Showing papers on "Bending moment published in 2016"

Structural performance of stainless steel circular hollow sections under combined axial load and bending – Part 1: Experiments and numerical modelling

Abstract: A comprehensive experimental and numerical investigation into the structural performance of stainless steel circular hollow sections (CHS) under combined compression and bending moment has been performed and is fully reported in the present paper and its companion paper. The experimental programme employed four CHS sizes made of austenitic stainless steel, and included material tensile coupon tests, four stub column tests and twenty combined loading tests. The initial loading eccentricities for the combined loading tests were varied to provide a wide range of bending moment-to-axial load ratios. In conjunction with the testing programme, a numerical modelling programme was performed to simulate the experiments. The developed FE models were shown to be capable of replicating the key test results, full experimental curves including the post-ultimate range and deformed failure modes. Upon validation of the FE models, a series of parametric studies were conducted in the companion paper, aiming at extending the current test data pool over a range of cross-section sizes and combinations of loading. The experimental data, together with the generated parametric study results, were analysed and employed to evaluate the applicability of the codified provisions given in the European code, American specification and Australia/New Zealand standard for design of CHS under combined loading. Improved design rules were also sought through extension of the deformation-based continuous strength method (CSM) to the case of stainless steel CHS under combined loading.

Analysis of mechanical behavior in a pipe roof during excavation of a shallow bias tunnel in loose deposits

Abstract: This paper presents a study on the mechanical behavior in a long pipe roof during excavation of a shallow bias highway tunnel in loose deposits. The mechanical parameters of the surrounding soil were obtained by triaxial consolidated-drained shear tests on large reconstituted specimens. Three-dimensional numerical modeling was conducted to simulate the tunnel construction process. Six typical construction stages were simulated to analyze the effects of tunnel support elements, topographic and geological conditions on the mechanical behavior of the pipe roof. The modeling results revealed the variation of force and bending moment distribution in the pipe roof during excavation. Three main conclusions were drawn: (1) for the shallow and asymmetrically loaded tunnel buried in loose deposits, a pipe roof at the entrance can effectively reduce the stresses and asymmetric loading between the tunnel support elements and enhance the tunnel safety during construction; (2) because of asymmetrical stresses, the umbrella arch could shoulder much of the axial force of the pipe roof and the protection arch could reduce the force on the pipe roof effectively; (3) influenced by the asymmetric topography, the maximum force and bending moment in the pipe roof occurred mainly in the upper right tunnel heading. As the stiffness of the retaining wall, protection arch, umbrella arch, and the surrounding loose deposits were different, the force and bending moment distribution in the pipe roof was highly non-uniform during excavation. The simulation results should be significant both for the pipe roof design and the construction of other tunnels in similar geologic conditions.

Axial-flexural interaction in square RC columns confined by intermittent CFRP wraps

Abstract: External reinforcing of concrete elements by CFRP composites is a well-accepted method adopted for strengthening all structural load-bearing members including reinforced concrete (RC) columns. Previous studies have been mostly focused on strengthening RC columns for pure axial-loads, while most RC columns practically function as beam-columns; that is, they are subjected to both axial loads and bending moments simultaneously. It is the objective of the current study to carry out an experimental assessment of the load bearing capacity and ductility of columns externally strengthened with intermittent CFRP wraps when subjected to simultaneous axial loading and bending moment. The assessment is accomplished by comparing intermittently wrapped columns with unconfined ones in terms of their strength and ductility. For this purpose, 10 square RC columns, 133 × 133 mm across and 500 mm in height, were subjected to zero, 30, 60, 90, and 120 mm loading eccentricities. The results of the study showed that, compared to unconfined RC columns, intermittent wrapping of square RC columns with CFRP improved their performance through enhanced load carrying capacity and ductility under eccentric loading. Finally, the P–M (axial loading-bending moment) interaction diagrams were drawn for the strengthened columns. Comparison of the experimental results with those obtained from the expressions suggested in different codes such as ACI 440.2R and fib bulletin 14 showed the conservative estimates of these codes in comparison to experimental measurements.

Shear Stress Calculation and Distribution in Variable Cross Sections of Box Girders with Corrugated Steel Webs

Abstract: Based on the condition of static equilibrium and the equivalent law of shearing stress of an infinitesimal segment, this paper provides a strict derivation of the general formula for shearing stress in a nonuniform box girder with corrugated steel webs in the elastic stage. The derived formula is applied to investigate the stress distribution in concrete flanges and corrugated steel webs. Additional shear stress was found to be caused by the bending moment, and the axial force should be included in calculations from the effect of variable cross sections, which are quite different from that of the uniform cross sections. Moreover, because the additional shear stress of the bending moment is self-balanced, the shear force distribution can be adjusted between the concrete slabs and steel webs. Research shows that shear stress decreases markedly in the webs, whereas the shear stress apparently increases in the inclined bottom flange in the action of the bending moment. This study also found and explai...

Axial Load–Moment Interaction Diagram of Circular Concrete Columns Reinforced with CFRP Bars and Spirals: Experimental and Theoretical Investigations

Abstract: North America’s current design codes and guidelines allow the use of fiber–reinforced polymer (FRP) bars as the primary reinforcement in concrete structures and provide design recommendations for using these bars. Because of a lack of experimental data, however, FRP bars have not been recommended for resisting compression stresses as longitudinal reinforcement in columns or compression reinforcement in flexural elements. This paper presents test results of an experimental program to investigate the structural performance of 10 full-scale circular concrete columns reinforced with carbon fiber–reinforced polymer (CFRP) bars and spirals subjected to combined axial compression loads and bending moments. The test variables include different eccentricity-to-diameter ratios and two types of reinforcement (CFRP and steel). The test results show that the CFRP- and steel-reinforced concrete columns behaved similarly up to their peak loads. The failure of the test specimens under different levels of eccentri...

Detection of Tension Loss in Cables of Cable-Stayed Bridges by Distributed Monitoring of Bridge Deck Strains

Abstract: Development of a simplified approach for monitoring the cables of cable-stayed bridges is described in this article. The method introduced in this paper uses the distributed measurement of strains along the bridge deck to detect the cables that have totally or partially lost their tensile force. The fundamental principle employed in formulating the method is the interrelationship between the individual cable forces and the bending moment along the bridge span. The proposed method was evaluated through an experimental program that involved fabrication and testing of a reduced scale model of a single plane cable-stayed bridge. Distributed strain along the span length was monitored by a Brillouin Optical (Neubrex, Hyogo, Japan) Time Domain Analysis fiber optic sensor system. Strain gauges, Fiber Bragg Grating sensors (Technica Optical Component, LLC, Beijing, China), and a finite element model of the bridge were employed for evaluating the efficiency of the proposed method. Several different damage c...

How two-dimensional bending can extraordinarily stiffen thin sheets.

Abstract: Curved thin sheets are ubiquitously found in nature and manmade structures from macro- to nanoscale. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state for small deflections. This assumption, however, goes against intuition. Simple experiments with a cantilever sheet made of paper show that the cantilever stiffness largely increases with small amounts of transversal curvature. We here demonstrate by using simple geometric arguments that thin sheets subject to two-dimensional bending necessarily develop internal stresses. The coupling between the internal stresses and the bending moments can increase the stiffness of the plate by several times. We develop a theory that describes the stiffness of curved thin sheets with simple equations in terms of the longitudinal and transversal curvatures. The theory predicts experimental results with a macroscopic cantilever sheet as well as numerical simulations by the finite element method. The results shed new light on plant and insect wing biomechanics and provide an easy route to engineer micro- and nanomechanical structures based on thin materials with extraordinary stiffness tunability.

Behaviour and design of stainless steel SHS and RHS beam-columns

Abstract: Previous studies on stainless steel tubular section beam-columns have revealed shortcomings in established codified design methods. These shortcomings stem principally from inaccurate predictions of the bending and column buckling end points of the design interaction curves, where the bending moment end points are tied to the elastic or plastic moment capacities without considering strain hardening, while the column buckling end points are often over-predicted. Inaccuracies also arise due to the adopted interaction factors, which do not fully capture the structural response of the stainless steel members under combined loading. These observations prompted the present research, which is aimed at developing more efficient design rules for stainless steel tubular section beam-columns. In the presented design proposals, the deformation-based continuous strength method (CSM), allowing for strain hardening, was used to determine the bending moment capacities (i.e. the bending end points), while the column buckling strengths (i.e. the column end points) were calculated according to recently proposed buckling curves. Based on these more accurate end points, new interaction factors were derived following a comprehensive numerical simulation programme. The accuracy of the new proposals was assessed through comparisons against over 3000 experimental and numerical results. Compared to the current design standards, the new proposal yields a higher level of accuracy and consistency in the prediction of stainless steel square and rectangular hollow section (SHS and RHS) beam-column strengths. Use of the proposed interaction factors but with the Eurocode bending moment capacities and revised column buckling strengths as the end points was also assessed and shown to result in more accurate and less scattered strength predictions than the current Eurocode provisions. The reliability of the proposals has been confirmed by means of statistical analyses according to EN 1990, demonstrating its suitability for incorporation into future revisions of international design codes for stainless steel structures.

Evaluation of seismic performance of pile-supported models in liquefiable soils

Abstract: The seismic performance of four pile-supported models is studied for two conditions: (i) transient to full liquefaction condition i.e. the phase when excess pore pressure gradually increases during the shaking; (ii) full liquefaction condition i.e. defined as the state where the seismically-induced excess pore pressure equalises to the overburden stress. The paper describes two complementary analyses consisting of an experimental investigation carried out at normal gravity on a shaking table and a simplified numerical analysis, whereby the soil-structure interaction (SSI) is modelled through non-linear Winkler springs (commonly known as p-y curves). The effects of liquefaction on the SSI are taken into account by reducing strength and stiffness of the non-liquefied p-y curves by a factor widely known as p-multiplier and by using a new set of p-y curves. The seismic performance of each of the four models is evaluated by considering two different criteria: (i) strength criterion expressed in terms of bending moment envelopes along the piles; (ii) damage criterion expressed in terms of maximum global displacement. Comparison between experimental results and numerical predictions shows that the proposed p-y curves have the advantage of better predicting the redistribution of bending moments at deeper elevations as the soil liquefies. Furthermore, the proposed method predicts with reasonable accuracy the displacement demand exhibited by the models at the full liquefaction condition. However, disparities between computed and experimental maximum bending moments (in both transient and full liquefaction conditions) and displacement demands (during transient to liquefaction condition) highlight the need for further studies.

Structural performance of stainless steel circular hollow sections under combined axial load and bending - Part 2: Parametric studies and design

Abstract: This paper reports the second part of the study on the structural behaviour of stainless steel circular hollow sections subjected to combined axial load and bending moment. A series of numerical parametric studies is presented, using the validated finite element (FE) models from the companion paper, with the aim of generating further structural performance data over a wider range of stainless steel grades, cross-section slendernesses and combinations of loading. The considered parameters include the outer cross-section diameter, the ratio of outer cross-section diameter to thickness and the initial loading eccentricity. Both the experimentally and numerically derived section capacities were compared with the strength predictions determined from the current European code, the American specification and the Australian/New Zealand standard, allowing the applicability of each codified method to be assessed. The comparisons revealed that the current design standards generally result in unduly conservative and scattered strength predictions for stainless steel circular hollow sections under combined loading, which can be primarily attributed to the neglect of strain hardening in the determination of cross-section resistances and to the use of linear interaction formulae. To overcome these shortcomings, improved design rules are proposed through extension of the deformation-based continuous strength method (CSM) to the case of circular hollow sections subjected to combined loading. Comparisons between the proposals and the test and FE results indicate a high level of accuracy and consistency in the predictions. The reliability of the proposed approach was confirmed by means of statistical analyses according to EN 1990.

Investigation on flexural strength of cold-formed thin-walled steel beams with built-up box section

Abstract: Built-up sections are widely used in cold-formed thin-walled steel frames. This paper mainly investigates the in-plane behaviour of built-up box beams with nested C section and U section under pure bending about strong and weak axis. The four-point bending test was conducted on a total of 7 groups of specimens, including built-up box sections (CU) and individual sections (C, U). A finite element model is developed and verified by the test results for further parametric analysis. The stress distribution at mid-span cross-section shows that the components in built-up beams can resist the bending moment together. For built-up box beams bending about strong axis, the reasonability of the capacity superposition method and equivalent method is assessed by the discussion on test results and numerical analysis results. The equivalent box section is suggested to calculate the flexural strength of built-up box beams bending about weak axis. Finally, the comparison between predicted and actual flexural strength indicates that this simplification of the proposed method can slightly under-estimate the flexural strength.

Control Parametric Analysis on Improving Park Restoring Force Model and Damage Evaluation of High-Strength Structure

Abstract: In the dynamic time-history analysis of structural elastoplasticity, it is important to develop a universal mathematical model that can describe the force-displacement characteristics for restoring force. By defining three control parameters (stiffness degradation, slip closure , energy degradation ), the Park restoring force mathematical model can simulate various components. In this study, the Park restoring force has been improved by adding two control parameters (energy-based strength degradation and ductility-based strength degradation ). Based on the testing data, the constitutive model is input and 55 numerical models are developed to analyze the effects of various parameters on structural behavior. Conclusion. (1) has determinative effect on structural behavior; the effect of is basically consistent with that of ; has significant effect on shear forces and bending moments; has significant effect on displacements and accelerations; has significant effect on shearing forces, acceleration, and total energy consumptions. (2) Based on the classification of four types of damage level, the recommended values for , , , , and are presented. (3) Based on the testing data of high-strength columns, the recommended values for the five control parameters of the improved Park restoring force model are presented.