Second-order inelastic analysis of cable-stayed bridges

This work aims to introduce a new layered approach to the nonlinear analysis of initially straight Euler-Bernoulli beams by the Boundary Element Method (BEM). The beam is studied in the context of both geometrical and material nonlinearity. The governing differential equations, derived by applying the principle of minimum total potential energy, are coupled and nonlinear, while the boundary conditions are the most general and may include elastic support or restraint. The boundary value problem, regarding the axial and transverse displacements, is solved using the Analog Equation Method (AEM), a BEM based method, together with an iterative procedure. Although a direct solution to the geometrical nonlinear problem has already been presented, in this work an alternative layered analysis is proposed. The discretization is applied in both the longitudinal direction and the cross-sectional plane, and an iterative process is commenced. First, initial fictitious load distributions are assumed at beam’s each cross-section, and the displacements, as well as their derivatives, are computed using the AEM. Second, the two stress resultants, i.e., the axial force and bending moment, are evaluated by appropriate integration over the cross-section. In the end, the derivatives of the stress resultants are evaluated, and the equilibrium of the governing equations is checked. If the equilibrium is satisfied, the process is terminated. Otherwise, the fictitious load distributions are updated, and the procedure starts over again. Several representative examples are studied, and the results are compared with those presented in the literature, validating the reliability and effectiveness of the proposed method.

Testing and numerical modelling of austenitic stainless steel CHS beam–columns

Adequate mechanical properties make stainless steel an excellent construction material for structures. The current stainless steel European structural code EN1993‐1‐4 (2015) is largely based on provisions given for carbon steel EN1993‐1‐1 (2005) and does not establish specific design rules for the global analysis of stainless steel structures. Thus, the same classification criterion applies in both codes for sway and non‐sway structures, as well as providing the same predicting expressions for the amplification of bending moments in basic structures, despite the considerable differences between the mechanical behaviour of these two materials. However, recent numerical research on stainless steel frames with H cross‐sections by Walport et al. (2019) showed that the degradation of stiffness due to material nonlinearities considerably affects the response of stainless steel frames, causing greater deformations and increasing second order effects.In order to contribute to the optimal design of stainless steel structures, this paper investigates the influence of the nonlinear material response of stainless steel alloys on frame‐type structures with Rectangular Hollow Sections based on the experimental results conducted by Arrayago et al. (2019), and the interaction of material and geometric nonlinearities.

Beam-like, architected microstructures (BAMs) can be used in various functional applications, such as micro-electro-mechanical systems (MEMS), energy harvesting, actuation, etc. Designing with high aspect ratios under large deformations, BAMs typically experience severe buckling instability. Therefore, it is of necessity to investigate the mechanical behaviors with respect to the geometric and material nonlinearities. This paper proposes a bilinear size-dependent model using the modified couple stress theory to full formulate the buckling response of the BAMs. Buckling-induced large deformation is studied using the geometric nonlinearity, and the recoverability is investigated based on the material nonlinearity. Experiments and numerical simulations are conducted to validate the theoretical results at the macroscale and microscale, respectively, and satisfactory agreements are obtained. Parametric studies are carried out to study the effects of the material length scale factor-to-thickness ratio χ=lt (i.e., geometric nonlinearity) and plastic factor η (i.e., material nonlinearity). χ and η are further discussed with respect to the effective bending stiffness B¯PAM and volume V¯PAM of the microstructures. The theoretical model presented in this study can be used to predict and tune the mechanical response of BAMs with different architected webbing patterns.

Many countries have set out their commitments for net-zero emission in order to address the increasingly detrimental impact caused by greenhouse gas and the consequent climate change. To accelerate the ambitious net-zero target while ensuring a sufficient energy supply, the exploitation of wind energy is one of the sustainable and clean solutions. Thus, it is foreseen that the investment in the offshore wind will continue worldwide in the coming years. For a successful deployment of offshore wind turbines, an adequate safety margin of their foundation supporting structures is of paramount importance. Prevailing design codes require a rigorous assessment against the ultimate limit state for the foundation supporting structures of offshore wind turbines. These structures are typically in the form of cylindrical shells, which are subjected to a combination of axial compression and overturning bending moment. In this paper, a numerical study is presented in the light of gaining better insights into the catastrophic collapse behaviour of cylindrical shells under combined loads. Nonlinear finite element analyses considering geometric and material nonlinearities are completed on a parametric range of structural models with different length-to-radius and radius-to-thickness ratios. A matrix of axial compression and bending moment combinations are analysed. The numerical results are compared with prediction by prevailing code formulae.

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

Dynamic soil–structure interaction (SSI) represents an interdisciplinary subject characterized by complex geometrical and material nonlinearities affecting both the soil and the structural components of the system under study. In the current practice, SSI problems are often solved using the so-called substructure method based on decomposing the superstructure-foundation-soil system into two subsystems whose response is determined independently. The direct method is a more general procedure to tackle SSI problems which is in principle capable of accounting for both soil and structural nonlinearities. Despite this generality, most of the current computational platforms are specialized either for structural applications or for geotechnical applications. Whereas the formers are capable to accurately reproduce the nonlinear response of the structural elements, they are usually poor in modeling soil nonlinear behaviour especially under earthquake loading. On the other hand, the latter do the reverse: they are advanced in modeling soil response but typically rough in reproducing the behaviour of the structural components of the system. Inevitably, all structures interact with the ground and therefore the need to model material and geometric nonlinearities maybe important both in the ground and structural elements. The variation of the stiffness mismatch between soil and structural elements during ground motions is one of the most influential parameters for the assessment of the kinematic component in SSI problems. The variation of the stiffness ratio is mainly governed by material nonlinearity that can develop in either the soil or the structural parts of the system. This paper presents a nonlinear constitutive model for beam elements that is compatible with performance–based earthquake engineering principles because it is capable to simulate the cyclic degradation of mechanical properties and to assess the damage suffered by the structural system. The proposed model is based on distributed plasticity and can be easily implemented in any computational platform allowing the use of an explicit solver. The article describes the theoretical aspects of the model. Validation and application of the model to the solution of a dynamic soil–structure interaction problem where the nonlinear behaviour of geomaterials is coupled with the inelasticity of structural elements, are presented in a companion paper (Andreotti and Lai in Bull Earthq Eng 2017).

Nonlinear aerostatic stability analysis of suspension bridges

Some transmission structures exhibit important geometric and material nonlinearities that should be considered in their analysis and design. Unless simplifying assumptions are made, reliability analysis of these structures is complex and can be very computer-time intensive. This paper describes an approximate method to conduct reliability analysis of nonlinear transmission structures. It is shown that for most transmission structures, the design point is close to the 50-year return period loads. Using this result, approximate g-functions for nonlinear problems are obtained with minimum computational effort. It is also shown that when the material strengths are highly correlated, g-functions that include interaction of axial load and bending moments may be reduced to g-functions with no interaction. These simplifying results are implemented in a microcomputer program, RELIAB, which can handle complex transmission structures such as large latticed structures, tension-only structures, or structures that exhibit nonlinearities. RELIAB's accuracy is ascertained by comparing results with another computer program, TRANSREL, which accounts for the residual strength of latticed towers following progressive failure of one or more components.

Nonlinear analysis of 3-D steel frames

An analysis is described that models the behavior of planar prestressed concrete cable‐stayed bridges up to failure taking into account geometric and material nonlinearities. The geometric nonlinearities arise from cable sag, large deformations of the system, and from the shift of the centroid of the deck section caused by the material or by cracking of the concrete. The effect of the axial forces on the stiffness of the members is also considered. Material nonlinearities are encountered when one or more of the structure components, namely the stay cables, prestressing tendons, the reinforcement, or the concrete, exceed their elastic limits. Parametric studies are made on cable‐stayed bridges with the following cable arrangements: fan, semifan and harp‐type cable arrangement. To demonstrate the influence of the different types of nonlinearity on the internal forces and reactions three analyses were performed—namely elastic, geometric nonlinear, and geometric and material nonlinear analyses—and the results...

An interaction formula proposed for stainless steel SHS and RHS beam–columns

Nonlinear inelastic dynamic analysis of suspension bridges

Geometrical nonlinearity arises from the continuous change of shape under increasing loads on thin or long span members, and the materials nonlinearity due to the nonlinear behavior of the materials composing the structural element. In this study the finite element method is used to analyze fibrous reinforced concrete slabs, material and geometric nonlinearities were considered. Concrete is represented by degenerate quadratic thick shell element. Concrete behavior in compression is modeled by elastic perfectly plastic or strain hardening plasticity. A tensile strength criterion is used to follow crack initiation and propagation. A parabolic stress degradation function, which is based on the fracture energy concept, is used to model the tension stiffening effect of steel fibers. The reinforcement is considered as smeared within the concrete layers, and assumed as either an elastic perfectly plastic material or as an elastic-plastic material with linear strain hardening. Von Karman assumptions which is based on the total Lagrangian approach is used for the geometric nonlinearity. The numerical results using for both normal and lightweight fiber reinforced concrete slabs were predicted satisfactorily. The average predicted failure load of the investigated cases to the experimental failure load was 0.899 with a standard deviation of 0.092.

Behaviour and design of steel members with web openings under combined bending, shear and compression