Slab Moments Research Articles

Residual strength capacity of reinforced reactive powder concrete two-way slabs subjected to drop weight

This paper presents an experimental investigation of the effect of the impact force on the residual strength capacity of simply supported reactive powder slabs. Eight specimens of reinforced reactive powder concrete slabs with dimensions of 500 x 500 mm and 70 mm in four categories were used. The influences of slab compressive strength (conventional concrete and reactive powder concrete), steel fiber proportion (1, 1.5, and 2%), percentage of reinforcement in the tension zone (ρ1=0.007, ρ2=0.011, ρ3=0.0179), and the number of impacts (two impacts, four impacts, and six impacts) were all investigated in this test. Investigations were carried out to ascertain each slab's residual response, including first cracking load, residual failure load, residual steel reinforcement strain, maximum central deflection, and crack pattern. The results showed that using reactive powder concrete instead of normal concrete increased the mechanical properties of concrete and resulted in a significant increase in failure load. In addition, the central deflection and strain increased. Increasing the reinforcement ratio increased the failure load while simultaneously decreasing the deflection due to the improvement in slab moment resistance. Furthermore, it was discovered through experiments that the addition of steel fiber to the mixture enhanced the slab’s post-cracking reactivity. The presence of steel fiber raised the slab strength resistance by 21.63% as the steel fiber ratio increased from 1% to 2%. This is because the addition of steel fiber increased the slab's tension resistance.

Analisis Kekuatan Pelat Lantai Dermaga di Pelabuhan Ciwandan Banten Terhadap Penambahan BMC

Pier 005B is located at Pelabuhan Indonesia II (Persero) Branch of Banten and has a length of 300meters and a width of 44 meters. It is planned that at Pier 005B, will be putted 1 (one) unit of Harbor MobileCrane (HMC) brand LHM 420 will be placed as a supporting tool for loading and unloading activities from andto ships. This HMC certainly has certain specifications and capacities, so it must be calculated properly againstthe additional load that can be accepted by the floor slab of Pier 005B. The research method used is descriptivequalitative. This HMC is capable of carrying a maximum load of 124 tons at a distance of 12 to 16 meters. Withthe HMC's own weight of 371 tons and the assumption of a human weight of 0.4 tons/meter2, the total weight ofHMC received by the floor slab is 22.68 tons/meter2. By using the SAP 2000 version 22 computer application,the ultimate internal forces due to the load on the floor slab are the ultimate moment of 7.27 ton.meter, theultimate shearing force of 7.61 tons and the limit of deflection of 7.17 mm. Then re-calculated the capacity ofthe existing floor slab in accordance with the Indonesian National Standard (SNI), obtained the internal forcesthat can be borne by the floor slab, namely the slab moment of 18.49 ton.meter, plate shear force of 22.38 tonand the deflection limit. plate by 14.58 mm. So it can be concluded that the floor slab of Pier 005B is capable ofcarrying the Harbor Mobile Crane (HMC) load.

WHEEL LOAD DISTRIBUTION IN STRAIGHT AND SKEWED CONCRETE SLAB BRIDGES STIFFENED WITH RAILINGS

This paper presents the parametric investigation of the influence of railings on the wheel load distribution in simply-supported, one-span, three- and four-lane straight and skewed reinforced concrete slab bridges using the finite element method. A total of 96 bridge cases were modeled using finite-element analysis (FEA) and bridge parameters such as span length, slab width, and skew angle are varied within practical ranges. Typical railings built integrally with the bridge were placed on both edges of the deck slabs. AASHTO HS20 truck loadings were positioned transversely and longitudinally to produce maximum longitudinal live load bending moments in the slabs. The FEA wheel load distribution and bending moments were compared with reference straight bridges without railings as well as to the AASHTO Standard Specifications for Highway Bridges and the AASHTO LRFD Bridge Design Specifications. AASHTO overestimates FEA moments for almost all bridge cases and this overestimation increases with the increase in the skew angle, and it is more significant in the presence of two railings. Also, it was found that the reduction in slab moment due to skewness and railings is cumulative. The presence of railings can be considered to be a possible method for strengthening and rehabilitating straight and skewed concrete slab bridges.

Seismic Analysis of Flat Slab by using ETABS

The flat slab is a two-way reinforced concrete slab that usually does not have beams and girders, and the loads are transferred directly to the supporting concrete columns. ETABS automates several slab and mat design tasks. Specially, it integrates slab design moments across design strips and designs the required reinforcement; it checks slab punching shear around column supports and concentrated loads; and it designs shear link and shear stud if needed. The actual design algorithms vary based on the specific design code chosen by the user. This manual describes the algorithms used for the various codes. Recent earthquakes in which many concrete structures have been severely damaged or collapsed, have indicated the need for evaluating the seismic adequacy of existing buildings. About 60% of the land area of our country is susceptible to damaging levels of seismic hazard. Many existing flat slab buildings may not have been designed for seismic forces. Hence it is important to study their response under seismic conditions and to evaluate seismic retrofit schemes. This system is very simple to construct, and is efficient in that it requires the minimum building height for a given number of stories. Unfortunately, earthquake experience has proved that this form of construction is vulnerable to failure, when not designed and detailed properly, in which the thin concrete slab fractures around the supporting columns and drops downward, leading potentially to a complete progressive collapse of a building as one floor cascades down onto the floors below. Although flat slabs have been in construction for more than a century now, analysis and design of flat slabs are still the active areas of research and there is still no general agreement on the best design procedure. To study the effect of drop panels on the behavior of flat slab during lateral loads, flat plate system is also analyzed. Zone factor and soil conditions- the other two important parameters which influence the behavior of the structure, are also covered. Software ETABS is used for this purpose. In this study relation between the number of stories, zone and soil condition is developed.

Study on the Influence of the Height of Steel Beam on Creep Effects of Composite Beams

The height of steel beam is an important parameter in the disign of structure. The effects of increasing the steel height of composite beam are quiet different from that of the pure steel beam because of composite and creep effects. To reveal the influences of this critical prarameter Rüsch constitutive equation of creep is used to obtain the exact results. With the increase of the steel height and after a limiting value is reached, the rate of the increase of the whole section stiffness becomes smaller, the rate of the increase of the compression zone of steel web becomes larger, yet the axial force and redistributed moment of concrete slab become almost constant. The deflection increases almost linearly and keeps a large slope with the increase of the steel height. Local buckling risk of the web must be considered.

INFLUENCE OF RAILING STIFFNESS ON WHEEL LOAD DISTRIBUTION IN TWO-SPAN CONCRETE SLAB BRIDGES

The American Association of State Highway and Transportation Officials (AASHTO) Standard Specifications or LRFD do not account for the presence of railings in the analysis and design of concrete slab bridges. This paper presents a parametric investigation of the influence of railing stiffness on the wheel load distribution in simply-supported, two-equal-span, and one-and two-lane reinforced concrete slab bridges using the finite-element analysis (FEA). A total of 160 bridge cases were modeled and bridge parameters such as span lengths and slab widths were varied within practical ranges. Various railing stiffness were investigated by assuming railings built integrally with the bridge deck and placed on both edges of the bridge. The FEA wheel load distribution and longitudinal bending moments were compared with reference bridge slabs without railings as well as to the AASHTO design procedures. Accordingly, the presence of railings reduced the FEA negative moments by a range of 54% to 72% and the FEA positive moments by a range of 40% to 61% depending on the railing stiffness. This reduction in slab moments due to the presence of railings could be considered an increase in the bridges load carrying capacity. The results of this investigation will assist bridge engineers in better designing and/or evaluating concrete slab bridges in the presence of railings. This could also be considered an alternative for strengthening existing concrete slab bridges.

Analysis of Non-Prismatic Two-Way Post-Tensioned Slabs

Using a moment-area procedure to analyze slab-beam with step haunches, rotational stiffness, carry over, and fixed-end moments of a flat slab are formulated for flat slabs with capitals and/or drop panels. Design factors derived are represented in graphical tables and may be used in the Equivalent Frame Method (EFM) for analyzing and designing two-way post-tensioned slabs. Both of equivalent prestressing loads: a point load and/or a concentrated moment are evaluated for the stiffer column-slab conjunction region due to tensioning prestressing tendons. The results clarify this prestressing equivalent load behavior, and provide a comprehensive basis of EFM for flat slabs. Compared to a prismatic member, a stiffer column-slab joint region increases the stiffness and carryover factor, and influences fixed-end moment of slab under gravity and prestressing loads. The expressions derived for design is available both hand-calculation and computer-aided program. A calculation example is given to illustrate the use of current expressions and existing tables and chart.

Rotation-free finite element ‘yield line’ analysis of non-isotropic slabs

A new, non-incremental advance in the lower bound finite element (FE) method for non-isotropic slab analysis is presented as a development of earlier work by the authors that was applicable only to isotropic slabs. The method provides a faster and simpler alternative to the full non-linear FE method in the non-linear analysis of slabs. Reinforced concrete was modelled as elastic perfectly plastic material, with rotation-free (RF) plate elements used to model slabs. They were modified to allow plastic yield lines to pass through elements satisfying non-isotropic yield conditions. Satisfying yield conditions and finding yield line directions differ significantly in their sophistication from their isotropic counterparts, as slab moment capacity is direction-dependent and yield line direction does not coincide with principal moment direction. Yield line effects were projected to element sides then used in curvature calculations. Analysis was performed incrementally, with the slab considered to behave linearly within each load increment. As a result, no iterations were required to reduce the unbalanced forces, as the behaviour within each load increment was in equilibrium. Accuracy was assessed against benchmark examples, and generally was within 2.5% of yield line collapse loads.

Influence of slab length on dynamic characteristics of subway train-steel spring floating slab track-tunnel coupled system

A subway train-steel spring floating slab track-tunnel coupling dynamic model, considering short and middle-long wavelength random track irregularities, and longitudinal connection between adjacent slabs of steel spring floating slab track, was developed. And the influence of slab length on dynamic characteristics of the system under different track conditions and train speeds are theoretically studied. The calculated results show: (1) In general, the acceleration of each component of the coupled system decreases with the increase of slab length under the perfectly smooth track condition; (2) Slab length has different influence laws on acceleration of each component of subway train-steel spring floating slab track-tunnel coupled system under random irregularity of track condition. The lower the dominant frequency distribution of vibration acceleration is, the higher influence slab length has; (3) With the increase of slab length, the force of rail, fastener and steel spring also decreases significantly, which helps to lengthen the service life of these components; (4) With the increase of slab length, the longitudinal bending moment of slab increases sharply at first, then it begins to drop slightly. When slab length exceeds the distance between two bogies of a vehicle, the longitudinal bending moment of slab changes little; (5) Slab length has significant influence on the dynamic force and displacement of the coupled system when train speed is higher.

Seismic Response of Underground Structure under Vertical Seismic Excitation

Seismic response of shallowly buried underground under vertical seismic excitation is studied. In order to simplify the analysis two steps are adopted in the analysis. In the first step structure is looked at as rigid body, and the dynamic response of the structure under vertical seismic excitation is obtained on the basis of soil-structure dynamic interaction analysis. In the second step at first the natural frequencies and mode shapes of the structure are obtained with consideration of the bending restraint of the side walls to roof slab, and then the dynamic response is determined by taking the dynamic response of rigid body in the first step as input, and furthermore the bending moment of roof slab is obtained. Key words: vertical seismic excitation, roof slab, soil-structure interaction, dynamic response

Suitable effective strip width of continuous bridge deck slabs system over flexible steel I-girders

Applying existing design standard provisions or analytical solutions is typically acceptable for the evaluation of slab negative moments subjected to moving traffic loads. As a breakthrough in computer technology, the finite element-based approach has become a notably versatile tool used for bridge deck analysis. In this study, a reliable finite element modeling technique is employed to discretize the models of a continuous bridge deck slab over steel I-girder system. The continuity between the girders and bridge slab has been carefully treated to ensure the overall structural action of the bridge deck. The key parameters affecting the deck slab moment such as slab system rigidity, girder spacing, patterns of moving loads and number of loaded traffic lanes are carefully considered in this study. The effective strip width concept has been used so as to take into account the evaluation of the slab negative moment. Based on the present numerical results, a set of reliable empirical formulas is proposed to determine the effective strip widths used for the direct assessment of the negative moment in a bridge deck slab. The application of these formulas is then compared with other provisions. Based on the suggested formulas, the slab reinforcement can be moderated for a common range of bridge deck proportions.

Finite-Element Analysis and Load Rating of Flat Slab Concrete Bridges

A significant portion of the nation’s aging bridge inventory consists of flat slab concrete bridges. Many of these bridges were constructed in the middle third of the 20th century, and although they are in generally good condition, they were not designed to carry modern highway loads. This research builds on prior studies that indicate that the equivalent strip width method—prescribed by AASHTO and widely used for the analysis of flat slab bridges—may be overly conservative and lead to underprediction of bridge structural capacity. The development of finite-element (FE) analysis software designed specifically for the load rating of flat slab bridges is presented. The FE software formulation and convergence were verified by comparison with predictions from commercial FE software under realistic loading scenarios. Results of live load tests of an instrumented, in-service flat slab bridge are reported. The FE model-predicted slab moments were shown to be conservative relative to the moments inferred from the load test data for a range of truck positions. Fourteen in-service flat slab bridges were load rated with both FE analysis and the equivalent strip method to assess the degree of conservatism inherent in the AASHTO approximate analysis. The results show an average increase in rating factor of approximately 26% when using FE analysis and that 58% of the bridges predicted to be under capacity using AASTHO approximate methods are sufficient based on FE analysis.

Stiffness reduction factor for post-tensioned flat plate slabs

The effective beam width model (EBWM) has been used for estimating force and drift demands on flat plate frames under lateral loads. The accuracy of this model depends strongly on how to estimate the effective stiffness of flat plate slabs. With an increase in slab moments due to lateral loads, slab cracks occur and propagate on the slab, which leads to a reduction in slab flexural stiffness. For post-tensioned (PT) flat plate slabs, the initiation and propagation of slab cracks can be delayed due to slab in-plane compressive stress induced by PT tendon forces. This study investigates the contribution of slab in-plane compressive stress to the slab stiffness reduction factor, which is defined as the ratio of slab stiffness obtained from a cracked slab section to that from the corresponding uncracked slab section. For this purpose, this study collected the test results of PT flat plate slab–column connection specimens and estimated the slab stiffness reduction factors (β) for those specimens with respect to a level of applied slab moment. Non-linear regression analysis is used to propose an empirical equation computing β for PT flat plate slabs using β estimated from the test results. The accuracy of the empirical equation for β is verified by comparing the lateral stiffness of a two-storey PT flat plate frame, obtained using the EBWM with the empirical equations for β, with that estimated from shaking table test results on the frame.

Flexural responses of concrete slab over flexible girders through FEA-based parametric evaluation

The determination of flexural responses in a concrete slab over flexible steel girder, forming a composite deck has been a timeconsuming subject for the design engineers. The existing provisions of the design standards such as AASHTO or analytical solutions based on local bending or plate theory usually ignore some significant parameters affecting the deck response, such as girder flexibility, number of loaded traffic lanes and ratio between deck width and girder span. This may lead to unrealistic prediction of bridge flexural responses used in the slab design practice. Although it is well known that finite element analysis is very versatile for structural analysis, very few studies have been reported dealing with explicit determination of deck slab response. The present study investigates the transverse negative bending moment of the slab cast over a number of steel girders, subjected to traffic loads, using verified composite Shell-Frame and Plate-Frame Models. The evaluation of such response is carried out through an extensive parametric study focusing on the effect of girder flexibility due to patterns of moving loads. Based on the numerical results, empirical relationships are proposed to determine the maximum slab moments anywhere along the girder span. The application of these relationships is then compared with other references. The suggested relationships seem to give more realistic and economical values of the considered transverse slab bending moment for a wide range of deck proportions.

비선형 해석에 의한 MRS 슬래브 단부 접합부의 모멘트 분포 연구

연구에서는 PC 구조의 단부를 연속으로 연결한 MRS(multi-ribbed moment resisting slab) 구조에 대한 해석 및 설계법을 제안하고자 하였다. MRS 구조에서는 더블티 부재가 역티보 위에서 부모멘트 철근에 의해서 연속으로 설계되므로, 부모멘트 철근이 좁은 지역에 밀집되는 문제가 발생할 수 있다. 따라서 선형 및 비선형 해석을 통하여 모멘트 분포 메커니즘을 분석하여, 적절한 설계법을 제시하였다. 또한 이 연구와 병행하여 실시한 실험 연구의 결과를 비선형상세 해석을 통하여 분석하였다. 그리고 단부구속효과 및 모멘트 재분배에 관한 연구를 위하여 비선형 골조 해석을 선택하여 변수별 연구를 수행하였다. 해석을 위한 재질 및 단면의 특성은 함께 진행된 실험 연구의 결과로부터 얻어졌으며, 비선형 골조 해석을 위한 소성힌지는 균열 모멘트, 공칭 모멘트, 부재 연성도 등의 값으로 모델링되었다. 선형 및 비선형 해석의 결과로부터 단부 회전 스프링과 부모멘트재분재를 통하여 MRS 구조의 단부 모멘트는 상당한 크기로 감소시킬 수 있음을 알 수 있었다.

Effective beam width for flat plate frames having edge beams

The effective beam width method has been widely used to predict lateral drifts and slab moments in flat plate frames subjected to lateral loads. However, the effective beam width method may not account for the contribution of the lateral stiffness provided by edge beams of the frames. This study examines the contribution of edge beams to the lateral stiffness of flat plate frames using the results of prior analytical and experimental research. It was observed that the lateral stiffness of flat plate frames with edge beams is larger than that of corresponding frames without edge beams. To account for the effect of the edge beam contribution on the effective beam width method, this study proposes a factor that modifies the effective beam width in the effective beam width method. To verify the accuracy of the effective beam width method with the proposed modification factor, this study estimated the lateral stiffness of the two-storey frames using the effective beam width method with the proposed modification factor, and compared that estimate with the lateral stiffness determined using experimental test results.

시공하중 및 균열 효과를 고려한 플랫 플레이트의 처짐 산정

테두리 보에 의한 휨강성이 확보되지 않은 철근콘크리트 플랫 플레이트의 구조설계는 강도 조건 뿐만 아니라 사용성에 의하여 지배받을 수 있다. 특히, 조기 재령 슬래브의 과하중 작용 및 균열 발생은 시공 중인 플랫 플레이트의 처짐을 크게 증가시키므로, 시공 순서 및 슬래브 처짐에 대한 영향은 플랫 플레이트 시스템 설계의 주요한 요소가 될 수 있다. 이 연구에서는 시공 순서 및 콘크리트 균열 효과를 고려한 슬래브 처짐 산정 과정을 제안한다. 시공단계 및 시공하중이 간편법에 의하여 정의되고, 각 시공단계별로 슬래브 모멘트 및 탄성 처짐, 유효단면 2차모멘트가 계산된다. 주열대와 중간대에서의 탄성 처짐은 유효단면2차모멘트 효과에 의해 비탄성 처짐으로 증폭되며, 슬래브 중앙부 처짐은 교차보법에 의하여 산정된다. 제안된 방법은 기존 실험 결과 및 비선형 해석 결과와의 비교를 통하여 검증된다. 또한, 제안법의 적용을 통하여, 시공 중인 플랫 플레이트의 처짐에 대한 시공주기 및 동바리 지지 층 수의 영향이 분석된다.

한계상태모델을 이용한 철근콘크리트와 포스트텐션 무량판의 통합해석

2층 규모의 철근콘트리트조 및 포스트텐션조 무량판구조를 1/3 스케일로 축소하여 제작한 실험체의 진동대 실험 결과를 바탕으로 무량판구조의 모델링 기법을 향상하고자 하는 연구를 수행하였다. 이 연구에서 적용한 모델링 방법은 슬래브의 휨모멘트에 의한 휨파괴, 불균형모멘트의 전달에 의한 휨파괴 및 펀칭전단파괴에 의한 슬래브-기둥 접합부의 모멘트 전달능력 상실등의 영향을 반영하는 매우 포괄적인 구조해석 방식이다. 펀칭전단파괴에 대해서는 중력비와 층간변위각에 기초한 한계상태 모델이 적용되었다. 이 논문에서 제안된 비선형 모델은 무량판구조의 진동대 실험 결과와 잘 부합하는 것으로 나타났다.

횡하중하의 포스트 텐션 플랫 플레이트 해석을 위한 강성감소계수

횡하중을 받는 포스트 텐션(PT) 플랫 플레이트 슬래브 골조의 해석은 일반적으로 유효보폭모델을 많이 사용한다. 횡 변위비와 불균형 모멘트을 예측하기 위한 유효보폭모델의 정확성은 PT 플랫 플레이트 슬래브의 유효강성을 어떻게 평가하느냐에 달려 있다. 슬래브 강성은 횡하중에 의한 작용모멘트의 증가와 함께 감소되기 때문에, 슬래브의 강성 감소현상은 플랫 플레이트 골조의 해석에 반영되어야 하며 균열의 영향 또한 고려되어야 한다. 횡하중을 받는 PT 플랫 플레이트 슬래브 구조의 정확한 해석을 위해 슬래브 강성감소는 유효보폭모델이 정확하게 되어야 한다. 이 목적을 위해 이 연구는 기존 연구자들에 의해 실시된 PT 플랫 플레이트 내부 및 외부 접합부의 실험 결과를 수집하였다. 그리고 이 연구는 시행착오를 통해 각 실험체의 횡강성에 유효보폭모델의 강성이 수렴하도록 슬래브의 폭을 감소시켰다. 슬래브의 모멘트 크기에 따라 비선형 회귀 분석을 수행함으로서 슬래브에 대한 강성감소계수 계산식을 제안하였다. 이 연구에서는 제안된 식의 정확성을 검증하기 위해서 PT 플랫 플레이트 골조의 실험 결과와 비교하였다. 제안된 식을 적용한 유효보폭모델은 작용하중의 크기에 따라 변화하여 PT 실험체의 실제 강성을 잘 예측하는 것으로 나타났다.

A modified equivalent frame method for lateral load analysis

The equivalent frame method (EFM) was developed for two-way slabs as a simple approximate method. Current design codes (ACI 318-05, Eurocode 2 and BS 8110) permit the EFM for the analysis of two-way slab systems under gravity loads, as well as lateral loads such as seismic loads. The EFM, however, was developed based on a semi-empirical formula, derived from the behaviour of two-way slab systems under gravity loads. This study shows that the EFM is not appropriate in accurately predicting the response of two-way slab systems under lateral loads. To improve the EFM under lateral loads, this study proposes a modified equivalent frame method (MEFM). To verify the MEFM, an idealised two-storey flat plate frame is considered and analysed by both the MEFM and elastic finite-element (FE) analysis for estimating slab moments and lateral drifts. Analysis results obtained from the conventional EFM and effective beam width method (EBWM) are also compared. The lateral stiffness, based on the proposed MEFM, was also compared with experimental data.