• Computers and Concrete
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• v.15 no.3
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• pp.373-389
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• 2015

The development of a finite element model for the geometric and material nonlinear analysis of bonded prestressed concrete continuous beams is presented. The nonlinear geometric effect is introduced by the coupling of axial and flexural fields. A layered approach is applied so as to consider different material properties across the depth of a cross section. The proposed method of analysis is formulated based on the Euler-Bernoulli beam theory. According to the total Lagrangian description, the constructed stiffness matrix consists of three components, namely, the material stiffness matrix reflecting the nonlinear material effect, the geometric stiffness matrix reflecting the nonlinear geometric effect and the large displacement stiffness matrix reflecting the large displacement effect. The analysis is capable of predicting the nonlinear behaviour of bonded prestressed concrete continuous beams over the entire loading stage up to failure. Some numerical examples are presented to demonstrate the validity and applicability of the proposed model.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.195-210
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• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• Steel and Composite Structures
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• v.27 no.2
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• pp.229-242
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• 2018

High strength steel is widely used in industrial applications to improve the load-bearing capacity and reduce the overall weight and cost. To take advantage of the benefits of this type of steel in construction, an innovative hybrid fabricated member consisting of high strength steel tubes welded to mild steel plates has recently been developed. Component-scale uniaxial and multiaxial cyclic experiments have been conducted with simultaneous constant or varying axial compression loads using a multi-axial substructure testing facility. The structural interaction of high strength steel tubes with mild steel plates is investigated in terms of member capacity, strength and stiffness deterioration and the development of plastic hinges. The deterioration parameters of hybrid specimens are calibrated and compared against those of conventional steel specimens. Effect of varying axial force and loading direction on the hysteretic deterioration model, failure modes and axial shortening is also studied. Plate and tube elements in hybrid members interact such that the high strength steel is kept within its ultimate strain range to prevent sudden fracture due to its low ultimate to yield strain ratio while the ductile performance of plate governs the global failure mechanism. High strength material also significantly reduces the axial shortening in columns which prevents undesirable frame deformations.

• Computers and Concrete
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• v.29 no.5
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• pp.323-334
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• 2022

In order to study the axial compression performance of basalt-fiber reinforced recycled concrete (BFRRC) filled circular steel tubular short columns, the axial compression performance tests of seven short column specimens were conducted to observe the mechanical whole-process and failure mode of the specimens, the load-displacement curves and the load-strain curves of the specimens were obtained, the influence of design parameters on the axial compression performance of BFRRC filled circular steel tubular short columns was analyzed, and a practical mathematical model of stiffness degradation and a feasible stress-strain curve equation for the whole process were suggested. The results show that under the axial compression, the steel tube buckled and the core BFRRC was crushed. The load-axial deformation curves of all specimens show a longer deformation flow amplitude. Compared with the recycled coarse aggregate (RCA) replacement ratio and the basalt fiber dosage, the BFRRC strength has a great influence on the peak bearing capacity of the specimen. The RCA replacement ratio and the BFRRC strength are detrimental to ductility, whereas the basalt fiber dosage is beneficial to ductility.

• Computers and Concrete
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• v.29 no.1
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• pp.15-29
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• 2022

Concrete-filled steel tubes (CFSTs) are increasingly used as composite sections in structures owing to their excellent load bearing capacity. Therefore, predicting the mechanical behavior of CFST sections under axial compression loading is vital for design purposes. This paper presents the first study on the nonlinear analysis of heated CFSTs with high-strength concrete core containing steel fiber and waste tire rubber under axial compression loading. CFSTs had steel fibers with 0, 1, and 1.5% volume fractions and 0, 5, and 10% rubber particles as sand alternative material. They were subjected to 20, 250, 500, and 750℃ temperatures. Using flow rule and analytical analysis, a model is developed to predict the load bearing capacity of steel tube, and hoop strain-axial strain relationship, and axial stress-volumetric strain relationship of CFSTs. An elastic-plastic analysis method is applied to determine the axial and hoop stresses of the steel tube, considering elastic, yield, and strain hardening stages of steel in its stress-strain curve. The axial stress in the concrete core is determined as the difference between the total experimental axial stress and the axial stress of steel tube obtained from modeling. The results show that steel tube in CFSTs under 750℃ exhibits a higher load bearing contribution compared to those under 20, 250, and 500℃. It is also found that the ratio of load bearing capacity of steel tube at peak point to the load bearing capacity of CFST at peak load is noticeable such that this ratio is in the ranges of 0.21-0.33 and 0.31-0.38 for the CFST specimens with a steel tube thickness of 2 and 3.5 mm, respectively. In addition, after the steel tube yielding, the load bearing capacity of the tube decreases due to the reduction of its axial stiffness and the increase of hoop strain rate, which is in the range of about 20 to 40%.

• Structural Engineering and Mechanics
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• v.20 no.1
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• pp.21-43
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• 2005

Masonry is a composite non-homogeneous structural material, whose mechanical properties depend on the properties of and the interaction between the composite components - brick and mortar, their volume ratio, the properties of their bond, and any cracking in the masonry. The mechanical properties of masonry depend on the orientation of the bed joints and the stress state of the joints, and so the values of the shear modulus, as well as the stiffness of masonry structural elements can depend on various factors. An extensive testing programme in several countries addresses the problem of measurement of the stiffness properties of masonry. These testing programs have provided sufficient data to permit a review of the influence of different testing techniques (mono and bi-axial tests), the variations caused by distinct loading conditions (monotonic and cyclic), the impact of the mortar type, as well as influence of the reinforcement. This review considers the impact of the measurement devices used for determining the shear modulus and stiffness of walls on the results. The results clearly indicate a need to re-assess the values stated in almost all national codes for the shear modulus of the masonry, especially for masonry made with lime mortar, where strong anisotropic behaviour is in the stiffness properties.

• Steel and Composite Structures
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• v.46 no.3
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• pp.293-318
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• 2023

This study aims to examine the elastic stiffness properties of Elliptic-Braced Moment Resisting Frame (EBMRF) subjected to lateral loads. Installing the elliptic brace in the middle span of the frames in the facade of a building, as a new lateral bracing system not only it can improve the structural behavior, but it provides sufficient space to consider opening it needed. In this regard, for the first time, an accurate theoretical formulation has been developed in order that the elastic stiffness is investigated in a two-dimensional single-story single-span EBMRF. The concept of strain energy and Castigliano's theorem were employed to perform the analysis. All influential factors were considered, including axial and shearing loads in addition to the bending moment in the elliptic brace. At the end of the analysis, the elastic lateral stiffness could be calculated using an improved relation through strain energy method based on geometric properties of the employed sections as well as specifications of the utilized materials. For the ease of finite element (FE) modeling and its use in linear design, an equivalent element was developed for the elliptic brace. The proposed relation was verified by different examples using OpenSees software. It was found that there is a negligible difference between elastic stiffness values derived by the developed equations and those of numerical analysis using FE method.

• Ocean Systems Engineering
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• v.6 no.2
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• pp.143-159
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• 2016

Cargo, such as a Tension Leg Platform (TLP), Semi-submersible platform (Semi), Spar or a circular Floating Production Storage and Offloading (FPSO), are frequently dry-transported on a Heavy Lift Vessel (HLV) from the point of construction to the point of installation. The voyage can span months and the overhanging portions of the hull can be subject to frequent wave slamming events in rough weather. Tie-downs or sea-fastening are usually provided to ensure the safety of the cargo during the voyage and to keep the extreme responses of the cargo, primarily for the installed equipment and facilities, within the design limits. The proper design of the tie-down is dependent on the accurate prediction of the wave slamming loads the cargo will experience during the voyage. This is a difficult task and model testing is a widely accepted and adopted method to obtain reliable sea-fastening loads and extreme accelerations. However, it is crucial to realize the difference in the inherent stiffness of the instrument that is used to measure the tri-axial sea fastening loads and the prototype design of the tie-downs. It is practically not possible to scale the tri-axial load measuring instrument stiffness to reflect the real tie-down stiffness during tests. A correlation method is required to systematically and consistently account for the stiffness differences and correct the measured results. Direct application of the measured load tends to be conservative and lead to over-design that can reflect on the overall cost and schedule of the project. The objective here is to employ the established correlation method to provide proper high-frequency responses to topsides and hull design teams. In addition, guidance for optimizing tie-down design to avoid damage to the installed equipment, facilities and structural members can be provided.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.237-248
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• 2022

Nowadays, more and more subway tunnels were planed and constructed underneath the ground of urban cities to relieve the congested traffic. Potential damage may occur in existing tunnel if the new tunnel is constructed too close. So far, previous studies mainly focused on the tunnel-tunnel interactions with circular shape. The difference between circular and horseshoe shaped tunnel in terms of deformation mechanism is not fully investigated. In this study, three-dimensional numerical parametric studies were carried out to explore the effect of different tunnel shapes on the complicated tunnel-tunnel interaction problem. Parameters considered include volume loss, tunnel stiffness and relative density. It is found that the value of volume loss play the most important role in the multi-tunnel interactions. For a typical condition in this study, the maximum invert settlement and gradient along longitudinal direction of horseshoe shaped tunnel was 50% and 96% larger than those in circular case, respectively. This is because of the larger vertical soil displacement underneath existing tunnel. Due to the discontinuous hoop axial stress in horseshoe shaped tunnel, significant shear stress was mobilized around the axillary angles. This resulted in substantial bending moment at the bottom plate and side walls of horseshoe shaped tunnel. Consequently, vertical elongation and horizontal compression in circular existing tunnel were 45% and 33% smaller than those in horseshoe case (at monitored section X/D = 0), which in latter case was mainly attributed to the bending induced deflection. The radial deformation stiffness of circular tunnel is more sensitive to the Young's modulus compared with horseshoe shaped tunnel. This is because of that circular tunnel resisted the radial deformation mainly by its hoop axial stress while horseshoe shaped tunnel do so mainly by its flexural rigidity. In addition, the reduction of soil stiffness beneath the circular tunnel was larger than that in horseshoe shaped tunnel at each level of relative density, indicating that large portion of tunneling effect were undertaken by the ground itself in circular tunnel case.

• Structural Engineering and Mechanics
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• v.77 no.1
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• pp.137-149
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• 2021

In engineering design, the axial equivalent elastic modulus of laminated FRP pipe was mostly calculated by the average elastic modulus method or the classical laminated plate theory method, which are based on relatively simplified assumptions, and may be not accurate enough sometimes. A new analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipe was established based on three-dimensional stress state. By comparing the results calculated by this method with those by the above two traditional analytical methods and the finite element method, it is found that this method for the axial equivalent elastic modulus fits well not only for thin-walled pipes with orthotropic layers, but also for thick-walled pipes with arbitrary layers. Besides, the influence of the layer stacking on the axial equivalent elastic modulus was studied with this method. It is found that a proper content of circumferential layer is beneficial for improving the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers, and then can reduce its material quantity under the premise that its axial stiffness remains unchanged. Finally, the meso-mechanical mechanism of this effect was analyzed. The improving effect of circumferential layer on the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers is mainly because that, the circumferential fibers can restrain the rigid body rotations of the oblique fibers, which tend to cause the significant deformations of the pipe wall units and the relatively low axial equivalent elastic modulus of the pipe.