Rigidity Ratio Research Articles

Flexural rigidity and ductility of RC beams reinforced with steel and recycled plastic fibers

This study compares between the mechanical properties of concrete either reinforced with recycled plastic (RP) or end-hooked steel (EHS) fibers with volume fractions of 1, 2 and 3%. Also, the effects of the fiber type and volume fraction on flexural responses were investigated using experimental program composed of seven reinforced concrete (RC) beams. Generally, results showed that the RP and EHS fibers remarkably enhanced both the mechanical characteristics of concrete and the flexural capacity of RC beams. Specifically, concrete matrix that reinforced with 2% volume fraction of RP or EHS fibers exhibited the highest capacities among all tested specimens. On the other hand, the compressive and the tensile strengths of the fibrous concrete which strengthened with 3% volume fraction (either RP or EHS fibers) were lower than their counterparts that reinforced with lower volume fraction (2%). As the fiber volume fraction increased up to 2%, the peak load of the RC beams increased followed by a reduction for higher fiber volumes. The peak load of the RC beam specimens reinforced with 2% of RP and EHS fibers were 57.1 kN and 60.7 kN, respectively compared to 39.6 kN for the control RC beam. Both RP and EHS fibers had a positive effect on the (effective/gross) flexural rigidity ratio, especially when used with volume fraction lower than 3%. RC beams reinforced with 1% of RP and EHS fibers yielded higher ductility in comparison with 2 and 3%. An analytical model constructed based on the distribution of stress-strains along the height of the RC beam was used to estimate the bending moments at different stages. Results well agreed with the experimental records.

Features of the Personal Anxiety and Mental Rigidity Ratio in the Structure of Alexithymia

The purpose of the current study was to determine the components of personal anxiety and mental rigidity, the significance of their severity and combination in the structure of alexithymia. Materials and methods. The study was conducted on 377 apparently healthy men and women aged 20-25 years. The assessment of the level of alexithymia in points was carried out using the 20-item Toronto Alexithymia Scale in the Russian version, then all participants were passed the Differential Assessment of Personal Anxiety Test and the Differentiated Mental Rigidity Assessment Test to determine the corresponding characteristics. The study participants were divided by gender, and each group into subgroups depending on the level of alexithymia severity. Results. Analysis of the average values revealed an increase in both the general levels of personal anxiety and mental rigidity with an increase in alexithymic potential, and individual components of these signs. A factor analysis was performed to identify the ratios of personal anxiety and mental rigidity components depending on alexithymia severity. It was revealed a three-factor structure with the greatest loads on the affective and cognitive components. With correlation analysis, the structures of the subscales of the Toronto Alexithymia Scale were investigated, and it was revealed that they are, to a high degree of probability, formed by various combinations of personal anxiety and mental rigidity components. Conclusion. The investigation confirmed the complex heterogeneous and multidimensional structure of the alexithymic potential and the essential role of various ratios of personal anxiety and mental rigidity components in its profile.

Experimental flow analysis of vertical axis turbine for power generation in open channel system

In this experimental study, flow structure over a three bladed vertical axis Darrieus turbine is investigated experimentally for Reynold Number, Re=9000 in an open channel. Rigidity ratio (σ), angle of attack, optimum values of blade chord length (CL), turbine radius (R) and height of turbine blades (H) are used as approximately 1.1 and α=-2°, CL=5 cm, R=13.75 cm and H=20 cm, respectively. According to the values, ¼ scale model of a vertical axis Darrieus turbine has been used in order to perform experimental flow analysis. In experimental flow analysis, two different azimuth angles, θ=270° and θ=240° are used to examine the flow characteristics in the Particle İmage Velocimetry (PIV) experiments. As a result of the experiments, time averaged velocity vectors , averaged streamlines , and averaged vortex fields , are obtained and interpreted time averaged velocity vectors , averaged streamlines , and averaged vortex fields , changes with the turbine blade positions. As a result, it is seen that turbine azimuthal angle affetcs the flow structure and streamline focal points, positive and negative vortex are formed in the flow region behind the turbine. Only one focal point at θ=240° is occurred while two focal points and one stagnation point are occurred at the angle of θ=270°.

Feasibility Study of Using Engineered Cementitious Composite and High-Strength Bars in Rigid Bridge Piers Based on Seismic Vulnerability Analysis

The main function of pier is to transmit the load from superstructure to foundation reliably. Under earthquake action, the main failure reason of bridge is the damage of bridge pier. The application of some high-performance materials is helpful to improve the seismic performance of bridge piers. Based on seismic vulnerability analysis, this paper studies the feasibility of using engineered cementitious composite (ECC) and high-strength bars in bridge piers. Taking a rigid pier as an example, a nonlinear numerical model is established by OpenSees software. The reasonable replacement height of ECC in plastic hinge regions, stirrup ratio of pier section, and replacement rate of high-strength bars are obtained through the seismic performance analysis of the pier. Then, seismic vulnerability of rigid pier with ECC and high-strength bars is analyzed. The results show that it is feasible to improve the seismic performance of the piers by using ECC and high-strength bars. Considering the economic rationality, the replacement height of ECC in plastic hinge regions can be determined according to the curvature change point. For the rigid pier, the economical and reasonable volume stirrup ratio is 0.78%. The ultimate curvature of RC/ECC pier bottom increases by 12.4% when the longitudinal bars of the pier are replaced by high-strength bars, and the energy dissipation capacity increases by 22.5% on average. Compared with the pier’s original design, the exceedance probability of each limit state of the rigid pier with ECC and high-strength bars is significantly reduced. Its seismic performance is superior, and the risk of seismic damage is significantly reduced.

Simulation of road treatment costs based on life-cycle cost analysis

Flexible pavement is the most widely used type of road pavement in Indonesia. The main factors in the selection of flexible pavements are the low initial cost and the limited budget for road maintenance. This study aims to examine the level of comparison of road treatment costs based on life-cycle cost analysis (LCCA) rigid and flexible pavement for 40-years analysis period. The road treatment simulation uses road deterioration models based on the equation in the second version of the HDM-4 manual with the International Roughness Index (IRI) and the treatment period as the main variable. Based on the LCCA, The NPV analysis showed that the rigid pavement treatment cost ratio is 0.818 or more economical 18.20% at a 10% discount rate and 0.915 or more economical 8.48% at a 12% discount rate than the flexible pavement. Meanwhile, the EUAC analysis result showed that the rigid pavement treatment cost ratio is 0.847 or more economical 15.31% at a 10% discount rate and 0.862 or more economical 13.79% at a 12% discount rate compared to flexible pavement. The results showed that the rigid pavement treatment cost was more efficient 8.48% - 18.20% compared to flexible pavement.

Dynamic Response of a Bridge–Embankment Transition with Emphasis on the Coupled Train–Track–Subgrade System

Dynamic response of a bridge–embankment transition is determined by, and therefore an indicator of, the coupled train–track–subgrade system. This study aims to investigate the approach of coupling the train–track–subgrade system to determine the dynamic response of the transition. The coupled system is established numerically based on the weak energy variation, the overall Lagrange format of D’Alembert’s principle and dynamics of the multi-rigid body, which is verified by in-site measurements. With this model, the influence of rail bending, differential settlement and other factors on the dynamic performance of the transition system is analyzed. The results show that when the train driving speed is 350 km/h, basic requirements should be satisfied. These requirements include that the irregularity bending of the bridge–embankment transition section should be less than 1/1000, the rigidity ratio should be controlled within 1:6, and the length of the transition section should be more than 25 m. In addition, the differential settlement should not exceed 5 mm. Among these factors, the differential settlement and the bending of the rail surface are the main ones to cause the severe dynamic irregularity of the transition section. Our analysis also indicates a requirement to strengthen the 18 m and 25–30 m distance from the abutment tail and the bed structure.

Evaluation of flexural stiffness on mechanical property of dual row retaining pile wall

The traditional pile design method of dual-row pile wall (DRPW) occasionally considers the effect of flexural stiffness ratio between front row (FR) to rear row (RR). DRPW can no longer satisfy the requirements of settlement and deformation for substantial digging depth. This study evaluated the influence of flexural stiffness on DRPW and proposed an optimization method, namely, variable stiffness technology. Two optimal types of DRPW, namely DRPW with enlarged section of FR and that with enlarged section of RR, were compared to the traditional equal-section DRPW. The effects of flexural stiffness ratio, excavation depth, and surcharge loading were investigated in this study using physical scale test and finite-difference method. The model piles were instrumented with strain gauges and dial meters to measure the bending moment and deflection, respectively. The three types of DRPW have the same volume, height, sum of cross-section area, and material. Favorable consistency was observed between the numerical simulation and model test. Overall, the flexural rigidity ratio of FR to RR has a remarkably impact on the mechanical property of DRPW; thus, increasing the stiffness of the front pile is effective. The three types of pile arrangement are ranked as follows: the DRPW with enlarged section of front pile > the DRPW with enlarged section of rear pile > the traditional equal-section DRPW.

Theoretical and experimental investigations on the effects of friction, bending rigidity, extensibility, and Poisson's ratio on fabric tensile properties

A three-point tensile model that consists of a noncontact model and a modified capstan model of contact sections, including coupling effects of factors, is established in this study. The tension ratio calculated using the Runge–Kutta method increases along with the extensibility, surface friction coefficient, and radius ratio and is inhibited by the power-law friction ([Formula: see text]). Moreover, the theoretical model in a case with all the factors and frictional modification shows high accuracy with the actual test of the quick-intelligent handling evaluation system, and the Poisson's effect can be negligible, especially with the power-law friction. It has been confirmed that greater surface roughness and thickness (lower radius ratio) with worse extensibility result in tighter fabric tensile properties. Therefore, this work can provide theoretical guidance for the measurement of fabric tensile properties and the evaluation of practical application of fabrics.

Investigation of cusp catastrophe model of rock slope instability with general constitutive equations

The unsteadiness of rock slopes is often triggered by water-softening. Based on catastrophe theory and the general constitutive equations of the strain-softening section in the weak interlayer, the present study investigated the catastrophic failure mechanism of rock slopes. Using theoretical analysis, the cusp catastrophe model for the failure of a rock slope with a strain-softening section in the soft rock strata was established, and the balance equation, bifurcation set, and formulas of displacement jumping and energy jumping were deduced. The changes of displacement jumping and energy jumping following the variation of the systematic rigidity ratio are discussed with regard to the occurrence of water-softening. Regardless of which type of constitutive equation is adopted, the control variables and sudden jump values of the rock slope’s displacement and energy can be determined by the systematic rigidity ratio when the systematic rigidity ratio is constant. Whether a rock slope is stable or not depends only on the mechanical and geometrical parameters of the system itself, and is unrelated to the constitutive equation of the strain-softening section. The sudden jump values of the displacement and energy are both inversely proportional to the systematic rigidity ratio. By comparing the formula of the systematic rigidity ratio deduced under different constitutive equations with the results obtained by other studies, the results of the present study were verified through the consideration of actual engineering projects. Based on catastrophe theory, the present paper discusses the principle of correctly selecting a constitutive equation to assess the rock slope stability in practical engineering.

A novel Omega-driven dynamic PANS model

A novel Omega (Ω) -driven dynamic partially-averaged Navier-Stokes (PANS) model is proposed in this paper. The ratio of the modeled-to-total turbulent kinetic energies fk is dynamically adjusted by the rigid vorticity ratio (the ratio of the rigid vorticity to the total vorticity), the key parameter of the Ω vortex identification method. Three classical flow cases with rotation and curvature are used to test the model. The results show that the turbulent viscosity is effectively adjusted by the new dynamic fk and the LES-like mode is activated, which can help the revelation of more turbulence information and improve the prediction accuracy. The new PANS model does not contain any explicit dependency on the grid size and enjoys good adaptability to the flow fields, and can be used for efficient engineering computations of the turbulent flows in the hydraulic machinery.

SIFAT FISIK DAN KIMIA PELEPAH AREN (Arenga pinnata Merr) UNTUK BAHAN BAKU ALTERNATIF PULP DAN KERTAS

The purpose of this study was to analyze the chemical components and dimensions of palm frond fibers. The method used is the TAPPI Standard and Haque et al. 2015 for testing chemical components, Schultze's method for fiber dimensions. The results of this study, the palm fronds chemical component, which is moisture content ranging from 17-19%, is included in the high category because it is above 10%, extractive content ranges from 19-59% including high category because it exceeds 10%, lignin content ranges from 21-25% including medium category Cellulose content ranged from 21-27% including the low cellulose category because <40%, holocellulose content ranged from 48-49% including the medium category and hemicellulose content ranged from 22-23% including the low category. Fiber dimensions include fiber length, fiber diameter, lumen diameter and fiber wall thickness and fiber derivative values including Runkell Ratio, Felting Power, Muhleph Ratio, Coofficient Of Rigidity And Felexibility Ratio including quality class II.

UNCONSTRAINED MODAL ANALYSIS OF DYNAMIC MODEL OF FLEXIBLE SPACECRAFT$^{\bf 1)}$

The influence coefficient of flexible coupling in dynamic modeling of flexible spacecraft is an important mechanical concept in dynamic modeling, which reflects the elastic vibration effect of spacecraft attitude and orbit motion and flexible accessories. The equivalent relationship between the influence coefficients of the flexible coupling, i.e. the inertial completeness criterion, is an important basis for the reduction of the order and the mode truncation of the dynamic model of the flexible spacecraft. Taking the center rigid body spacecraft with flexible appendages as the research object, the constrained mode and unconstrained mode are used to describe the structural deformation of flexible appendages, and the dynamic model of flexible spacecraft is established by using Euler Lagrange equation. Based on the research results of Hughes, the unconstrained modal identity of flexible spacecraft and the inertial completeness criterion for dynamic model reduction are proved and applied. The relationship between the inertia of two dynamic models is discussed, and the inertial completeness criterion of unconstrained mode is derived by using the inertial completeness criterion of constrained mode. Finally, the numerical simulation of the flexible spacecraft model composed of the central rigid body with two side solar panels and one side solar panels is carried out to find out the unconstrained mode translational coupling coefficient of the flexible appendages. The change of the unconstrained mode eigenvalue and translational coupling coefficient with the rigid flexible mass ratio is analyzed, and the mass characteristic identity of the unconstrained mode inertial completeness criterion is used to test the model The flexible spacecraft model is tested.

Забезпечення вібростійкості процесу розточування однолезовим інструментом на токарному верстаті

Heightening of a chatter stability of boring process at turning is an actual problem. The basic circuit of a dominating vibratory system of process is developed for the theoretical analysis of oscillating processes for boring bars at boring process and the mathematical model of dynamic system of the lathe that allows us to define influence of design data of boring bars on a process of chatter stability is constructed. On the basis of mathematical model with use of transmitting function the influence of a direction of principal axises of rigidity of boring bar-slide elastic system on static characteristic of elastic tool system is determined. Experimental researches of boring bars have given the chance to define their frequency characteristics by a method of harmonic perturbation and to use them at boring process simulation. It is displayed, that ensuring of conditions of vibrational stability of internal turning on machine tools by boring bars can be carried out by a rational choice of their design data taking into account rational orientation of principal axises of rigidity of elastic tool system in relation to a direction of cutting force, a choice of a rational ratio of rigidity on these axes and heightening of damping ability of a cantilever part of boring bar.

Effect of surrounding frame members on the buckling behavior of steel shear walls restrained by stiffeners

AbstractNumerous studies have addressed the influence of the surrounding frame members on the in‐plane properties of steel shear walls with stiffeners. However, the effect of the out‐of‐plane stiffness on the buckling strength of stiffening plates has not been elucidated. Herein, the influence of surrounding frame members on the buckling behavior of steel shear walls reinforced by cross stiffeners was investigated. A calculation formula for the elastic buckling strength of the stiffened plate was proposed by eigenvalue analysis. In addition, the relationship between the buckling strength and out‐of‐plane stiffness of the surrounding frame members was revealed and a calculation formula for the buckling strength considering the out‐of‐plane stiffness was put forward. Finally, through experimental tests and large deformation analysis, the effect of vertical frame members on the elasto‐plastic property of the stiffened plate was shown. The results obtained are as follows. This study proposes an elastic buckling strength calculation formula for a stiffened plate by correcting the elastic buckling strength calculation formula of an orthotropic plate using the ratio between the torsional rigidity of an actual stiffened plate and that of the plate regarded as anisotropic. The rate of decrease in elastic buckling strength of the stiffened plate due to the out‐of‐plane stiffness of the surrounding frame member can be evaluated by the flexural rigidity ratio between the surrounding member and the stiffened plate. The rate of decrease in elastic buckling strength of stiffened plates due to the out‐of‐plane stiffness of the left and right surrounding vertical frame members with different bending stiffnesses and intermediate vertical frame members can be evaluated by the buckling stress ratio determined from the out‐of‐plane stiffness of the surrounding vertical frame members. It is possible to obtain a stable behavior even if the out‐of‐plane stiffness of the surrounding member is relatively small, if the elastic buckling strength is higher than the shear yield strength of the stiffened plate. It was confirmed that the effect of the end constraint condition on the elasto‐plastic behavior of a stiffened plate was negligible. The results obtained in this study can facilitate the construction of novel earthquake‐resistant steel shear walls.

Evaluation of the experimental curvature ductility of RC beams externally strengthened with CFRP bands

This paper presents an experimental research about bending response of a set of reinforced concrete beams strengthened with external CFRP (RCB-SCFRPs). The aim of the research was to make an evaluation of curvature ductility using experimental data and to generate simplified expressions to estimate the ductility of RCB-SCFRP. In addition, the experimental behavior and the resulting failure modes on bending are also studied by experimental tests. Seventeen natural-scale RCB-SCFRPs with different configurations of reinforced steel bars and FRP (Fiber-reinforced polymer) bands from three manufacturers are designed and loaded under monotonic four points bending tests. In fact, three groups of RCB-SCFRPs were designed in order to evaluate the effect of FRP longitudinal ratio and the external transverse FRP reinforcement (Groups I and II) and to obtain the failure bending modes described in ACI 440.2R [1] (Group III).Flexural capacity and curvature ductility are some of the most important and well-known parameters for analysis and design of traditional RC beams. The calculation of these same parameters in the application of RCB-SCCFRP is not straightforward to compute. Because of this difficulty, the present research focuses on the study of bending behavior and evaluating ductility in terms of FRP axial rigidity, and the steel and CFRP reinforcement ratio.For this purpose, the experimental bending moment-curvature (M-Ф) diagrams were constructed using a proposed approach based on geometric compatibility. The effect of the transverse FRP reinforcement such as U-clamps is not completely clear, but in most cases, the RCB-SCFRPs with transverse reinforcement showed the best performance in final curvature and a greater ductility. Test results indicate that the RCB-SCFRP bending behavior was critically influenced by the FRP properties. Additionally, the FRP axial rigidity had a critically adverse effect on the curvature ductility of the RCB-SCFRPs tested.Furthermore, several expressions based on internal forces equilibrium for predicting the failure bending mode and curvature ductility of RCB-SCFRPs are proposed, which are consistent with experimental data.Finally, a simplified method is proposed to obtain a well-estimated value of curvature ductility considering FRP axial rigidity and steel reinforcement ratio, which could be very helpful to the researcher and designer engineer.

Concentric Precurved Bellows: New Bending Actuators for Soft Robots

We present a new mechanical bending actuator for soft and continuum robots based on a pair of concentric precurved bellows. Each bellows is rotated axially at its base, allowing independent control of the curvature and bending plane of the concentric bellows pair. Rotation of precurved nested tubes is a well-known principle by which needle-sized concentric-tube robots operate, but the concept has never been scaled up to large diameters due to the trade-offs of increased actuation forces, decreased range of motion, strain limits, and torsional windup. In this letter, we show that using bellows structures instead of tubes allows two important breakthroughs: (1) actuation by rotation of precurved concentric elements can be achieved at much larger scales, and (2) torsional lag (i.e. when the relative tube angle at the tip differs from that at the base) and torsional instability are virtually eliminated due to the high ratio of torsional rigidity to flexural rigidity endowed by the bellows geometry. We discuss the development of two types of 3D printed concentric precurved bellows prototypes (revolute and helical), perform model parameter identification, and experimentally verify a torsionless mechanics model which accounts for direction-dependent rigidities.

Effect of vessel diameter on variation of fiber morphology in Acacia mangium

Abstract Paper quality depends on fiber diameter and wall thickness, and their derivatives. Fiber deformation occurs due to pressure from the vessel during development. The diameter and wall thickness of the fibers were measured following the direction of pressure exerted by the vessel on the face of the fiber cells. Fiber cell diameter measured perpendicular to and parallel with vessel enlargement was referred to as radial and tangential diameter, respectively, and likewise for fiber wall thickness. Differences in radial and tangential diameter and wall thickness of fiber cells in relation to their distance from vessels were analyzed. The radial diameter of fibers adjacent to large vessels decreased from the first to the fifth fiber, and from the first to the second fiber adjacent to small vessels. Conversely, tangential fiber diameter increased from the first to the fifth fiber for fibers adjacent to large vessels, and from the first to the second fiber adjacent to small vessels. The fibers adjacent to the vessel seem to have thicker walls in both the tangential than radial directions up to 2 and 5 fibers for small and large vessels, respectively. The first two fibers adjacent to small diameter vessels may produce higher strength paper than those up to five fibers from large diameter vessels, because the Runkel ratio, Coefficient of rigidity and Muhlsteph ratio values of fibers adjacent to small vessels are lower than fibers adjacent to large vessels. The opposite occurs for flexibility coefficient values.

Ultrastructure of royal palm (Roystonea regia) leaf sheath

Abstract. Adzkia U, Nugroho N, Siregar IZ, Karlinasari L. 2020. Ultrastructure of royal palm (Roystonea regia) leaf sheath. Biodiversitas 21: 967-974. The royal palm (Roystonea regia (Kunth) F.Cook is one of the palm species that are many planted along the streets as part of urban landscapes. As biologically products, in nature they can self-cleaning with drop off their big leaves. The study aims to examine the morphological characteristics of ultrastructure and elemental content, crystallinity, as well as fibers derivation characteristics from the royal palm. The samples were taken out from leaf sheaths that divided into three sections along the width of i.e. outside, middle, and inside; in two conditions of leaf sheaths namely green and brownish-dry. The morphology structure and elemental content were observed by the Scanning Electron Microscopy (SEM) and the Energy Dispersive X-ray analysis (EDX), while the crystallinity was analyzed using X-ray diffraction (XRD), and fiber characteristics were measured to determine cell dimensions as well as to calculate Runkle ratio (RR), muhlsteph ratio (MR), coefficient of rigidity (CR), felting powder (FP), and flexibility ratio (FR). The diameter of palm fiber bundles was decreased from outside towards inside. The model of vascular tissue was rounded which located in the central region of the fiber bundles. The silicon content in the inside section was lower than those in the middle and outside sections. It was in line with the degree of crystallinity in the inside section which that higher than other sections. The highest degree of crystallinity was about 18 %. The fiber length of royal palm leaf sheath was in values around 6000 μm. However, the royal palm leaf sheath had thick fiber walls and thin lumen, as well as other fiber derivation characteristics of muhlsteph ratio, the coefficient of rigidity and the flexibility ratio, were in low-quality values. For that reason, the study provides information that the royal palm sheath was recommended as a composite reinforcing material.

Experimental and numerical investigation on the detailed buckling process of similar stiffened panels subjected to in-plane compressive load

Abstract There are two aims in the present paper. The first one is to see and understand the detailed buckling process, especially the interactions between material nonlinearity and geometric nonlinearity on the post-buckling stage, of stiffened panels subjected to in-plane compressive load. The second one is to validate the similarity criteria of designing different sizes of stiffened panels which have the same buckling modes and proportional ultimate strength. These similar relationships make it possible to predict the buckling behavior and ultimate strength of a full-size structure by testing its scale-down model. To these ends, three different sizes of stiffened panels with the same flexural rigidity ratio, plate slenderness and column slenderness, were designed, manufactured and tested. In order to trace and analysis the detailed buckling process, three-dimensional digital image correlation (3D-DIC) method was employed. So, the integrated evolution process of global deformation and strain distribution fields of the stiffened panels were obtained. These data also provide accurate data to verify the numerical or theoretical method in predicting the bulking, especially post-buckling process and ultimate strength of stiffened panel. Results show that the three stiffened panels have reasonable similarity relationships of the buckling failure process. Finally, finite element models with measured initial imperfections were established to reappear the experimental process. The numerical results agree well with the experimental data.

Structures and mechanical behaviors of soft nanotubes confining adhesive single or multiple elastic nanoparticles

The mechanical interaction between soft membrane nanotubes and confined nanoparticles plays essential roles in numerous cellular activities such as inter- and intracellular transport and signaling, membrane tubulation and pearling transformation driven by adsorbed nanocomponents, and cooperative cell uptake. The aim of this work is to theoretically analyze how structures and mechanical behaviors of particle-in-tube complexes are regulated by the particle elasticity, covering the cases of a single particle and multiple particles of spatial periodicity. Depending on the interplay of membrane tension, adhesion energy, nanoparticle size, and the rigidity ratio between the nanoparticles and soft tubes, characteristic interaction states in terms of wrapping degrees of the confined particles have been identified, and the corresponding wrapping phase diagrams are determined. As the particles become softer, the adhesion energy required for the partial-wrapping state becomes lower but that for full-wrapping is larger, and a rich variety of characteristic system configurations are observed including the bulged or undulated cylinders, necklaces of spheres or prolates, and sausage-string shapes. Moreover, two fundamental modes of interaction between multiple nanoparticles and the soft nanotube are revealed, the cooperative wrapping and individual wrapping. Based on perturbation analysis at small tube deformation and configurational assumptions of catenoid, torus, and one-sheeted hyperboloid at more general tube deformation, we have also obtained analytical solutions on the wrapping of rigid spherical nanoparticles in soft tubes. Comparison between wrapping of elastic particles by a flat membrane and by a soft membrane tube is discussed. This study enriches our knowledge on the diversity of membrane tubules in morphologies and structures.