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Buried pipelines are commonly damaged when laid across strike-slip faults, always leading to some level of destruction with fault movement. The moment of the neutral axis of a pipe section was obtained by integration, and the equations for the bending moment and the bending strain on a pipeline’s section were presented here, based on a trilinear stress–strain model. The calculation method for the lateral soil pressure and pipeline’s bending strain near the fault-crossing point was improved. Lateral soil pressure was regarded as being related to lateral pipeline movement and, for accurate calculation, this part of the pipeline was divided into finite element segments. An iterative process for solving for pipe bending strain was derived, and the algorithm and program for calculating bending strain and the potential damage position of the pipeline’s sections was compiled based on Matlab software. Compared with finite element method (FEM) results and the current standard method, in the situation of a pipeline being in tension under the action of a strike-slip fault (intersection angle

There are many researches has been done to replace the constituent materials in the concrete to meet out the scarcity of the available raw materials and also, they have proven a successful one up to a certain level. But in this study, we are focused on to improve the structural behaviour by adding steel fibres in concrete without replacing any constituent materials. The scope of this project is to study experimentally the strength properties of the beam on inclusion of steel fibres. It also aims to investigate the structural behaviour of conventional concrete beams and steel fibre reinforced beam when steel fibre is used as a secondary reinforcement in beams. To overcome the deficiency of the conventional concrete, fibres have been added as secondary reinforcement. Steel fibres are added below the neutral axis of the RC beam in order to overcome the development of micro cracks under applied stress in the RC beam. The addition of steel fibres to the concrete has many advantages and the most notable among them is the improvement in the mechanical characteristics of the concrete. In our project steel fibres and modified steel fibres (adding fibres below the neutral axis) are added in the proportion of 1 % to the concrete. The tests for the fresh concrete and hardened concrete are carried out and their results are compared. The project is further extended to check the performance of the steel fibres in the reinforced concrete beams when they are added below the neutral axis. Two-point loading is applied to the structural members and the corresponding deflections are noted down. The performance of the SFRC beam and the modified steel fibre reinforced concrete (MFRC) beam is compared with the conventional RC beam. The discussions and conclusion are arrived based on the test results.

In order to investigate the influence of modulus of the base layer on the strain distribution for asphalt pavement, the modulus ratio of the base layer and the AC layer (Rm) is introduced as a controlled variable when keeping modulus of the AC layer as a constant in this paper. Then, a three-layered pavement structure is selected as an analytical model, which consists of an AC layer with the constant modulus and a base layer with the variable modulus covering the subgrade. A three dimensional (3D) finite element model was established to estimate the strains along the horizontal and vertical direction in the AC layer under different Rm. The results show that Rm will change the distribution of the horizontal strains along the depth in the AC layer; the increase of Rm could reduce the maximum tensile strain in the AC layer, but its effect is limited; the maximum tensile strain in the AC layer does not necessarily occur at the bottom, but gradually rises to the middle with the increase of Rm. Rm could significantly decline the bottom strain in the AC layer, and there is a certain difference between the bottom and the maximum strain when Rm is greater than or equal to one, which will enlarge with increasing Rm. Rm could change the depth of the neutral axis in the AC layer, and the second neutral axis will appear at the bottom of the AC layer under a sufficiently large Rm. The average vertical compressive strain in the AC layer will significantly enlarge with the increase of Rm.

In the present study, the flexural behavior of concrete-filled steel tube (CFST) beams strengthened by welding round steel at the soffit of the beam has been investigated. First, a total of six specimens were tested under four-point bending load, which includes one reference beam and five retrofitted beams strengthened by welding round steel of different diameters at the soffit of the beams. Then, the corresponding nonlinear finite-element models have been developed and calibrated against the experimental results. By combining indoor experiments and numerical simulations, the bending moment versus mid-span curvature curves, the flexural capacities, flexural stiffness, ductility, vertical deflection curves, strain distribution across the cross-section, and neutral axis offset of the test beams have been systematically analyzed. The results show that the welded round steel at the soffit can improve the flexural bearing capacity and stiffness of the CFST beams significantly. This can be attributed to the CFST beams benefitting from the flexural bearing effect of the round steel and the downward offset of the neutral axis which causes more core concrete to be in compression. Further, the larger the diameter of the round steel, the greater the benefit. Finally, comparisons have been made with the flexural stiffness calculated using the existing design codes, such as AIJ standard, BS5400, Eurocode 4 and AISC specification. The comparisons show that the flexural stiffness of the unstrengthened CFST beam can be predicted by AIJ and BS5400 perfectly, whereas those of the strengthened CFST beams can only be accurately calculated by AISC.

The ductile behavior of reinforced concrete (RC) cross-sections has always been desirable for building codes and standards. However, the threshold to distinguish ductile and brittle behavior of RC cross-sections proposed by building codes has yet to be evaluated [1-4]. This behavior mainly depends on the type of RC cross-section whether it is under- or over-reinforced. While there is not much research conducted on general comparison of the three codes of ACI 318-19, BS 8110 and Eurocode 2 (EC2) regarding design and analysis of RC structural elements, the specific detailed investigation on the threshold for under- and over-reinforced RC cross-sections has yet to be conducted. This article aims to determine the most accurate threshold used to distinguish under- and over-reinforced RC cross-sections amongst the three aforesaid codes by scrutinizing fundamentals and assumptions. A RC cross-section with strain distribution diagram over the section for the three statuses of under-reinforced, balanced, and over-reinforced cross-section is discussed in this research. A theoretical approach is adopted to compare the threshold through the depth of neutral axis of balanced steel concrete cross-sections. The method of calculation is associated with the maximum tensile strain of longitudinal steel bars at the cross-section. The depth of neutral axis is considered to be equal to effective depth of the cross-section multiple by a coefficient. This coefficient is the focus of the comparison. The coefficient is directly given as a number by BS 8110 and EC2. In ACI 318-19 there is no direct value given for the threshold, which leaves no choice other than the accurate calculation of depth of neutral axis for the balanced reinforcement which is in form of an equation. The article concludes that ACI 318-19 provides the most accurate threshold to classify under- and over-reinforced RC cross-sections while EC2 provides the least accurate threshold. The accuracy of threshold proposed by BS 8110 is between those of ACI318-19 and EC2. The scope of this research is confined to singly- and doubly-reinforced concrete cross-sections with any shape using ordinary concrete.

Boundary constraint induced inhomogeneous effects are important for mechanical responses of nano/micro-devices. For microcantilever sensors, the clamped-end constraint induced inhomogeneous effect of static deformation, so called the clamped-end effect, has great influence on the detection signals. This paper is devoted to developing an alternative mechanical model to characterize the clamped-end effect on the static detection signals of the DNA-microcantilever. Different from the previous concentrated load models, the DNA adsorption is taken as an equivalent uniformly distributed tangential load on the substrate upper surface, which exactly satisfies the zero force boundary condition at the free-end. Thereout, a variable coefficient differential governing equation describing the non-uniform deformation of the DNA-microcantilever induced by the clamped-end constraint is established by using the principle of minimum potential energy. By reducing the order of the governing equation, the analytical solutions of the curvature distribution and static bending deflection are obtained. By comparing with the previous approximate surface stress models, the clamped-end effect on the static deflection signals is discussed, and the importance of the neutral axis shift effect is also illustrated for the asymmetric laminated microcantilever.

A new model is developed for bending of functionally graded (FG) porous shape memory alloy (SMA)/poroelastic composite cantilever beams. The model generalizes the ZM model for dense SMAs to cases involving potentially high degrees of porosity. The accuracy of the proposed model is verified against experimental data as well as simulations involving finite element analysis (FEA) of porous architected SMAs with fully detailed geometries. Using the new model, a bending theory is derived for a porous composite cantilever beam reinforced with a FG porous (FGP) SMA layer. The derivation involves expressing the effective material parameters of the porous SMA as polynomial functions of porosity, which facilitates analytical treatment of the bending theory. Moreover, the theory accounts for the distribution of solid phases within a beam cross section as a function of applied load during a complete loading cycle. Results such as the load-deflection behavior of the beam, as well as the location of the neutral axis and distribution of axial stress as a function of the applied load are validated against FEA data. The validated theory is further utilized to investigate the influence of several parameters on the behavior of the composite beam, including the index gradient, temperature, and thickness of the SMA layer.

In this paper, a novel curvature sensor, is showed. The proposed sensor is based on two FBGs, properly embedded in a 3D printed patch: the FBGs measure the strain in two point at a different distance from the monitored structure and the curvature of the structure under test is estimated from the difference in their strain. The simple and compact sensor exhibits a curvature sensitivity of 1.39 nm/m−1 with a resolution equal to $7.2\cdot 10^{-4}\,\,\text{m}^{-1}$ . The curvature test shows a very excellent agreement between the curvature recorded with the new sensing device and that of the reference sensor. Neutral axis position of the monitored structure can be also estimated with this sensor.

Post-tensioned (PT) rocking piers have been recently emphasized for satisfactory self-centering capacity and accelerated bridge construction (ABC) technique in high seismic regions. In this paper, quasi-static cyclic and nonlinear time-history analyses (NLTHAs) are conducted on the PT rocking piers incorporating internal energy-dissipation (ED) bars, based on two modeling techniques. The influences of three parameters consisting of the transverse reinforcement ratio, the area of ED bars and the initial total axial load on the hysteretic behavior of PT rocking piers are studied. The emphases of the quasi-static analyses are on the concrete strain and the neutral axis depth which are seldom referred in the previous researches. Furthermore, NLTHAs are conducted on a set of PT rocking piers under two suits of near-fault and far-fault ground motions (NFGMs and FFGMs) to compare the seismic behaviors of PT rocking piers with different design parameters. The results reveal that the area of ED bars and the initial total axial load are the key parameters that affect the seismic performance of PT rocking piers. In addition, pulse-like NFGMs with a high ratio (>0.2 s) between the peak ground velocity (PGV) and the peak ground acceleration (PGA) result in larger structural seismic responses than FFGMs, except for the acceleration response. The maximum displacement response subjected to FFGMs is almost unaffected by the area ratio of ED bars.

One hundred sixty-two parallel bamboo strand lumber (PBSL) beams were tested for the bending properties under three-point bending with variable span. Two typical failure types were classified, type I was tension failure of the bamboo fiber located below the neutral axis at mid-span, while type II was shear failure which was mainly found in specimens with large depth-span ratio. The shear modulus $${\text{G}}_{{{\text{LR}}}}$$ of PBSL was also calculated according to Timoshenko’s bending theory. To evaluate the shear modulus, 45° off-axis compression tests had been done. The results showed that the mean values of shear modulus for $${\text{G}}_{{{\text{LT}}}}$$ , $${\text{G}}_{{{\text{TR}}}}$$ , and $${\text{G}}_{{{\text{LR}}}}$$ are 1254.5 MPa, 408.1 MPa, and 716.4 MPa, respectively. The bending test result was compared with the shear modulus measured by 45° off-axis compression test. It was found that the shear modulus measured by three-point bending test with variable span was significantly less than the shear modulus obtained by 45° off-axis compression test. The empirical equation of shear factor s corresponding to depth-span ratio h/l was proposed. The calculation results gained from the proposed formula are in good agreement with the 45° off-axis compression test results.

A number of models have been proposed to estimate the shear strength of steel fiber reinforced concrete (SFRC) beams. Nevertheless, the previous models have not been widely accepted in terms of consistency and applicability. This study presents a mechanical model to estimate the shear strength of SFRC slender beams without shear reinforcements. The basic assumptions of the proposed model are agreeable with that of the Critical Shear Crack Theory (CSCT), which has been effectively verified by extensive experimental measurements. The calculation of shear strength considers the contributions of various shear-resisting mechanisms, including the shear resistance provided by the compression zone, residual tensile strength and dowel action in main reinforcements, while neglecting the shear resisted by the aggregate interlock. To obtain the shear resistance provided by residual tensile stress along the critical shear crack and determine the neutral axis depth, a compact constitutive law is presented for the residual tensile stress of SFRC with determined crack width. The impact of steel fibers on each shear-transfer action is studied and considered in the formula of each shear-resisting mechanism. The proposed mechanical model can estimate the shear strength of SFRC slender beams without shear reinforcements, the deformation capacity and the location of the critical shear crack. For design purposes, a simplified model is also presented considering the relation between various shear-resisting mechanisms and critical shear crack. The accuracy of mechanical model and simplified model is extensively verified by comparing predicted values of proposed models and previous eight models with experimental data of the two databases.

A complex procedure for analyzing the design of the spindle assembly for a modernized lathe is proposed. A feature of the problem under consideration is the implementation of an express procedure for assessing the structure spindle performance by the method of initial parameters at the initial stages of design. The effectiveness of the finite element method application at the final stages of design, including in verification calculations based on strength and stiffness criteria is shown. The structural and design schemes of a two-support hollow spindle using the module for analyzing the stress-strain state of beams APM Beam are presented. Attention is focused on the universality of the APM Beam module, which combines the algorithms of the matrix method of initial parameters and effective algorithms of finite elements. The sufficiency of the use for the strength problem classical analytical representation, solved by the method of initial parameters, in the case of considering the operations of finishing turning with an insignificant torque, is noted. The necessity of using the finite element method for technological operations such as face milling with a significant portion of the torque is shown. The transverse layout of the main motion drive of the lathe is considered and the spatial diagram of the forces acting on the spindle is determined. A feature of the procedure for constructing the transverse layout of this drive is the use of the parametric kernel of the APM Graph module. The calculation of the static strength according to the value of the equivalent stresses arising in the spindle structure is carried out. Diagrams of bending moments and stresses of bending and torsion are constructed, according to which it is possible to analyze the operability of the designed structure. An estimate of the shear stress level in the cross-section of the structure is given by the finite element method. The stress fields are plotted in the dangerous section of the spindle, reflecting the distribution of equivalent stresses over the selected cross section. It is noted that the greatest stresses act at the points farthest from the neutral axis of the beam, which corresponds to the known provisions on the distribution of stresses in cross-sections.

There is a common practice of providing openings in the hot-rolled steel section. The openings are provided normally along the neutral axis of the beam. Such beams are called castellated, cellular or perforated beams depending upon the shape of the openings provided. Sometimes due to some unavoidable situation, it is not possible to provide the concentric openings. In such circumstances, an alternative is to provide eccentric openings. Therefore in this paper, the study of castellated has been carried out by varying eccentricity. The study has been split into two parts. In the first of the investigation, an experimental study has been executed to evaluate the realistic behaviour of perforated beams, and in the second part of the investigation, a parametric study has been carried out by varying openings eccentricity. The range of eccentricity is taken as 0, 25 mm and 50 mm in both tension and compression zones. From the experimental study, it has been observed that failure modes are found to be are web post-buckling and Vierendeel mechanism. From the analytical study, it is observed that even eccentric openings are also performing similar to the concentric openings. The eccentricity of perforations provided should not be more than 20% depth of the beam section. Percentage decrease in strength for +ve eccentricity is 16%, whereas for −ve eccentricity, it is 9.30%. The use of reinforcement around the eccentric openings is recommended.

Preflex beam composite girders are widely used in the bridge industry. Understanding the post-cracking behavior of preflex beam girders under cyclic loading is essential to improve monitoring and maintenance. The aim of this study was to evaluate the relationship of the deterioration of the lower flange concrete under cyclic loading to the resulting changes in stiffness, neutral axis location, reinforcement bar stress, and steel-lower-flange stresses of the preflex beam. The study also compared the preflex beam behavior with a conventional girder without prestress under cyclic loading. The experimental study included two specimens of the same details, of which one was preflexed and the other was a conventional non-preflexed specimen. The cracking and post-cracking behavior of the specimens were investigated under multiple cyclic loading stages. The study concluded that changes in the concrete crack width can be used to fairly estimate changes occurring in the neutral axis location, rebar stress, and steel-lower-flange stress of the preflex beam under cyclic loading. The smaller width and shorter length of concrete cracks, implying smaller changes in the preflex beam girder, improved its behavior remarkably compared with the non-preflexed girder with wider and longer concrete cracks under cyclic loading. Furthermore, the study concluded that a closer spacing of the shear ribs reduces the crack width. However, the number of cracks would be larger.

SUMMARY Distal femur fractures in the elderly have been historically treated with locked plating or retrograde intramedullary nailing with good, reliable results. However, in certain more complex fracture patterns (native or periprosthetic), increased density of fixation via dual-plate or nail plate combination can help achieve immediate weight-bearing. It can also potentially increase rates of union by shifting and maintaining the neutral axis, distributing forces more evenly across the fracture site. Here, we discuss the indications, pros and cons of both dual-plate and nail plate combination techniques in a concise case-based format.

The objective of this paper is to present the study of thermal effect in the rectangular plate made of rubber, copper and glass materials using transition theory. The extension and contraction regions presented by the transition points of the differential equation in defining the deformed fields. The analysis also makes the neutral surface separating the two regions. It has been observed that with increased compressibility of materials, the value of neutral axis on the surface of tension must be concentrated on the surface compression. The value of circumferential stress has a maximum at the neutral surface of the rectangular plate made of rubber material in comparison with rectangular plate made of copper and glass materials. With the introduction of thermal effects the value of the circumference as well as radial stresses increases in temperature $$\left( {\Theta_{1} = 0^\circ F,\Theta_{2} = 1000^\circ F} \right)$$ and decreases in temperature $$\left( {\Theta_{1} = 700^\circ F,\Theta_{2} = 0^\circ F} \right)$$ . Rectangular plate made of rubber material is more comfortable than that of copper and glass materials. Numerical results are shown graphically.

This paper used partially debonded high-strength reinforcements (PDHSR) to develop self-centering reinforced concrete (RC) columns. The experimental results showed that the RC columns with PDHSRs had slighter seismic damage, more stable seismic resistance and smaller residual drift up to a large lateral drift compared with the RC columns with normal steel rebars. To simulate the lateral behavior of RC columns with PDHSRs for satisfying the requirements of performance-based design, this paper emphasized the prediction of the lateral behaviors of the RC columns with PDHSRs subjected to seismic load. Firstly, the basic information of the experiments was briefly introduced, secondly, the calculation method considering the steel-bond slip to predict the lateral behaviors of the RC columns was described in detail. Furthermore, several equations for calculating the neutral axis depth of the rectangular column section were proposed without enormous mathematical iterations. Several RC columns with normal steel rebars and the tested columns with PDHSRs were used to validate the applicability of the proposed calculation method. The results proved that the lateral behaviors of them can be predicted with good agreement. Finally, a parametric study was conducted based on the proposed calculation method to discuss the influences of some key structural parameters on the lateral behaviors of the RC columns with PDHSRs. Through regressive analysis, a simplified formula was developed for evaluating the effective lateral yield stiffness of RC columns with PDHSRs.

Due to unphysical coupling induced by the material inhomogeneity, FG (functionally graded) nanobeam problems were formulated in a very complex way so that they cannot be analytically solved. In this paper, an uncoupled theory is proposed for FG nanobeams considering their small size effects. First, with the aid of the neutral axis, the axial displacement is expressed in terms of generalized displacements for FG nanobeams. Based on the nonlocal strain gradient theory, the generalized stresses and strains are accordingly defined and uncoupled constitutive relations are derived. Based on the principle of virtual work, an uncoupled theory is eventually established, including governing equations and boundary conditions. Within the present framework, analytical solutions to FG nanobeams are obtained for the first time for general boundary conditions. These solutions not only re-evaluate the previous results but shed light on the small size effects of FG nanobeams.

This paper presents the results of 1g model tests performed on instrumented model foundations, i.e., unpiled raft, single piled raft, single disconnected piled raft (DPR) and 3 × 3 DPR in sand under vertical load by using different granular materials and thickness of the granular cushion layer to investigate the effects of granular cushion on the performance of DPR system. The Settlement Efficiency (η) of the DPR which is nonlinear in nature is found to increase as the cushion thickness decreases and the mean particle size (d50) of the cushion material increases. A cushion thickness of two times the pile diameter and cushion material having d50 more than or, equals to 2 mm might serve as the suitable cushion material for the optimum performance of 3 × 3 DPR. The neutral axis and the zone of occurrence of maximum axial load of the pile in DPR are found to move downward with increasing cushion thickness. The piles in DPR are found to carry 35% of the total superstructure load within the settlement range considered in the study.

Self-Compacting-Concrete (SCC) is easily flowable, steady and segregation free without any bleeding. The concrete flows freely due its self weight and fills the formwork in congested reinforcement, without any mechanical consolidation. The fibers are added in SCC which acts as crack arresters and enhances the tensile strength and toughness of concrete by reducing crack propagation. In this paper micro steel fibers(S) and nylon fibers (N) are used in different combinations. Micro steel fibers are used in the different percentages of 0, 0.1, 0.2, 0.3, 0.4 by volume of concrete and Nylon fibers are kept constant as 0.1% by volume of concrete. The mix proportions are S0/N0.S 0.1/N0.1,S0.2/N0.1,S0.3/N0.1 and S0.4/N0.1. To assess the filling and passing ability, slump flow and J ring tests were conducted on fresh properties of SCC mixes and the results obtained were checked against the specifications given by EFNARC guidelines. The compressive strength of SCC is obtained for the fiber combinations stated above and the maximum strength is attained for S0.3/N 0.1 fiber combination. Hollow beams with circular openings of 50 mm diameter along neutral axis are casted with SCC containing different combinations of fibers as mentioned above and the beams are tested under flexure to ascertain the bending or flexural strength. It is found that the beams with 0.3% of micro steel fiber content along with 0.1% nylon fiber content (S0.3/N0.1) shown the maximum strength both in compression and flexure when compared to solid beam (without fibers).

A dynamic analysis of rotating functionally gradient (FG) beams is presented for capturing the steady bending deformation by using a novel floating frame reference (FFR) formulation. Usually, the cross section of bending beams should rotate round the point at the neutral axis while centrifugal inertial forces are supposed to act on centroid axis. Due to material inhomogeneity of FG beams, centroid and neutral axes may be in different positions, which leads to the eccentricity of centrifugal forces. Thus, centrifugal forces can be divided into three componets: transverse component, axial component and force moment acting on the points of the neutral axis, in which transverse component and force moment can make the beam produce the steady bending deformation. However, this speculation has not been presented and discussed in existing literatures. To this end, a novel FFR formulation of rotating FG beams is especially developed considering centroid and neutral axes. The FFR and its nodal coordinates are used to determine the displacement field, in which kinetic and elastic energies can be accurately formulated according to centroid and neutral axes, respectively. By using the Lagrange's equations of the second kind, the nonlinear dynamic equations are derived for transient dynamics problems of rotating FG beams. Simplifying the nonlinear dynamic equations obtains the equilibrium equations about inertial and elastic forces. The equilibrium equations can be solved to capture the steady bending deformation. Based on the steady bending state, the nonlinear dynamic equations are linearized to obtain eigen-frequency equations. Transient responses obtained from the nonlinear dynamic equations and frequencies obtained from the eigen-frequency equations are compared with available results in existing literatures. Finally, effects of material gradient index and angular speed on the steady bending deformation and vibration characteristics are investigated in detail.

A fictitious crack model is introduced into cracked reinforced concrete beams to assess the changing beam stiffness under loads. Firstly, nonlinear concrete stress distributions near cracks are built based on the model. Then the stress of the steel bar at the cracked section is considered as cohesive stress. The concrete and steel stresses are substituted into the equilibrium equations of forces to solve the concrete stress. Based on the solution, the section inertias are estimated by iterating the calculation of the cracking open displacement, and finally the beam stiffness is assessed. Experimental data from seven concrete beams after cracking are adopted to validate the effectiveness of the proposed method, and the results show that the fictitious cracks ahead of actual cracks increase their depth with the load, which will raise the neutral axis and change the inertias of cracked sections and their neighboring sections. These changes are taken into account in the stiffness assessment, so the results predicted by the proposed method are shown to coincide well with the nonlinear deflections measured in the experiments.

In this research, the behavior of RC beams retrofitted with steel fiber-reinforced self-compacting concrete jacket (SFRSCC-J) is investigated. For this purpose, by constructing 25 different beams, flexural load-carrying capacity of beams retrofitted with different concrete jackets is examined. The variables studied are the type of concrete (conventional and self-compacting), the strength grade of concrete (C40, C50, and C60), and the presence or absence of reinforcement bar and steel fiber in the jacket. The beams were subjected to three-point flexural loading, and the response was evaluated in terms of load–displacement diagrams. The results show that by adding SFRSCC-J to the perimeter of the beams, their bearing capacity can be increased up to about 7.4 times to reach the yield load, and about 5.1 times to reach the ultimate load. Moreover, the combination of steel fibers (SFs) and steel rebar reduced the cracks more, and at the final moment, the cracks extended to the neutral axis of the cross-section. In the retrofitted beams with the combination of rebar and SFs, the bonding between the reinforcement and the concrete increased and the reinforcement bars slipped less into the specimen. Thus, with a better distribution of stress, besides the concentration of the cracks in the middle of the span, the diagonal cracks decreased, and as the load increased, crack lengths increased less.

This study introduces a theoretical analysis for functionally graded materials (FGMS) OF t-section beams. Analytical methods are set in the form of equations using the effective principal axes, in order to provide a method for predicting the normal stress distribution of the FGMS beam under both axial load and bending moments. Considering the elastic modulus to be an exponential function, the effect of the non-homogeneity parameter on the distribution of the normal stress, as well as on the position of the neutral axis along the beam height, is discussed for several different loading cases. The results obtained show that the non-homogeneity parameters have great effects on the normal stress distribution and the position of the neutral axis. This indicates that, with the less hard region increases, and the neutral axis transfers toward the harder region.

The present study deals with buckling, free vibration, and bending analysis of Functionally Graded (FG) and porous FG beams based on various beam theories. Equation of motion and boundary conditions are derived from Hamilton’s principle, and the finite element method is adopted to solve problems numerically. The FG beams are graded through the thickness direction, and the material distribution is controlled by power-law volume fraction. The effects of the different values of the power-law index, porosity exponent, and different boundary conditions on bending, natural frequencies and buckling characteristics are also studied. A new function is introduced to approximate the transverse shear strain in higher-order shear deformation theory. Furthermore, shifting the position of the neutral axis is taken into account. The results obtained numerically are validated with results obtained from ANSYS and those available in the previous work. The results of this study specify the crucial role of slenderness ratio, material distribution, and porosity condition on the characteristic of FG beams. The deflection results obtained by the proposed function have a maximum of six percent difference when the results are compared with ANSYS. It also has better results in comparison with the Reddy formulae, especially when the beam becomes slender. Doi: 10.28991/cej-2020-03091604 Full Text: PDF

The residual strength capacity of ship hull with full corrosion appearance in every structural member has been considered in a large number of research works; however, the influence of local corrosion on the ultimate strength and cross-section properties has not been taken into account and analyzed. Hence, this study aims to assess the effect of corrosion appearance in the flange section and web section on the ultimate vertical bending moment and several cross-section properties of a bulk carrier. To perform this task, a probabilistic corrosion rate estimation model and the common structural rule model are introduced and employed. The incremental-iterative method given by the International Association of Classification Societies-Common Structural Rules (IACS-CSR) is applied to determine the ultimate vertical bending moment, neutral axis position at the limit state, and other properties of the cross-section. The calculation results and discussions relative to the effect of corrosion on ship hull are presented.

Prestressed force loss always occurs in prestressed concrete (loss prestressed). The most common form used in pre-tensile beams is straight tendons and for post-tensile beams are curved tendons. In planning a prestressed concrete bridge structure, the loss of prestressed force must be considered, because the stress on the prestressed concrete tendon decreases continuously over time. The number of factors that are interrelated, for the effectiveness of the design, location of tendons along the spans need to be considered, so that the tensile strength that occurs in the extreme fiber beam is limited or none at all in the cross section. This final project will examine the shape of the PC beam I Girder with 4 tendon setting conditions namely straight tendon cable which is on the neutral axis so that the eccentricity = 0 (condition1), straight tendon cable which is at 1/6 h so that the eccentricity ≠ 0 (condition 2), tendon cable with draped / parabolic shape (condition 3), and tendon condition with harped shape (condition 4). The biggest prestressed loss results were PC I Girder (condition 2) = 395.81 MPa (26.07%), while the smallest prestressed loss is PC I Girder (condition3) = 367.44 MPa (24.2%). Condition 1 and 2 in girder is not suitable for use because it exceeds the value of the allowable stress at the limit of prestressed and deflection permits on girder are safe for each condition.

We investigate the three-dimensional dynamics of a variable-length, geometrically-exact beam. The beam is released / retracted from a guide. Geometrically exact beam theory, like regular beam theory, is phrased in terms of the deformation of a neutral axis and the rotations of the cross-sections normal to the neutral axis. In contrast to beams in linear elasticity, geometrically exact beams allow large rotations of the beam’s cross-section and large deformations of the line of centroids. We derive the necessary governing equations for the system which, in three dimensions, contain non-trivial contributions from three-dimensional rotations coupled to the varying length of the cable. These equations are then solved through a Galerkin finite element method, after first mapping the physical domain to a fixed computational domain. Large rotations are incorporated into the finite element procedure by utilizing the exponential representation of the rotation tensor. Finally, as an important application of our computational formulation, we investigate the three-dimensional dynamics of a spinning, vibrating, variable-length, flexible beam through a sequence of increasingly complex examples.

Nondestructive monitoring systems currently applied to evaluate existing bridges. This study aims to assess the service life of YangHwa steel bridge, Seoul, Korea, using short period nondestructive structural health monitoring system due to static and moving trucks effects. Different static and dynamic loads were carried out to evaluate the bridge behavior though change trucks’ positions and speeds. The reliability index, neutral axis position, curvatures modal, and frequency and dynamic factor changes are extracted and evaluated. A novel similarity index is investigated, and the analysis of wavelet spectrum is applied to evaluate the bridge behavior. The results show that the bridge is safe using different indices, such as reliability, neutral axis, similarity performance, and curvature modal, dynamic factor and frequency changes. All these indices values are reported to be lower than the standard American Association of State Highway Officials (AASHTO) values and previous inspections, and no abnormal conditions are observed. The similarity index and wavelet spectrum analysis are found to be useful tools to estimate the similarity performance and to estimate the dominant frequency change of the bridge, respectively.

Endovascular and endoscopic surgical procedures require micro-scale and meso-scale continuum robotic tools to navigate complex anatomical structures. In numerous studies, fiber Bragg grating (FBG) based shape sensing has been used for measuring the deflection of continuum robots on larger scales, but has proved to be a challenge for micro-scale and meso-scale robots with large deflections. In this letter, we have developed a sensor by mounting an FBG fiber within a micromachined nitinol tube whose neutral axis is shifted to one side due to the machining. This shifting of the neutral axis allows the FBG core to experience compressive strain when the tube bends. The fabrication method of the sensor has been explicitly detailed and the sensor has been tested with two tendon-driven micro-scale and meso-scale continuum robots with outer diameters of 0.41 mm and 1.93 mm respectively. The compact sensor allows repeatable and reliable estimates of the shape of both scales of robots with minimal hysteresis. We propose an analytical model to derive the curvature of the robot joints from FBG fiber strain and a static model that relates joint curvature to the tendon force. Finally, as proof-of-concept, we demonstrate the feasibility of our sensor assembly by combining tendon force feedback and the FBG strain feedback to generate reliable estimates of joint angles for the meso-scale robot.

In this paper a three-dimensional model of a novel electronic package has been developed using Finite element analysis to evaluate the shear load, tensile, bending and thermal stresses. Simulations of a complete flexible flip chip electronic packaging method are performed to minimize stresses on the packaged electronic device to improve robustness and reliability. Three component under-fill adhesives (Loctite 4860, Loctite 480 and Loctite 4902) and three circuit substrate materials (Kapton, Mylar and PEEK) are compared and the optimal thickness of each is found by shear load, tensile load, bending test and thermal expansion simulations. A fixed die size of 3.5 mm × 8 mm × 0.53 mm has been simulated and evaluated experimentally under shear and bending load. The shear and bending experimental results show good agreement with the simulation results and verify the simulated optimal thickness of the adhesive layer. The Kapton substrate together with the Loctite 4902 adhesive were identified as the optimum in the simulation. The simulation of under-fill adhesive and substrate thickness identified an optimum configuration of a 0.045–0.052 mm thick substrate layer and a 0.042–0.045 mm thickness of the Loctite 4902 adhesive. The bending simulation has also been used to determine the neutral axis of the encapsulated electronic package in this paper, thus identifying the optimal material and thickness for the encapsulation layer of the package.

Bending is a conventional manufacturing process of sheet forming. This process induces reasonable residual stress through the thickness. Prediction of this residual stress profile is more difficult in bilayer sheet bending due to different material properties and thickness of layers. In this article, the residual stress distribution will be derived analytically for a bilayer sheet. The induced stress profile due to loading and released stress after unloading has been derived by integration along with the thickness. Also, the neutral axis movement due to non-uniform plastic deformation has been involved in the solution. The stress distribution has been derived analytically for elastic–perfect plastic, elastic–linear plastic and elastic–power law hardening material behavior. The results obtained from the proposed equation are compared by a finite element analysis. The finite element analysis contains bending a bilayer sheet to a specified curvature radius by a three-roll bending process. Comparing the results of the analytical solution and finite element analysis shows good agreement. The location of the neutral axis and the maximum of residual stresses in the thickness have been predicted very well with the proposed equation.

Purpose 3D printing of composites has a high degree of design freedom, which allows for the manufacture of complex shapes that cannot be achieved with conventional manufacturing processes. This paper aims to assess the design variables that might affect the mechanical properties of 3D-printed fibre-reinforced composites. Design/methodology/approach Markforged Mark-Two printers were used to manufacture samples using nylon 6 and carbon fibres. The effect of fibre volume fraction, fibre layer location and fibre orientation has been studied using three-point flexural testing. Findings The flexural strength and stiffness of the 3D-printed composites increased with increasing the fibre volume fraction. The flexural properties were altered by the position of the fibre layers. The highest strength and stiffness were observed with the reinforcement evenly distributed about the neutral axis of the sample. Moreover, unidirectional fibres provided the best flexural performance compared to the other orientations. 3D printed composites also showed various failure modes under bending loads. Originality/value Despite multiple studies available on 3D-printed composites, there does not seem to be a clear understanding and consensus on how the location of the fibre layers can affect the mechanical properties and printing versatility. Therefore, this study covered this design parameter and evaluated different locations in terms of mechanical properties and printing characteristics. This is to draw final conclusions on how 3D printing may be used to manufacture cost-effective, high-quality parts with excellent mechanical performance.

We present an evaluation of the silicon solar cell as well as the photovoltaic (PV) module size and its effect on thermomechanical stress. The evaluation is based on finite-element method (FEM) simulations. Within these simulations, we perform parameter variations of the number of solar cells within a PV module from 60-140 cells, of the cell size from 156.0-161.75 mm, and the cell format from full cells down to quarter cells. The FEM simulations cover the lamination process, mechanical load, and thermal cycling for glass-foil as well as glass-glass modules. The presented results reveal correlations between the solar cell and module size with the stress in the solar cells. We also find that the interaction of the laminate with the module frame plays a significant role in thermal cycling. Of the varitations under investigation, the increase in cell size has the largest effect on the stress. However, at a mechanical load of 2400 Pa, glass-foil modules with less than 96 solar cells have a negligible failure probability. The advantage of placing the solar cells in the neutral axis of the laminate is proven by the negligible tensile stress values for all variations of the glass-glass modules.

The study of the literature showed the absence of a detailed algorithm for calculating the strength of reinforced concrete elements of a rectangular profile under oblique out-of-center compression using a nonlinear deformation model. This article, which presents such an algorithm, is intended to fill this gap. The peculiarity of the proposed method is that a local coordinate system is introduced for each component of the reinforced concrete section (concrete platform, reinforcing bar) with the beginning of the report located on the neutral axis of the section. This makes it possible to equate the longitudinal deformations to zero, e 0 =0, on this axis, and significantly simplify the formulas for determining the curvature and other parameters. The results of calculating the destructive load of Nult using the method are compared with the experimental data presented in the work of M. S. Toryanik. The comparison was made for 7 short samples that differ in cross-section size, reinforcement, concrete class, and load application eccentricity. The similarity of the results is established, the difference is from -6.8 to +6.1 %, which can be considered acceptable, so the proposed method is recommended for implementation in the design standards.

Composite action between steel girders and concrete slab is an important mechanical feature that needs to be maintained so that bridges can carry the applied load safely. This mechanical feature is maintained through the shear studs installed at the top flange of the steel girders. These shear studs keep the steel girders and the concrete slab working as one unit, resulting in a stronger section than if each element works separately. The composite action can be investigated using several methods of which one is the study of the position of the neutral axis (NA). The variation of the position of the NA over time gives an indication about the structural performance of the composite section. In this study, the variation of the position of the NA over time is investigated. Two bridges located in Manitoba were investigated in this study. The variation of the NA is observed as a result of variation of ambient temperature (temperature). Regression models are suggested to relate variation of the NA to the temperature that was measured beside the web of one of the bridge girders. Repeatability analysis over 4 years was conducted, confirming that the NA varies cyclically over years. It is suggested that this variation indicates that there is a change in the degree of composite action assuming that cold temperatures will induce more connection between the steel girders and the concrete slab as a result of thermal contraction of the shear studs. In addition, the stiffness of the material could be affected due to change of temperature. The other possibility is that an axial force develops in the beam as a result of the bearing restraint during the passing of vehicles on the bridge. The results found in this study will eventually lead to enhancements of the design procedures that currently assume a fixed position of the NA over time of composite sections of bridges, similar to the bridges presented in this study.

In this paper, two types of natural fibers (jute fiber and cotton fiber) were arranged in different cross-section positions on natural fiber-reinforced epoxy composites (NFR-EC) by using a novel hole arrangement–threading–glue filling method. A three-point bending experiment was carried out to reveal the flexural response, failure types, and energy absorption properties of NFR-EC. An analytical model was applied to analyze the force distribution of natural fibers and epoxy in NFR-EC. Results showed that the hole arrangement–threading–glue filling method successfully manufactured an NFR-EC, which can adjust the volume fraction and cross-section position of natural fibers and the cross-sectional shape of NFR-EC. The addition of fibers below the neutral axis of the cross-section significantly improved the flexural properties and energy absorption capacity of NFR-EC.

Sectional deformation quantities, such as curvature and ductility, are of prime significance in the displacement-based seismic design and performance evaluation of structural members. However, few studies on the estimates of curvatures at different limit states have been performed on asymmetric flanged walls. In this paper, a parametric study was performed for a series of T-shaped wall cross-sections based on moment-curvature analyses. By investigating the effects of the axial load ratio, reinforcement content, material properties, and geometric parameters on curvatures at the yield and ultimate limit state, we interpret the variation in curvature with different influencing factors in detail according to the changes of the neutral axis depth. Based on the regression analyses of the numerical results of 4941 T-shaped cross-sections, simple expressions to estimate the yield curvature and ultimate curvature for asymmetric flanged walls are developed, and simplified estimates of the ductility capacity including curvature ductility and displacement ductility are further deduced. By comparing with the experimental results, we verify the accuracy of the proposed formulas. Such simple expressions will be valuable for the determination of the displacement response of asymmetric flanged reinforced concrete walls.

Most of the existing codes are using stress block parameters which were derived for normal strength concrete. Rectangular stress-block parameters used for normal strength concrete cannot be used safely for higher grade concrete like HPC, hence new stress-block parameters are established from the experimental investigations. Theses parameters can be made very much useful in the design of HPC members. Present research aims at behaviour study of HPC using stress block parameters. High performance concrete single span beams were tested under monotonic four-point bending. Considering the experimental stress-strain curves of HPC for grade 60, 80 and 100 MPa, an idealized stress block curve is established and the stress block parameters are derived. Based on the idealized stress block curve, the equations for ultimate moment of resistance, depth of neutral axis, limiting moment of resistance and maximum depth of neutral axis are proposed. Based on the observation of experimental load deformation curves, an ideal load deformation curve is proposed, which follows four significant events identified as, first cracking, yielding of reinforced steel, crushing of concrete with spalling of cover and ultimate failure. The predicted values compare well with the experimental values. The average location of the first crack observed was at 0.535 times the span of the beam from the left support of the observer in the tension zone.

When subjected to time-dependent dynamic loading, concrete structures possess tension cracks. Such existing internal cracks have a breathing action (opening-closing-reopening), rendering such structures nonlinear elastic. For a single load and/or under proportional load variations, these structures have a bilinear mechanical response at the neutral axis in the form of discontinuity. The bilinearity ratio (β) is the aspect that co-relates the two values of flexural rigidity. Typically the value of bilinearity ratio is usually worth up to 10. In this research article, the bilinear dynamic response of a fully cracked concrete fixed beam under the action of sinusoidal loading has been studied by modelling it as a damped bilinear single degree of freedom system. In addition, the comparison of unilinear and bilinear models was explored. The simulations were performed using the software MATLAB. It has been found that such a class of homogeneous dynamical system exhibits linear behavior for a specific sense of applied loads. Moreover, in the case of fundamental resonance, the waveforms for displacement and acceleration exhibit jump phenomena in the form of a sudden change in the sense of the applied load. The shortcomings of current dynamic analysis practice have been addressed, and the practical importance of the work has been examined.

This paper presents a nonlocal dynamic stiffness model (DSM) for free vibration analysis of Functionally Graded (FG) nanobeams. The nanobeam is investigated on the basis of the Nonlocal Elastic Theory (NET). The NET nanobeam model considers the length scale parameter, which can capture the small scale effect of nano structures considering the interactions of non-adjacent atoms and molecules. Material characteristics of FG nanobeams are considered nonlinearly varying throughout the thickness of the beam. The nanobeam is modelled according to the Timoshenko beam theory and its equations of motion are derived using Hamilton’s principle. The DSM is used to obtain an exact solution of the equation of motion taking into account the neutral axis position with different boundary conditions. The DSM is validated by comparing the obtained results with published results. Numerical results are presented to show the significance of the material distribution profile, nonlocal effect, and boundary conditions on the free vibration of nanobeams. It is shown that the study can be applied to other FG nanobeams as well as more complex of framed nanostructures.

In 1921, Timoshenko improved upon the Euler‒Bernoulli beam theory by adding the effect of transverse shear strains. In the Euler–Bernoulli beam theory, transverse shear strains are neglected, and cross- sections remain plane and perpendicular to the neutral axis. In the Timoshenko beam theory, cross-sections still remain plane but are no longer perpendicular to the neutral axis. Although the transverse shear strain approaches zero, the Timoshenko beam theory does not converge on the Euler‒Bernoulli beam theory due to the shear locking. Many authors have attempted to overcome this problem and although they have brought acceptable results, these still have theoretical limitations. Therefore, in this paper, the author presents an improved method of calculating the beam considering transverse shear strain to overcome the theoretical limitations of previous authors. The problem is addressed by the use of numerical methods which achieve convergence and avoid the issue of shear locking.

In this work, the embedding of fiber Bragg gratings (FBGs) in 3D printed patches is proposed with the multiple aims to demonstrate the capabilities of the FBGs to monitor the deformation state and the temperature of the sensorized devices and to show the possibility to use this approach in the realization of robust and efficient packages for fiber optical sensors. FBGs are embedded in the monitored structure, avoiding the complex wiring typical of strain gauges, and provide local strain measurements in real-time. The possible application of the patch as sensing device is investigated showing that the thickness of the substrate, influencing the neutral axis position, acts as gaining factor on the deformation sensitivity of the FBG, while the temperature sensitivity in more than ten time greater than the bare FGB one thanks to the high thermal expansion of the plastic material of which the patches are made. Such results enable the application the 3D-printed patches as packages for FBGs in the deformation and temperature monitoring.

Increasing the bending and shear capacities of reinforced concrete members is an interesting issue in structural engineering. In recent years, many studies have been carried out to improve capacities of reinforced concrete members such as using post and pre-tensioning, Fiber Reinforced Polymer and other techniques. This paper proposes a novel and significant technique to increase the flexural capacity of simply supported reinforced concrete beams. The proposed method uses a new reinforcement bar system having bent-up bars, covered with rubber tubes. This technique will avoid interaction of bent-up bars with concrete. They are located in the zone where compressive and tensile forces act against one another. The compressive force in the upper point of the bent-up bars is exerted to the end point of these bars located under neutral axis. Moreover, the tensile stress is decreased in reinforcements located under the neutral axis. This will cause the Reinforced Concrete (RC) beam to endure extra loading before reaching yield stress. These factors may well be considered as reasons to increase bending capacity in the new system. The laboratory work together with finite element method analysis were carried out in this investigation. Furthermore, bending capacity, ductility, strength, and cracking zone were assessed for the new proposed system and compared with the conventional model. Both the FEM simulation and the experimental test results revealed that the proposed system has significant impact in increasing the load bearing capacity and the stiffness of the RC beams. In the present study, an equation is formulated to calculate bending capacity of a new reinforcement bar system beam.

Residual stress is always present in steel structures and can cause a premature plasticity of the steel and considerably affect the stiffness, ultimate bearing capacity, and fatigue resistance of members or joints. This paper presents experimental and numerical investigations on residual stresses in a hot-bent circular steel tube. Longitudinal residual stresses are measured through a cutting method. The residual stress distribution is symmetrical for both extrados and intrados of a hot-bent circular tube. The maximal tensile or compressive residual stress occurs at the extrados or intrados near the neutral axis of steel tubes. A parametric study with 54 numerical models is then conducted to investigate the influencing factors of the residual stress (e.g. bending ratio, diameter-to-thickness ratio, and steel yield strength). According to the results, the bending ratio (as the most important factor) has a significant influence on the residual stress distribution and magnitude. The results imply that the residual stress and diameter-to-thickness ratio exhibit no distinct correlation. The hot-bent circular tubes with higher steel yield stresses exhibit greater residual stresses. The effects of the yield strength fy can be simplified in the form of the residual stress multiplied by fy/345. Finally, the residual stress model of the hot-bent circular tube is proposed as a polyline formation. It fits the actual residual stress distribution well when the self-equilibrium characteristics are considered.

Symmetric Tape Round (STAR) wires are only 1.6-1.9 mm in diameter and are made by winding 2.5-mm-wide REBCO tapes on an AWG 18 (1.02-mm diameter) copper wire former. Such ultra-small diameter wires are possible by the use of symmetric tapes where the REBCO film is positioned at the geometric center, close to the neutral axis. Such symmetric tape architecture is achieved by a strategic selection of the thickness of the copper stabilizer to match the thickness of the Hastelloy substrate. The substrate itself is made thin, to enable good tolerance to bend strain. The optimized STAR wire architecture is found to be mechanically robust and retain nearly 98% of its critical current of over 500 A at 77 K, self-field even when bent to a small radius of 15 mm. The superior bend strain tolerance of STAR REBCO wires make them suitable for use in canted cosine theta coils for future compact accelerator magnet applications.

The bending properties of RE-Ba-Cu-O (REBCO, RE = rare earth) coated conductors are a stringent constraint for coil and cable applications. While the use of thinner substrates reduces the stresses/strains in the REBCO layer, it is also possible to enhance the mechanical properties of these tapes by optimizing the stabilizer thickness in order to reduce the distance between the neutral axis and the REBCO layer. In this paper, we present both experimental and analytical results showing a significant improvement in the critical current (I c ) retention at small bend diameters (less than 2 mm) for tapes with various substrate thicknesses by using an optimized copper thickness on the REBCO side only. The presented analytical method accounts for the neutral axis shift caused by the progressive plastic deformation in the various layers (Hastelloy, silver, and copper). The Ic dependence of different substrate tapes on the thickness of single-sided electroplated copper stabilizer was measured at bending diameters ranging from 0.81 to 12.5 mm by means of a single-turn helical winding on a cylindrical former. The strains were then calculated and an optimized copper thickness is determined for the various configurations. Based on these results, an optimal design for ultra-small diameter REBCO wires is also presented.

During the design process of monolithic ribbed slabs, engineers face a common issue how to correctly evaluate stiffness of the beams. When Bar and Plate elements are used for analysis of the slabs, the neutral axis of those members are in the same level, therefore the stiffness of (T) shape cross-section is not considered correctly in the calculations. In this case the internal forces are obtained incorrectly as well as deflections of the beams are overestimated. A simple method is discussed in this paper, which allows engineers to calculate internal forces and deformations of mentioned type slabs more accurately with FEM programs by using Bar and Plate elements. The method is based on Bar elements moment of inertia adjustment. After the comparative analysis of differences between moment of inertia of (T) and (+) shape cross-sections as well as deflection discrepancies, the adjustment coefficient expression is presented. In order to reflect the actual behaviour of ribbed slabs even more accurately the influence of shear deformations is also considered. In this case not only the member geometry but the material properties, loading scheme and even supports are taken into account in the calculations of the adjustment coefficient. Selection of the most appropriate (effective) flange width of (T) shape cross-section is also analysed in this paper. Comparative calculations were done using different effective flange widths beff calculated by EC2 (Eurocode 2), “STR” (Lithuanian Construction Technical Regulations) and ACI (American Concrete Institute) methods. In order to assess the reliability of the proposed calculation method and the calculation results all plates were also analysed using Solid elements. Application of the presented expressions of moment of inertia coefficient will allow engineers to evaluate stiffness of (Γ) and (T) shape cross section beams simply, fast and accurately enough for most of structural engineering calculations.

This paper firstly figures out a similar scale model regarding ultimate strength experiment of a typical ultra large container ship (ULCS) through combined ultimate longitudinal bending and torsion analysis, in which the similarity theory is proposed to design the scale model for reflecting the progressive collapse behaviors of true ships in ultimate strength model test. The present study presents the similarity between scale model and true ship in cross-section considering the height of neutral axis, the section modulus, the inertia moment about neutral axis and the polar inertia moment should fit the geometrical similarity theory, and in strength considering buckling strength and shear ultimate strength of plates and stiffened panels should fit the strength similarity theory. Numerical investigations are conducted on the ultimate strength of a 10,000 TEU container ship and the similar scale model under pure hogging bending, pure torsion and combined bending and torsion, respectively. The nonlinear finite element method (NFEM) is adopted considering the effects of initial deformations and both material and geometric nonlinearities. Finally, the numerical results are compared with each other and discussed showing a good agreement in both elastic and inelastic range during the progressive collapse behaviors, which means the similar scale model can represent the true ship regarding ultimate strength test. And the similarity theory is verified quite stable after the uncertainty analysis.