in the computational environment of MATLAB® software to solve the nonlinear governing equation. The complicating effect coming from moving boundary imposes a kinematic constraint on the solution field. Hence, the solution methodology not only ensures energy balance of the system, but also satisfies shear force balance at each incremental load step. The geometric nonlinear incremental curved beam model is validated with deflection and stress results of commercial finite element software ABAQUS®. The geometry of master leaf spring of a previously reported study is considered as curved beam for the purpose of validation. After the validation study, results are generated for different curved profiles with two different combinations of support connection mechanisms and different height to span ratio for each type of them. In addition, to observe effect of roller radius, results are generated with different roller radius to height ratio for each type of the two curved beam systems. Investigations are made on the effects of the geometric parameters, support connection mechanisms and curved profile shape on large deflection characteristics of curved beam and the present study leads towards several meaningful observations.

Combined effect of bending and flattening on heat transfer performance of cryogenic sintered-wick heat pipe

Heat transfer characteristics of a cryogenic sintered-wick miniature bent and flattened heat pipe has been experimentally investigated in this paper. The heat pipes are made of oxygen free copper for the container and nitrogen is used as the working fluid. The wick was composite wick made from sintered copper powder and grooved copper pipe. The original cylindrical copper heat pipe was 6 mm in outer diameter and 200 mm in length. The heat pipes with the bending radius of 21 mm and the bending angle of 0°, 30°, 60° and 90° and the final thickness of 2.5, 3.0, 4.0 mm were constructed and tested. The operating temperature of heat pipe was at approximately 78.25 ± 0.10 K. It was found that the performance of the heat pipe in terms of thermal resistances depends on both bending angle and final thickness. Both bending and flattening affect the thermal resistance by increasing it. The bending increased the thermal resistance from 0.88 to 1.07 K/W (6 mm, 0° to 6 mm, 90°) and the flattening increased the thermal resistance from 0.88 to 2.24 K/W (6 mm, 0° to 2.5 mm, 0°). And the combined effect of bending and flattening increased the thermal resistance from 0.88 to 1.56 K/W (6 mm, 0° to 3 mm, 90°). The bending affects heat pipe by wick deformation that obstructs liquid flow. The flattening affects the thermal resistance by the collapse of wick structure which causes a broken liquid path of returned working fluid from the condenser to the evaporator and by liquid clogging in the condenser.

Accounting of the thread embedment in timber structures dowel-type joints. Load–slip relationship

This work is devoted to the development of a calculation proposal for dowel-type joints in timber structures that takes into account the increase in load capacity due to the use of threaded dowels. While the method is based on acknowledged criteria of structural standards, it also considers the crushed areas that appear in the timber near the zone of contact with the dowel’s thread. Thereby, it comes closer to the actual mechanical behaviour of the whole joint when it suffers a relative displacement between its different parts under an external load. The equations proposed in this study to define the load capacity of the joint take into account the rope effect produced by the axial forces arising on the dowel due to the combined effect of bending of the dowel and compression of the timber fibres embedded in its thread. A comparison of the results of the new analytical method proposed with those of a battery of experimental tests is shown.

Motion track modeling and analysis of belt spindle under combined effects of bending moment-torque-thermal deformation

The motion track of belt spindle is important for the radial error of belt spindle. An analytical modeling method for the motion track of belt spindle under the combined effects of bending moment-torque-thermal deformation is proposed in this paper. Three running phases of belt spindle have been analyzed and modeled: the start-up phase with leaping change due to the change in force and bending moment, the accelerating phase with axis deflection, and the constant speed phase with axis regression because of the combined effects of bending moment-torque-thermal deformation. The simulation and test were completed on the belt spindle of SKVM850 machine tool, which illustrates the variation law of the radial error of belt spindle during the whole running phases.

A fracture mechanics analysis of cutting and machining

The process of cutting and machining is analysed using concepts developed in the fracture analysis of beam specimens. Increasing cutting forces and decreasing tool rake angles lead to a sequence of deformation processes from elastic bending to elastic–plastic bending and finally to shear yielding in the chip. The conditions for each mode of deformation are identified. Fracture toughness is included in the analysis as is, in addition, the notion of root rotation at the crack tip. Under some circumstances this gives rise to the condition of the tool tip touching the crack tip during which energy is transferred directly to the fracture process. The tool–chip interface is characterised by Coulomb friction and by the inclusion of an adhesion toughness to model the effects of hot polymeric chips sticking to the rake face of the tool. The combined effects of bending and shearing leading to chip curling and coiling are also analysed.

Direct Design of Partially Prestressed Concrete Hollow Beams

Tests were conducted on three hollow partially prestressed concrete beams subjected to combined loading in bending, shear and torsion. The beams were designed using the Direct Design Method which is based on the Lower Bound Theorem of the Theory of Plasticity. All beams were of 300 × 300 mm cross-section, 3.8 m in length, and possessed a 200 × 200 mm hollow core and 50 mm wall thickness. The two main variables studied were the ratio in the web of the maximum shear stress due to the twisting moment, to the shear stress arising from the shear force, which varied between 1.09 and 6.85, and the ratio of the maximum twisting moment to the maximum bending moment which varied between 0.35 and 2.62. Good agreement was found between design and experimental failure loads. All beams failed near the design loads and underwent ductile behaviour up to failure. The results indicate that the Direct Design Method can be successfully used to design partially prestressed concrete hollow beams which will cater for the combined effect of bending, shear and torsion loads.

Combined effects of bending and elongation on polymer optical fiber losses

The combined effects of bending and elongation on fiber losses as rays propagate along deformed polymer optical fibers (POFs) are investigated. The variations in power attenuation for various curvature radii and elongations are studied. The experimental results indicate that the combination of bending and elongation significantly affects the power loss of POF. From the results an equation is proposed to predict the power losses for different bent radii and elongations. The maximum difference between the proposed equation and the experimental results is less than 5%.