Plastic Moment Research Articles

Effect of battens’ spacing on the cyclic response of built-up columns

Built-up columns have been widely used in buildings and bridges. However, despite wide application in steel construction, the seismic design of these columns has not been covered in either the design codes or the literature. On the other hand, past earthquakes have shown that built-up battened columns have been vulnerable to seismic actions. Therefore, it is crucial to investigate the seismic response of these columns and determine their governing failure mode, deformation, and bending moment capacity. This study investigated the effect of battens’ spacing on the cyclic response of built-up columns through experimental works and numerical simulations. Four columns with different batten spacing and chord distances were constructed and subjected to quasi-static cyclic loading. Besides, 24 built-up battened columns with different batten spacing, chord distances, and axial forces were simulated in ABAQUS software and subjected to similar cyclic loading. The obtained results indicated that the bulging of chord webs and the local buckling of chord flanges were the main reason for the failure of columns. Besides, the batten spacing significantly affected the bending moment capacity of built-up columns. Moreover, because of local buckling in flanges, built-up columns did not reach their plastic moment capacity. It was also observed that design codes’ limitations for batten spacing were not conservative and did not result in a similar safety margin for the bending moment capacity of built-up columns.

Bending and flexural-buckling strength of steel members considering strain-rate-effects at elevated temperatures

PurposeIn this study, the bending strength, flexural buckling strength and collapse temperature of small steel specimens with rectangular cross-sections were examined by steady and transient state tests with various heating and deformation rates.Design/methodology/approachThe engineering stress and strain relationships for Japan industrial standard (JIS) SN400 B mild steels at elevated temperatures were obtained by coupon tests under three strain rates. A bending test using a simple supported small beam specimen was conducted to examine the effects of the deformation rates on the centre deflection under steady-state conditions and the heating rates under transient state conditions. Flexural buckling tests using the same cross-section specimen as that used in the bending test were conducted under steady-state and transient-state conditions.FindingsIt was clarified that the bending strength and collapse temperature are evaluated by the full plastic moment using the effective strength when the strain is equal to 0.01 or 0.02 under fast strain rates (0.03 and 0.07 min–1). In contrast, the flexural buckling strength and collapse temperature are approximately evaluated by the buckling strength using the 0.002 offset yield strength under a slow strain rate (0.003 min–1).Originality/valueRegarding both bending and flexural buckling strengths and collapse temperatures of steel members subjected to fire, the relationships among effects of steel strain rate for coupon test results, heating and deformation rates for the heated steel members were minutely investigated by the steady and transient-state tests at elevated temperatures.

Reliability of Design of Floor Slab Systems Using Plastic Moment Distribution Method

This research study the reliability of designing continuous floor slabs with varying end conditions under affected ultimate Loads by plastic theory. This paper has adopted an approach using the plastic moment distribution method in the design of solid slabs .16 rectangular slabs have the same depth but different end conditions and dimensions in x and y- directions were investigated. The results obtained from the continuous solid slabs by plastic moment distribution method achieved the conditions of equilibrium, mechanisms, and plastic moment and it was compared with computer program adopted elastic theory method under loading combination ultimate limit state and serviceability limit state. The results are compared according to the parameters of the British Code (BS 8810) allow that any value of bending moments by the plastic method must be not less than 30 % of the elastic moment at supports and at span (maximum sagging moments) in plastic are high in elastic analysis. After comparing, all the obtained results showed that they are in agreement with the determinants of the British code, The method adopted in this study gave the values of the plastic moment (MP), at which the plastic hinge (PH) is formed and true mechanism of failure.

Evaluating the Vertical Extension Module of a Building with Installed Rotary Dampers at Joints

In this study, the shape of a vertical expansion module with a rotary-type damping device is proposed. The external energy dissipation capacity is confirmed through experiments and the performance of the module is simulated. It can be easily applied to high-rise structures, as the module is directly supported by the bearing walls without the need for a separate base system. Additionally, as the damper can be replaced, it is possible to enhance seismic performance even after construction. The simulation results show that the rotary-type damper is more effective in reducing the displacement, shear force, and moment than free and fixed joints. In the pushover analysis of a system modeled using the moment hinge of the rotary damper of the joint, the best response reduction effect is obtained when the yield moment of the hinge is defined as 1% of the frame plastic moment. As a result of the analysis of the multi-degree-of-freedom system considering a harmonic load, we determined that it is efficient for the hinge to yield after the displacement, and the acceleration response of the resonant structure reaches steady state during the installation. In the multi-degree-of-freedom system with slab joints added to the analytical model, the displacement response decreased gradually as the natural period of the structure decreased and the joint increased. This provides evidence that the damper does not affect the overall behavior of the structure. The most important design factor of the rotary-type friction damper, shown through the experiment, is the relationship between the frictional surface and the tightening force of the bolt.

Mechanical performance of coupled buckling-restrained steel plate shear walls

In order to improve the seismic behavior of coupled steel plate shear wall (CSPSW), a new type of coupled buckling-restrained steel plate shear wall structure is proposed. To study the mechanical characteristics of coupled buckling-restrained steel plate shear wall (CBRSPSW), calculating equations for coupling degree of this novel coupled shear wall is derived. The finite element software ABAQUS is used to conduct the parametric studies on the FE models of CBRSPSW and CSPSW. Besides, the ratio of the plastic sectional bending resistances of coupling beam and frame beam γ was selected as the main parameters to control the coupling degree. The mechanical properties of CBRSPSW and CSPSW, like failure mode, shear distribution, column internal force and coupling beam rotation, are analyzed and compared. Besides, the influences of the beam plastic moment ratio γ on the these properties are also studied. Through the numerical research, the coupling degree of CBRSPSW and CSPSW is recommended to be controlled within 0.35–0.45 so that rational mechanical behavior can be obtained.

In-plane cyclic tests of double-skin composite walls with concrete-filled steel tube boundary elements

This paper focused on a new type of double-skin composite wall in which concrete-filled steel tubes are used as boundary elements, and steel-bar space trusses are used to stabilize the faceplates. The new composite wall is architecturally attractive and has some perceived advantages in strength and construction. However, limited knowledge exists regarding its behavior under the combined cyclic in-plane lateral load and axial compression. This paper reports the test results of five experimental specimens subjected to the intended combined loading. Among the tested specimens, four developed the preferred flexure-dominated limit state, while one developed the undesired shear-dominated limit state. The specimens with the flexure-dominated limit states exhibited ductile behavior up to the drift of 0.036 rad with minor strength degradations. It was found that local buckles in the faceplates of the composite wall did not compromise wall lateral resistance. The effect of using supplementary steel headed studs to stabilize faceplates is also addressed in the paper. Aside from the experimental work, a simplified model was established to compute the wall plastic moment and lateral resistance of the wall with the flexure-dominated limit state. Predictions from the model were found to agree well with the test results, suggesting the model can be used for future design and analysis of the composite wall.

Inverse optimal damper placement via shear model for elastic–plastic moment-resisting frames under large-amplitude ground motions

A new method of optimal damper design is presented for elastic–plastic planar frame structures under large-amplitude earthquake ground motions. The transformation of a moment frame into the 1st-mode equivalent shear mass system leads to an efficient search of the optimal damper placement along the building height for the elastic–plastic moment frame. In the optimization procedure, a linear elastic bare frame is transformed into the 1st-mode equivalent shear mass system first. Then the optimization of the damper placement is conducted for the elastic shear mass system. After that, the damped shear mass system is inversely transformed into the elastic–plastic moment frame with the added dampers. This inversely transformed damper system in the moment frame is employed as an initial design and the local search-based optimization is conducted for the efficient distribution of dampers not only along the building height, but also among the different bay. The proposed method greatly reduces the computational task in the whole optimization procedure because only a limited number of time-history response analyses is required for elastic–plastic moment frames. It is demonstrated through numerical examples that the proposed method efficiently provides the damper designs with high accuracy. Finally, the importance of using the large-amplitude ground motions for damper optimization is demonstrated through the incremental dynamic analysis (IDA) for the optimally designed models.

The European Yield Model (EYM) for laterally loaded timber connections with smooth nails

ABSTRACT The European Yield Model (EYM) is a commonly accepted procedure to calculate the capacity of laterally loaded connections with dowel type fasteners. The standard procedure is specified in EC5 (EN 1995-1-1 2004) and uses characteristic values as input parameters for the calculation of characteristic values of the resistance of the connection. These characteristic values are the basis for an engineering design of structures. Nevertheless, there are situations, e.g. the design of a test set-up or a pushover analysis in earthquake engineering, when mean values of the resistance of a timber connection are needed. In this context, analytical equations and mechanical models were assessed on two levels by comparing theoretical values to experimental results. The first part of the research considered all the input parameters. The mechanical definition of the plastic moment proved to be more appropriate than the definition of a modified plastic moment according to EC5 for the determination of the yield moment of nails. On the other hand, it was confirmed that the embedment strength of Norway spruce softwood can be predicted reliably and slightly conservatively according to code regulations given by EC5. The definition for the withdrawal strength according to EC5 also seems to define a conservative lower boundary. The situation is not so clear for the embedment strength of oriented strand board (OSB). Test results are very scarce and do not account for the inhomogeneity regarding the thickness of the boards with higher density at the surfaces, which is the section where contact forces are transferred. In the second part, over 110 specimens considering eight different types of nailed connections were tested to assess different calculation procedures. The study focused on nailed connections with OSB and solid timber. This combination together with smooth nails as fasteners is very common in Europe for light-frame structures, especially in areas of low and medium seismicity because they exhibit large deformation capacity without losing strength. On the level of mean values, relationships are found between 1.00 and 1.47 for experimental results over calculated resistance, and it was found that the EYM is more conservative when the thickness of the sheathing is 10 mm instead of 18 mm, which means, that the expected failure mechanism changes from one to two plastic hinges. The findings are approximately the same if the relationship is studied on the level of characteristic values. Here, the relationship of values from experimental investigations over analytical calculation lays between 1.27 and 1.58 for a mechanism with one plastic hinge and between 0.90 and 1.12 for a mechanism with two plastic hinges. Based on these results, the question arises, if the EYM is the appropriate tool to predict the capacity of laterally loaded connections if comparatively large deformations occur between the connected parts. This question should be studied more detailed in the future.

A study on scantling formulae of plate members due to lateral pressure under the effect of axial loads

Existing rule scantling formulae of plate members are based on conventional plastic design theory, and do not necessarily reflect complicated plate bending phenomena under axial loads. In this study, we first formulated the effect of axial load on the fully plastic moment based on the von Mises yield criterion for longitudinally stiffened plate in addition to the well-known formula for transversely stiffened plate. In addition, we derived a theoretical formulation of the lateral pressure corresponding to 2-point hinge and 3-point hinge formation taking account of the effect of the additional lateral force due to the axial loads on the deflected plating, using a simple plate strip bending model assuming a long plate with a large aspect ratio.Then, a series of elastic-plastic FE analyses was carried out to verify the structural behavior and the effect of axial load on the plate plastic bending strength. The plate strength was evaluated based on the residual deflection criteria of two cases (0.26 mm and 4.0 mm), and the results were compared with the theoretical derivation. As a result, it was found that assumption of linear strength reduction to the axial stress can cover the transversely stiffened plate under compressive axial stress conservatively. As to the transversely stiffened plate under tensile axial stress and the longitudinally stiffened plate, the strength reduction was in accordance with the reduction in the fully plastic moment based on the von Mises yield criterion in the conservative side. Finally, based on the findings, the required plate thickness coefficients were proposed on an empirical basis both for transversely and longitudinally stiffened plate under compressive and tensile axial loads.

Research on distortional buckling capacity of stainless steel lipped C-section beams

Stainless steel lipped C-section components have complex nonlinear buckling behaviour, and the relevant calculation theories need to be improved. Therefore, based on experiments on the distortional buckling capacity of 8 stainless steel lipped C-section beams, a finite element model is established using the ABAQUS software, and the accuracy of the model is verified. Then, a series of parametric analyses are carried out, focusing on the influences of cold working, initial geometric imperfection and distortional buckling slenderness. Next, a further parametric analysis of the distortional buckling slenderness of stainless steel beams is conducted using the finite strip program CUFSM, and the effects of geometric parameters (section height, flange width, lip width and thickness) and the coupling between different parameters on the distortional buckling slenderness are analysed. A simplified formula of the critical stress of elastic distortional buckling for stainless steel lipped C-section beams is proposed and its accuracy is verified. Finally, based on the direct strength method, taking the full section plastic moment as the reference bearing capacity, a calculation formula of the distortional buckling bearing capacity is proposed. The results of the formula are compared with the experimental results, which proves that the formula can accurately predict the distortional buckling bearing capacity of stainless steel lipped C-section beams.

Assessment of structural adequacy of semi-rigid safety barriers

A procedure for assessing the structural adequacy of semi-rigid barriers, consisting of the determination of load-carrying capacity using plastic analysis and the calculation of the impact load, is presented. To reflect the dynamic effects of the soil, the plastic moment of posts is defined by multiplying the dynamic resisting force of a post by the distance from the impact loading point to the position of a plastic hinge. The impact load was determined by using a modified Olson model, idealizing the vehicle lateral acceleration-time relationship as a triangle instead of the half-sine function of the Olson model. For semi-rigid vehicle barriers with relatively small lateral stiffness, the proposed structural adequacy assessment procedure and FEA provided approximately the same results. However, for semi-rigid vehicle barriers with large lateral stiffness, the assessment procedure using the first impact load, different from the assumption of the modified Olson model, produced a rational design.

Non‐linear Analysis of Circular Composite Columns

AbstractComposite columns provide many advantages for the application in multi‐story and high‐rise buildings. However, EN 1994‐1‐1 does not provide rules for the design of circular concrete sections with fully encased steel profiles according to the simplified methods. Normally, the simplified method for the design of composite columns is based on a normal force‐moment interaction diagram which assumes plastic cross‐section resistance. However, the moment resistance is to be reduced by a reduction factor αM, considering among other the difference between strain‐limited and plastic moment resistance. This reduction factor is developed and calibrated for composite compression members with concrete encased sections, partially encased sections and concrete filled rectangular and circular tubes. Comparison of plastic moment resistance to results based on strain limitation show that the application for circular section with encased steel section but without a steel tube may lead to unsafe results.The paper discusses different approaches for the determination of the N‐M Interaction curve and the design on cross‐section level. The results obtained from these methods are then compared to each other for different dimensions of cross‐sections of circular columns; and for different ratios of reinforcements, various steel grades and for normal and high strength concretes. Furthermore, the investigation focuses on the validation of the reduction factor αM and shows for which section types the values according to Eurocode 4 cannot be applied.

Partial shear diagram of slim‐floor beams

AbstractSlim‐floor beams which have the steel sections fully or partially integrated into the concrete slab lead to a significant reduction of the construction height. Due to its flat lower surface, it provides favourable solution for technical installation. According to EN1994‐1‐1, for composite beams plastic moment resistance is assumed. In the case of slim‐floor sections, due to the reduced construction height by the integration of the steel beam in the concrete and its extended bottom flange, a large compression zone height may be expected, thus concrete failure in the compression zone may happen before reaching the plastic moment resistance Mpl,Rd. Here, strain limit resistance becomes decisive. For design with partial shear connection, EN1994‐1‐1 provides the partial shear diagram based on the plastic bending resistance Mpl,Rd which is not always suitable for slim‐floor beams. Based on strain limited method, the more suitable partial shear diagram of different slim‐floor beams can be developed. From parametric studies of different types of slim‐floor beams, the impacts of critical parameters on the design are highlighted, and the limitations of the current plastic resistance based partial shear diagram are suggested. A simplified calculation method for situation beyond the limitation are also proposed to guarantee an economical design of those beams.

Structural Study of Steel‐Concrete Double Composite Girder Bridge

AbstractIn Japan, the steel‐concrete composite girder bridge is widely used to reduce construction and maintenance cost, and improve constructability and the construction period. As an effort to decrease box girder construction cost, the narrow box girder bridge, which has a reduced box girder width, has been developed. Compared with a conventional box girder bridge, this type of box girder bridge simplifies the structure inside the box by narrowing the space between web plates. Furthermore, it is possible to reduce the number of members, welding length and painting area. The average economical span length is approximately 90m. Similarly, in European countries, a new type of composite girder bridge was developed and constructed for the same purpose as the bridge in Japan. The steel‐concrete double composite girder bridge, which has two concrete slabs on the upper and lower surfaces of the girder only in the region of the intermediate supports, is a type of medium span bridge. An advantage of adopting this structural system is that the cross sections of both the sagging and hogging bending moment areas are classified into the compact section at the ultimate limit state; that is, the maximum flexural strength of these sections can be taken full plastic moment. There are few constructed examples of this type of bridge in Japan. Because of the handling difficulty, the shop manufacturing cost of a box girder is, generally, more expensive than that of an I‐girder. Additionally, the design method for bridges has been revised since January 2018 and has changed from the allowable stress design method to the limit state design method in Japan. Therefore, the authors propose a new type of steel‐concrete double composite I‐girder bridge. The trial design of three‐span continuous girder bridges was conducted. In this paper, the effect of double composite action, for instance, the reduction of the girder height in the region of the intermediate supports, and applicable span length are discussed.

CHANGES IN THE CODE OF RULES
 FOR THE DESIGN OF STRUCTURES
 MADE OF CONCRETE WITH POLYMER
 COMPOSITE REINFORCEMENT

The article presents information about the
 changes made to the code of rules for the
 design of concrete structures reinforced with
 polymer composite reinforcement. New rules
 for the formation of relative deformations at
 the base point of a two-line diagram of concrete
 under axial tension, used to calculate
 reinforced concrete elements for the second
 group of limit states, are described. The rules
 for calculating re-reinforced structures of
 T-or I-beam cross-sections with a shelf in a
 compressed zone by the method of limiting
 forces are presented. The rules for taking into
 account the inelastic properties of concrete of
 the stretched zone when determining the elastic-
 plastic moment of resistance for the extreme
 stretched fibre of concrete with a rectangular
 cross-section and a T-shape with a shelf
 located in the compressed zone are clarified.

An analytical model for the behavior of I-shaped beam to cylindrical column connections at room temperature and high temperatures

PurposeIn this paper, a closed-form analytical solution for the prediction of moment-rotation and the rotational stiffness-rotation curves of I-shaped beam to cylindrical column connections, commonly used on offshore platforms, at room and elevated temperatures, are presented.Design/methodology/approachAn analytical solution for the prediction of moment-rotation and the rotational stiffness-rotation curves of I-shaped beam to cylindrical column connections is presented. The results of this model are compared with those of a non-linear coupled mechanical-thermal finite element model and small-scale experimental tests previously provided by the authors.FindingsIn this paper, a closed-form analytical solution for the prediction of moment-rotation and the rotational stiffness-rotation curves of I-shaped beam to cylindrical column connections, commonly used on offshore platforms, at room and elevated temperatures, is presented. The required yield and plastic moments in this model are provided as an extension to Roark's relationships. The results of this model are compared with those of a non-linear coupled mechanical-thermal finite element model and small-scale experimental tests previously provided by the authors. A reasonable agreement has been found between the analytical model results and the experimental/numerical modeling results.Originality/valueThis article is extracted from the author’s doctoral thesis, and all its achievements belong to the authors of the article.

Development of a new improved structural integrity assessment correlation for throughwall axially cracked 90° shape imperfect pipe bends under in-plane opening bending moment

In the present work, a systematic and detailed investigation on the plastic collapse load of 90° structurally defected pipe bends under in-plane opening bending was performed using three-dimensional finite element (FE) analyses. The analysis considers the material behavior as elastic-perfectly plastic (EPP) with a large strain formulation option. The structural defects in the pipe bend models included were ovality at mid-portion and throughwall axial crack (TAC) at the crown portion. Ovality varied from 0 to 20 % with 5 % increment at each step while the normalized throughwall axial crack (TAC) parameter length a/D from 0 to 1 with an increment of 0.2 in each step. As per the recommendation of clause NB-3213.25 in Section III of ASME B&PV code, Twice-elastic slope (TES) technique was extensively used to determine the plastic collapse moment (PCM) for all simulated pipe bend models from their corresponding reaction moment versus angular rotation curve. The analysis illustrated that both ovality and throughwall axial crack (TAC) significantly affected PCM load of pipe bends and when combined, the effect was almost double. In pipe bend models with thin walls and short bend radius, both ovality and TAC were found to be more vulnerable and the effect decreased with an increase in bend radius and thickness. The experimental results for pipe bend's plastic collapse moment available in open literature were used to validate the present finite element (FE) procedure and a new improved structural assessment correlation proposed for pipe bends with ovality and TAC defects.

Damage indices and fragility assessment of coupled low-yield-point steel plate shear walls

A new multiple lateral force resisting system consisting of coupled low-yield-point steel plate shear walls (C-LSPSW) was proposed as a promising alternative to improve the ductility, energy-dissipation capacity, architectural flexibility, and economic efficiency of steel plate shear walls (SPSWs). To investigate its seismic performance and damage behavior, eight C-LSPSW specimens with different configuration parameters, including two different stories and four different section sizes of coupling beams (CBs), were designed and the corresponding numerical models were established by verified modeling approach. The incremental dynamic analyses (IDA) were conducted on these specimens, and the multi-stage damage indices of the C-LSPSW system were proposed based on different damage states. The design suggestions for the C-LSPSW system were proposed in terms of the fragility analyses. The analytical results demonstrated that the ductile damage mechanism with the sequence of “infill plates to CBs or horizontal boundary elements (HBEs) to vertical boundary elements (VBEs)" was achieved more easily in the C-LSPSW system, which gave full play to the superiority of multiple seismic defense lines. Under high seismic excitation, the failure probability of the C-LSPSW system was smaller than that of the LSPSW system, and the coupling superiority was more obvious in higher structures. The optimum performance of C-LSPSW system was observed when the plastic moment capacity ratio of CBs to HBEs (MpCB/MpHBE) was 2.0. As a result, an optimal solution with MpCB/MpHBE = 2.0 was suggested as a good compromise between the architectural requirements, material efficiency, and seismic performance.

Model parameter prediction of lumped plasticity model for nonlinear simulation of circular reinforced concrete columns

This paper presents the model parameter estimation of a lumped plasticity model to realistically simulate the nonlinear load-deformation response of circular reinforced concrete columns under cyclic lateral loading. The model parameter calibration is based on an experimental database consisting of 210 circular columns with various input parameters, such as material strength, reinforcement layout, specimen geometry, and test configuration. The model parameter values for the initial stiffness, plastic rotation capacity, moment strength, and cyclic damage parameters are calibrated to the first-cycle envelope of each set of test data. Empirical predictive equations are developed to estimate the model parameters as functions of the input parameters using four different regression techniques: stepwise, ridge, lasso, and elastic net regression. The equations developed with lasso regression provided a reasonable trade-off between the prediction error and the number of input parameters. Important input parameters that affect the model parameters are the volumetric transverse reinforcement ratio, spacing of confinement steel, and axial load. As an application of the proposed column model, seismic fragilities of bridge columns in two bridge classes with different interior bent type are compared based on an existing distributed plasticity model and the proposed lumped plasticity model. The seismic vulnerability prediction discrepancy between the proposed and existing models tend to increase as the level of ground motion intensity increases. The prediction trend between the two models may differ by bent configuration and deck mass. The proposed column model reduces the seismic vulnerability of one-column bent bridge class, but increases the vulnerability of two-column bent bridge class.

Experimental and numerical investigation of steel-grout-steel sandwich shells for wind turbine towers

Aiming at enhancing a wind turbine tower's performance while keeping its external diameter below transportability-imposed limits, a steel-grout-steel sandwich base segment comprising a high diameter-to-thickness ratio is investigated herein, as an alternative to plain steel towers. An experimental campaign was firstly carried out, involving downscaled tower specimens which comprise the above said cross-section under bending loads, followed by the development of an elaborate finite-element (FE) model which can accurately capture the experimental behavior in terms of strength, stiffness and failure mechanism. A full-scale version of the validated model, representing the bottom segment of a wind turbine tower under design loads, was finally employed for the conduction of a parametric analysis, as regards the structure's geometry and material properties, and the investigation of the sandwich concept's possible advantages over a conventional steel structure. Owing to the synergy between the steel tubes and the grout core, the composite specimens almost reached their plastic moment capacity, premature buckling was prevented, and ductility was preserved, despite the significantly high diameter-to-thickness ratio of the steel tubes and the thin grout core. Although performance deteriorates as the diameter-to-thickness ratio of the two steel tubes increases, the relative advantage of the sandwich tower over a plain steel one becomes more prominent, especially when high-strength grout is used. It is thus demonstrated that a sandwich-type shell comprising a thin layer of grout may improve a wind turbine tower's load capacity, stiffness and stability without increasing the total amount of steel, nor extending its base diameter beyond transportability-related restrictions.