I-shaped Beams Research Articles

Effect of load height on elastic buckling behavior of I-shaped cellular beams

The effect of load height on the elastic moment gradient factor (Cb) for laterally unsupported I-shaped cellular steel beams under uniformly distributed load is numerically investigated in this paper. This study is carried on simply supported cellular beams for different cross-sections, beam slenderness, size and spacing of circular openings. The effect of web and flange slenderness on the elastic buckling behavior of cellular steel beam is also investigated in the present work. For determining the effect of load height on Cb, three different possible levels of loading positions; viz., uniformly distributed load applied at the shear center, at the top flange, and at the bottom flange are considered and the numerical results are compared with the standard case of uniform moment condition.It is observed that the presence of web perforations in the case of cellular steel beam significantly affects the elastic stability of beams. Numerically obtained Cb factors for cellular beams are compared with those obtained from equations mentioned in SSRC guidelines applied to the cellular beams. A significant variation is observed between Cb factors obtained from numerical finite element analysis and the equations mentioned in SSRC guidelines applied to cellular short span beams having slender webs and closely spaced openings for considered three different levels of loading positions. This variation is due to the fact that the instability in the cellular steel beam is associated with severe web distortion which is ignored in the formulations of SSRC guidelines. The equations of SSRC guidelines to cellular steel beams are applicable for longer span beams wherein the lateral-torsional buckling mode is governing. The uniformly distributed load applied at the top flange of the cellular beam is the most critical condition and resulting in the least Cb factors.

Experimental Study on Joint Properties of Steel Secondary Beam Connected with Concrete Main Beam Using an Embedded Part

In this paper, a joint of I-shaped steel secondary beam connected with concrete main beam using an embedded part was simplified from a practical engineering by adopting the scale 1:3. Six specimens were tested. The effects of different concrete main beam heights (245 mm and 295 mm), concrete floor slab, rigidity of steel secondary beam and height difference between the secondary beam and main beam tops on the mechanical performance and failure mode of specimens were analyzed. Results show that flexural failure is often found in the steel secondary beam. But the failure mode is changed to joint failure in the main beam if the rigidity of steel beam is increased locally at the mid-span region. Moreover, setting floor slab and increasing rigidity of steel secondary beam can all improve the load-carrying capacity of the joint. The safety of joint can be obtained by strengthening the stirrups adjacent to the embedded part and longitudinal steel bars under the part.

Technical Note: Unbraced Length Requirements for Steel Special Cantilever Column Systems

AISC Seismic Provisions Section E6.4b for steel special cantilever column systems (SCCS) requires clarification based on inquiries to the AISC Steel Solution Center. In the 2016 edition, it is unclear if bracing is required for all special cantilever columns or for columns with unbraced lengths that exceed the maximum beam brace spacing of Lb per Section D1.2a for moderately ductile members. Instead of using Equation D1-2, which is applicable to I-shaped beams only, equations for SCCS columns have been derived for both I-shaped members and rectangular HSS or box-shaped members. The proposed revision provides specific situations when bracing is required.

Shear behavior of I-shaped wood-steel composite beam

To expand the application of wood as a building material, a new type of I-shaped wood-steel beam that consisted of laminated veneer lumber and cold-formed thin-walled steel was considered in this paper. The shear performance of nine wood-steel composite beams was tested to evaluate the effects of shear span ratio, web thickness, and flange thickness. Then, the failure pattern and failure mechanism of the composite beams were analyzed. The main affecting factors of shear capacities were also discussed. Furthermore, the calculation formula for bearing capacities of composite beams was established and the calculation results were compared with the experimental results. The experimental results showed that the combined effect of composite beams was excellent. The shear capacity was mainly affected by shear span ratio and web thickness. The calculation formula of the shear capacity was established based on the shear flow theory and the specification for structural steel buildings. The formula was derived from the micro-segment balance method and the reciprocal theorem of shear stress. The calculation results according to the formula were in good agreement with the experimental values.

Damage identification using deep learning and long-gauge fiber Bragg grating sensors.

This study proposes an innovative structural damage identification method using dynamic response measured by long-gauge fiber Bragg grating (FBG) sensors and accelerometers to train deep convolutional neural networks (DCNNs). At the same time, the pre-trained model is applied to another structure through transfer learning (TL) technology. To verify this method, the I-shaped steel beam vibration test was conducted at first. Three types of data, acceleration, wavelength, and the fusion of the former, are utilized to train convolutional neural network (CNN) models, and the models are then tested and compared. In TL, another CNN is pre-trained using FBG data of steel beam. Next, the data of T-shaped reinforced concrete (RC) beam are employed to train the pre-trained model. The performance of the CNN is evaluated by training history and the confusion matrix. The results show the CNN-based damage identification method can classify the damage pattern accurately. The CNN trained by fusion data has both high classification accuracy and faster training speed. TL technology can greatly reduce the training time of other target tasks in the same fields.

Improving calculating theory of multiple-cavity reinforced concrete floor panels

It is a known fact that core slabs are introduced as I-shaped beams (T-beams) to simplify calculations and are considered according to the beam theory. However, such a view may cause erroneous calculation results. This is particularly evident when calculating the second group of limit states. The aim of this survey is to examine the influence of the cross current representation of core slabs for samples of various length by defining the impact of these factors (the shape of the cross-section and length) on the bearing and nonrigid capacity as well as a cracking load. The paper makes the calculating theory of reinforced concrete framing clear, in particular, core slabs according to the limit states. The author dwells upon samples of slabs of various lengths with a natural cross-sectional shape in comparison with I-shaped samples of similar length. The author should emphasize that it is assumed both in analytical calculations and in software based on FE analysis in order to save time and computing resources. The author performs a computational investigation of core slabs in a nonlinear setting with forming a plastic centroid in the middle of a slab in the study. It is found out that the slab length affects the calculation results of the considered shapes. The shorter the length, the clearer cut the deviation in the load deflection plots.

The Collapse Analysis of the Lateral-Torsional Buckling of I-Shaped Stepped Steel Beams

The use of a non-prismatic member such as a stepped beam as a design method has the ability to function as a tool for steel beams optimization. A cover plate is partially welded on the upper and lower flange of the member at the maximum bending moment location to increase its flexural strength and, under critical load, flexural members bend about its strong axis, displace to the lateral direction, and twist coincidentally through a phenomenon known as the Lateral-Torsional Buckling (LTB). There is, however, no equations in the AISC 360-16 specification to calculate the critical moment of a stepped beam (Mst). Therefore, this research focuses on developing Mst for a simply supported stepped beam which deforms on its shear center under static-transverse loading through the use of a collapse analysis and the behavior of the beam. The results showed the welded cover plates consequently increased the LTB resistance of the prismatic I-shaped steel beam from 9.8% to 202% while the critical moment increased more significantly with an increment in the ratio of the cover plate length to the unbraced length (α). The cover plate thickness was observed to have dominantly affected only a large α ratio while the post-buckling characteristic of large α showed a sudden collapse phenomenon. Furthermore, the LTB modification factor was generated in this study due to the initial geometrical imperfection from the first mode of Eigen shape with maximum amplitude Lb/2000 (Cb1) and stepped beam shape (Cst) which were required to estimate the critical moment of a stepped beam based on the AISC equation for a prismatic beam.

Numerical investigation on shear strength of tapered perfect end web panels

Plate girders are used as an alternative in construction when hot rolled I-shaped beams show poor strength or do not meet design requirements. Under high bending moments and shear forces, it is more efficient to use tapered plate girders. Current design codes lack specific design rules to estimate shear strength of plate girders with tapered web. The aim of this research is to investigate the elastic buckling and ultimate shear strengths of tapered end web panels in plate girders. More than two hundred detailed finite element models of plate girders with tapered end web panels are constructed and analyzed to cover a wide range of geometric parameters including: aspect ratio of end web panel, depth–to-thickness ratio of end web plate, inertia of intermediate stiffeners, and angle of tapering. Upon validation of the numerical solution, numerical results are used to establish a mathematical expression for the ultimate shear strength of prismatic and tapered end web panels. Design requirements of intermediate stiffeners are also proposed to achieve >95% of shear strength of web when stiffened with infinitely rigid stiffeners.

Mechanical Analysis of Shape Memory Alloy Beams under Asymmetric Bending

Based on the bending theory of beams, combining with the constitutive relationship of shape memory alloy materials, the asymmetric bending of shape memory alloy beams under concentrated load was studied. Considering tension-compression asymmetry on both sides of the tension and compression in the process of bending, tension-compression asymmetry coefficient was introduced, by using the step-by-step method. The stress distribution, neutral axis displacement, curvature and phase boundary of the beam sections of the I-shaped cross-section shape memory alloy beam were analyzed. The results show that under the same load, the maximum offset of the neutral axis displacement increases with the increase of tension-compression asymmetry coefficient. Under the same tension-compression asymmetry coefficient, the displacement and curvature of the neutral axis increased with the increase of load; as tension-compression asymmetry coefficient increased, the proportion of mixed phase increased gradually, the proportion of martensite phase decreased, and the asymmetry of phase boundary became more obvious. Under the same conditions, the rectangular section is more suitable. The cross section of I shaped cross section was prone to occur phase transformation.

Nonlinear shear analysis of I-shaped beams with arbitrary inclination angles of shear reinforcement

We studied the effect of the inclination angle of stirrups and wire mesh on the web-crushing strength of reinforced concrete I-beams beams. Experimental studies were carried out in Kuban State Technological University. The variable parameters of the tested specimens included concrete compressive strength, level of prestressing, cross-sectional shape, shear span, shear reinforcement ratio and angles of inclination of stirrups or wire mesh. The strength of beams was calculated with the Cyclic Softened Membrane Model for reinforced concrete (CSMM), developed at the University of Houston and implemented in the OpenSees software package. The modeling of the web of the beams was fulfilled with quadrilateral finite elements with the assigned material FAReinforcedConcretePlaneStress. The flanges of the beams resisting the bending moment were modeled with nonlinear volumetric elements having fiber section. Uniaxial Kent-Scott-Park concrete material and uniaxial bilinear steel material were assigned to the flanges. Calculation results are close to experimental data having wide variation of the materials properties and structural parameters of beams.

Flexural Behaviour of Delta Hollow Flange Steel Beam with and without stiffeners

In recent years of construction, steel has been considered as the most commonly used construction materials. Cold Formed steel has many structural benefits like high strength, greater stiffness, high ductility with excellent structural properties and fire resistance. The Cold formed steels are usually used in day by day in residential, commercial and industrial buildings around world. It also reduce the cross section of an element. Steel structure are faster in construction. The main aim of this paper is to study new steel beam. Rather than normal I-shaped beam, it is innovated to form Triangular Hollow Flange Beam (THFB) with slender web using required welded connection to improve the flexural capacity. THFB is also called as Delta Hollow Flange Beam (DHFB). Hollow Tubular Flange Beam provide more strength, stiffness, and stability than a flat plate flange with the same amount of steel. Flanges resist the applied moment, whereas web plates resist the induced shearing force. To improve the flexural resistance the use of the stiffeners also plays an important role, hence the flexural behavior of DHFB with the addition of transverse stiffeners has been investigated in this research work. Initially the section for the research has been chosen, Ultimate load has been calculated manually, Weld used for the sections are designed and they were analyzed through the Finite Element software called ‘ANSYS’. Later, five different specimen which includes specimen with and without stiffeners has been tested experimentally. The flexural test was carried out, along with that other properties like Ductility properties also calculated. From both analytical and experimental study DHFB shows positive results. They were highly used in various application which includes purlins, girts, portal frames and steel frame structures. Steel structure are faster in construction.

Hysteretic behavior of link beams with different cross-sections and stiffener arrangements

In conventional engineering practice, the use of stiffeners and flanges on both faces of stiffened web panels for I-shaped link beams provides fully restrained boundary conditions. In tubular link beams, however, the stiffened web panels possess simply supported boundary conditions due to the use of single-sided stiffeners and flanges.This study investigates the boundary condition effects of stiffened web panels in tubular and I-shaped link beams on their rotation capacity assuming similar area, moment of inertia, length and stiffener spacing. Based on the numerical results, I-shaped link beams demonstrated an approximately 78% higher rotation capacity compared to tubular link beams under the same conditions which could be due to the better behavior of the stiffened web panels of I-shaped link beams.In order to improve the boundary conditions in tubular link beams, a new stiffener arrangement is proposed. This novel arrangement led to 30% increase in stiffener spacing and 15% decrease in stiffener sizing. Furthermore, another stiffener arrangement is suggested to boost the rotation capacity of long tubular link beams by utilizing additional stiffeners on flanges. Using this arrangement, the rotation capacity was enhanced up to four times the conventional tubular link beams through the Tension-Field Action taking place in the flanges due to additional flange stiffeners.

Optimization of partially connected composite beams using nonlinear programming

Due to concrete being consistently used in the filling of prefabricated linear steel structural floor slabs, the practice of constructing steel-concrete composite structures is becoming more and more popular. The joint action of the two materials is generally ensured by mechanical connectors that considerably increase the performance of the composite element structure. For a majority of practical cases, these elements are formed by a concrete slab connected to I-shaped steel beams. In this study, models of finite elements for the steel-concrete composite beams with partial interaction are optimized using the sequential linear programming algorithm. The design variables are considered with two approaches: in the first, only the parameters that define the cross section of the steel “I” profile vary, while in the second, besides the aforementioned parameters that define the cross section of the “I” profile, also considered are those that define the concrete section. In addition, the optimum distribution of the shear connectors along the composite beam are verified; in other words, the longitudinal rigidity of the deformable connection is considered to be a design variable. The design constraints are those defined in standard specifications referring to the dimensioning of concrete, steel and composite steel-concrete structures, as well as the side constraints with respect to the parameters defining the cross section and the step-size for the non-linear optimization algorithm. The results for the composite beam optimization problems are presented taking into consideration different boundary conditions. For a given optimized project, the analysis of the results is done regarding the influence of the constraints on the optimization process, the graph of the load-slip curve along the composite beam, and the values obtained for the design variables.

Impact of Reinforcement Ratio on Shear Behavior of I-Shaped UHPC Beams with and without Fiber Shear Reinforcement.

In the presented paper, the impacts of steel fiber use and tensile reinforcement ratio on shear behavior of Ultra-High Performance Concrete (UHPC) beams were investigated from the point of different tensile reinforcement ratios. In the scope of the experimental program, a total of eight beams consisting of four reinforcement ratios representing low to high ratios ranged from 0.8% to 2.2% were casted without shear reinforcement and subjected to the four-point loading test. While half of the test beams included 30 mm end-hooked steel fibers (SF-UHPC) with 2.0 vol%, the remaining beams were produced without the fiber to show possible effectiveness of the fiber use. The shear performances were discussed in terms of the load—deflection response, cracking pattern and failure mode, first cracking load and ultimate shear strength. In this sense, all the non-fiber beams were failed by shear with a dramatic load drop, regardless of the tensile reinforcement amount, before the yielding of reinforcement and they produced no deflection capability. The test results showed that while the inclusion of steel fibers to the UHPC mixture with low reinforcement ratios changed the failure mode from the shear to flexure, it significantly enhanced the ultimate shear strength in the case of higher reinforcement ratio through the SF-UHPC’ superior mechanical properties and fibers’ crack-bridging ability.

Rotation Capacity of I-Shaped Beams under Alternating Axial Forces Based on Buckling-Mode Transitions

AbstractDuring earthquakes, I-shaped beams (I-beams) in a braced structure are subjected to the flexural moment synchronized with reversed axial forces transmitted from buckling restrained braces. ...

Presenting a New Detail for the Rigid Connection Between I-Shaped Beam and Concrete-Filled Steel Tube Column with Stiffened Channel Link

Connections play an important role in the response of steel moment resisting frames to seismic loading. Prequalified rigid connections are applicable to I-shaped or box columns. In I-shape beam to concrete-filled tube (CFT) column connections, continuity and doubler plates cannot be added to the column. Various details have been proposed to address this issue, many of which are not constructionally convenient to implement. The aim of this study is to present a simple and suitable detailing for I-shape beam to concrete-filled tube column connections. To that end, six full-scale experimental samples were built and subjected to cyclic quasi-static loading. In the samples, stiffened and un-stiffened channel links were used to connect the beam to the column. In each sample, the stiffeners were installed on a different position on the channel link. The results showed that compared to the connection in which the beam is directly connected to the column, using the stiffened channel link with stiffeners along the beam’s flange increases the strength and ductility of the connection by 12% and 72%, respectively. Considering their desirable performance and easy implementation, these connections can be considered as a suitable detailing for I-shape beam to CFT column connections in seismic regions.

Effect of longitudinal stiffeners’ spacing in lateral-torsional buckling

This study focused on the experimental assessment of the effect of the spacing between longitudinal stiffeners welded to I-shaped beams under the action of lateral-torsional buckling. In this procedure, 192 aluminum beams on a 1:9 scale were tested under simple-support conditions with a laterally unbraced length ranging from 0.55 m through 1.95 m. Moreover, the stiffeners’ spacing was also ranged from 3 to 9 times the depth of section. The structural behavior of the beams is discussed in terms of their flexural capacity, spacing between longitudinal stiffeners, lateral displacement of compression flange and failure angle twist. Results show that the spacing of longitudinal stiffeners influences the flexural capacity of I-shaped beams, so that, when the spacing of longitudinal stiffeners decreases, flexural capacity tends to increase, especially in the elastic buckling zone.

Steel Fiber Use as Shear Reinforcement on I-Shaped UHP-FRC Beams

In the presented paper, the effectiveness of steel fiber use on the shear and flexure behaviors of ultra-high performance concrete (UHPC) beams and the feasibility of steel fibers in place of shear reinforcement were investigated experimentally. In this framework, a total of four I-shaped UHPC beams were produced for a high tensile reinforcement ratio of 2.2%. While two of them were non-fiber UHPC beams with and without the shear reinforcement to show the contribution of steel fibers, the remaining beams were made from the ultra-high performance steel fiber-reinforced concrete (UHP-FRC) having the short straight fibers with 1.5% and 2.5% by volume. The shear and flexural parameters, such as the load–deflection response, cracking pattern, failure mode, deflection, and curvature ductilities were discussed based on the four-point loading test results. While the reference beam without fiber and shear reinforcement failed by the shear with a sudden load drop before the yielding of reinforcement and produced no deflection capability, the inclusion of steel fibers to the UHPC matrix transformed the failure mode from shear to flexure through the fibers’ crack-bridging ability. It might be deduced that the moderate level of steel fiber use in the UHP-FRC beams may take the place of shear reinforcement in practical applications.

Development of Hybrid Machine Learning Models for Predicting the Critical Buckling Load of I-Shaped Cellular Beams

The principal purpose of this work is to develop three hybrid machine learning (ML) algorithms, namely ANFIS-RCSA, ANFIS-CA, and ANFIS-SFLA which are a combination of adaptive neuro-fuzzy inference system (ANFIS) with metaheuristic optimization techniques such as real-coded simulated annealing (RCSA), cultural algorithm (CA) and shuffled frog leaping algorithm (SFLA), respectively, to predict the critical buckling load of I-shaped cellular steel beams with circular openings. For this purpose, the existing database of buckling tests on I-shaped steel beams were extracted from the available literature and used to generate the datasets for modeling. Eight inputs, considered as independent variables, including the beam length, beam end-opening distance, opening diameter, inter-opening distance, section height, web thickness, flange width, and flange thickness, as well as one output of the critical buckling load of cellular steel beams considered as a dependent variable, were used in the datasets. Three quality assessment criteria, namely correlation coefficient (R), root mean squared error (RMSE) and mean absolute error (MAE) were employed for assessment of three developed hybrid ML models. The obtained results indicate that all three hybrid ML models have a strong ability to predict the buckling load of steel beams with circular openings, but ANFIS-SFLA (R = 0.960, RMSE = 0.040 and MAE = 0.017) exhibits the best effectiveness as compared with other hybrid models. In addition, sensitivity analysis was investigated and compared with linear statistical correlation between inputs and output to validate the importance of input variables in the models. The sensitivity results show that the most influenced variable affecting beam buckling capacity is the beam length, following by the flange width, the flange thickness, and the web thickness, respectively. This study shows that the hybrid ML techniques could help in establishing a robust numerical tool for beam buckling analysis. The proposed methodology is also promising to predict other types of failure, as well as other types of perforated beams.

New scheme for beam with side plates for seismic applications to mitigate construction difficulties

The most common method to prevent lateral torsional buckling is the use of lateral bracings. However, when the presence of lateral bracings is considered an obstacle, side plates can be used to increase the torsional resistance of I-shaped steel beams. However, some construction difficulties will be faced when a beam with side plates is used. This study proposes a new scheme that uses side plates to prevent lateral torsional buckling, while also avoiding construction difficulties. This scheme involves a beam with side plates that do not cover an area near the beam end to provide space for bolt installation and welding of the beam flange during erection. A cover plate is then added to strengthen the beam end to prevent premature failure. The performance of the proposed beam scheme is confirmed through experimental tests. The performance of the beam designed using the proposed beam scheme is found to be satisfactory in terms of lateral torsional buckling. A finite element analysis model is then established and validated using the test results. A parametric study is conducted, and as the final result, design guidelines for this new beam scheme are proposed.