I-shaped Beams Research Articles

Asymptotic Numerical Method for dynamic buckling of shell structures with follower pressure

Asymptotic Numerical Method (ANM) is applied to non-linear dynamics of thin-shells subjected to conservative and non-conservative loads such as follower pressure. ANM is decomposed into several stages: the finite element discretization of the non-linear equations of motion of the shell dynamics, a homotopy transformation of the semi-discrete non-linear equations, a perturbation technique to expand the quantities into Taylor series according to the homotopy parameter and the time integration scheme to solve the series of linear problems resulting from the perturbation technique. ANM is applied here with the 7-parameter shell elements thanks to the Enhanced Assumed Strain (EAS) concept and implicit Newmark integration. In the case of non-conservative force, follower pressure also requires to be decomposed in either Taylor series or rational Padé approximants. The academic case of the cylindrical roof with dynamic snap-through phenomenon is investigated for the purpose of comparing ANM strategies and the classical Newton–Raphson (NR) method. Two engineering cases including an I-shaped thin-walled beam and a closed thin-shell cylinder under dynamic external follower pressure are also investigated. ANM turns out to be accurate, robust and efficient in terms of computation time, providing an alternative method to the well-established Newton–Raphson method.

Method for Constructing a Compact Component Mode Synthesis Model for Analyzing Nonlinear Normal Modes of Structures with Localized Nonlinearities

Abstract Nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations, especially for systems with numerous degrees-of-freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis (CMS) technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. The proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the CMS modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with a significant reduction in computational costs.

Experimental investigation on shear behavior of I-shaped concrete beam with Fe-SMA rebars

Vertical prestress loss causes cracking in prestressed box-girder bridge webs. As a new type of prestressed material, iron-based shape-memory alloy (Fe-SMA) rebars can be used as vertically prestressed rebars to compensate for the loss of vertical prestress in box-girder webs. In this study, box-girder webs were simplified into I-shaped beams, and the shear performance of these I-shaped beams with vertical Fe-SMA rebars in the shear span was analyzed to estimate the feasibility of using Fe-SMA rebars. The effects of the activation state, layout spacing, and rebar diameter on the shear performance of the I-beams were explored. The variations in the cracking load, ultimate load, and main tensile strain were systematically investigated. The results indicate a significant transformation from brittle to ductile bending shear failure following Fe-SMA activation. Moreover, the ultimate deflection exhibited a significant increase exceeding a factor of 2. The activation of the Fe-SMA was beneficial for delaying specimen cracking and improving shear strength. Specifically, the shear cracking and ultimate loads increased by 24.21 % and 12.11 %, respectively. Simultaneously, the activation of the Fe-SMA rebar significantly reduced the primary tensile strain within the shear span segment and effectively delayed crack development. The diagonal fracture width of the specimens with the activated Fe-SMA was significantly reduced (67.24 %, 57.14 %, and 52.22 %, respectively) at three different stress settings (400, 450, and 500 kN). Furthermore, a methodology for estimating the shear cracking and bearing capacity of I-beams with vertical Fe-SMA rebars is proposed. The calculated values are in excellent agreement with the experimental data, thereby serving as a valuable reference for future research.

A new approach for optimal design of fire insulation coating of steel I-shaped beams and H-shaped columns

A new approach for optimal design of fire insulation coating of steel I-shaped beams and H-shaped columns

Dynamic Monitoring of Steel Beam Stress Based on PMN-PT Sensor

Steel beams are widely used load-bearing components in bridge construction. They are prone to internal stress concentration under low-frequency vibrations caused by natural disasters and adverse loads, leading to microcracks and fractures, thereby accelerating the instability of steel components. Therefore, dynamic stress monitoring of steel beams under low-frequency vibrations is crucial to ensure structural safety. This study proposed an external stress sensor based on PMN-PT material. The sensor has the advantages of high sensitivity, comprehensive frequency response, and fast response speed. To verify the accuracy and feasibility of the sensor in actual engineering, the LETRY universal testing machine and drop hammer impact system were used to carry out stress monitoring tests and finite element simulations on scaled I-shaped steel beams with PMN-PT sensors attached. The results show that: (1) The PMN-PT sensor has exceptionally high sensitivity, maintained at 1.716~1.726 V/MPa in the frequency range of 0~1000 Hz. The sensor performance is much higher than that of PVDF sensors with the same adhesive layer thickness. (2) Under low-frequency random vibration, the sensor’s time domain and frequency domain output voltages are always consistent with the waveform of the applied load, which can reflect the changes in the structural stress state in real time. (3) Under the impact of a drop hammer, the sensor signal response delay is only 0.001 s, and the sensitivity linear fitting degree is above 0.9. (4) The simulation and experimental results are highly consistent, confirming the superior performance of the PMN-PT sensor, which can be effectively used for stress monitoring of steel structures in low-frequency vibration environments.

Experimental investigation of prestressed beam made from ultra-high performance fibre reinforced concrete

The paper presents experimental results prestressed beam made of high-strength fiber reinforced concrete. The I-shaped beam with a height of 0.2 m and a length of 2.8 m was tested in a four-point scheme until the bending load capacity was achieved. The element was prestressed with one tendon Y1860S7 with a diameter of 12.5. The fiber reinforced concrete was made with KrampeHarex DM12.5/0.175 fibers. Concrete was tested in compression (fc ≈ 110 MPa) and in tension, checking the resistance in both the splitting test (fct,sp ≈ 17.5 MPa) and the three-point bending test (fct,fl ≈ 11.9 MPa). After fabrication and prestressing of the beam, changes in strains on the element's surface were observed for 19 days, after which destructive test was conducted. During the test deflections and deformations of the element were recorded. The failure was as a result of bending and followed yielding of the prestressing strand and the subsequent formation of one localised crack. The calculation of the load carrying capacity in the light of the SIA 2052 standard, assuming the elasto-plastic material model of the fibre reinforced concrete, showed good agreement with the experimental results

Effects of shear on the lateral torsional buckling of singly-symmetric I-beams

This paper presents an investigation on the negative effects of shear on the lateral torsional buckling (LTB) of singly-symmetric I-shaped beams due to web distortion associated with shear. Results from a parametric FEA study including eigenvalue buckling analyses and large-displacement analyses were utilized considering both stiffened and unstiffened webs to consider the impact of shear on the LTB resistance. Moment gradients caused by constant shear and a shear gradient were considered. The FEA solutions demonstrate that shear can significantly reduce the lateral-torsional buckling resistance. The FEA results were used to develop design equations that account for the reduction in the LTB capacity from shear. The solutions were compared with conventional methods proposed by Winter to account for the effects of web distortion on girders with slender webs. Results from the study show that (i) the average flange area should be used to account for the effects of shear of singly-symmetric beams; (ii) post-buckling strength has limited impact on the shear effects with regards to the LTB resistance; and, (iii) compared to Winter's approach, the proposed method can capture the variation of the moment reduction factor with the shear force in the unbraced length, and is able to predict moment resistances with reasonable accuracy compared to refined FEA solutions using both eigenvalue analysis and large-displacement analysis. Design examples are provided to demonstrate the calculation procedure.

Flexural behaviour of built-up I-shaped bamboo scrimber beams: experimental tests and design method

ABSTRACT This paper presents the flexural behaviour of built-up I-shaped bamboo scrimber beams under four-point bending. Ten bamboo scrimber beams were tested, employing different types of connections between the web and flanges. The load-deflection relationship, failure mode and load-slip relationship of beams were obtained through experimental tests. Besides, the measured strains of bamboo scrimber in various regions were used to analyse the flexural mechanisms of I-shaped beams. Test results showed that the beam with a glued connection exhibited debonding at the web-flange interface, hindering the development of flexural capacity of the beam. By using self-tapping screws or bolted steel angles to strengthen the connection, the slip between the web and flanges was considerably reduced, resulting in the increased flexural capacity of beams. The rupture of the bottom flange near the concentrated point load led to the final failure of strengthened beams. The design method for mechanical fastened glulam beams in Eurocode 5 was adopted to assess the flexural capacity of bamboo scrimber beams. Comparisons between experimental results and calculated results per Eurocode 5 indicate that the method is capable of predicting the flexural resistances of I-shaped bamboo scrimber beams with reasonably good accuracy.

Evaluation of Rotation Capacity and Bauschinger Effect Coefficient of I-Shaped Beams Considering Loading Protocol Influences

Recent catastrophic earthquake events have reinforced the necessity of evaluating the seismic performance of buildings. Notably, the buildings can go into the plastic phase during a striking earthquake disaster. Under this condition, the current design codes assume seismic response reduction by virtue of the energy dissipation capacity of the structural members. In the strong-column–weak-beam design, which involves I-shaped beams and boxed columns, the mechanism is defined as a standard design scheme to prevent the building from collapsing. Therefore, energy dissipation relies highly on the I-shaped beam performance. However, the I-shaped beam performance can differ depending on the loading history experienced, whereas this effect is untouched in the prevailing evaluation equation. Hence, this study first performs cyclic loading tests of 11 specimens using different loading protocols. The experimental results clarify the fluctuation in the structural performance of I-shaped beams depending on the applied loading hysteresis, proving the necessity of considering the stress history for proper assessment. Furthermore, the database of experimental results is constructed based on the previous experimental studies. Ultimately, the novel evaluation equation is proposed to reflect the influences of the loading protocol. This equation is demonstrated to effectively assess the member performance retrieved from the experiment of 65 specimens, comprising 11 specimens from this investigation and 54 specimens from the database. The width–thickness ratio, shear span-to-depth ratio, and loading protocols are utilized as the evaluation parameters. Moreover, the prediction equation of the Bauschinger effect coefficient is newly established to convert the energy dissipation capacity under monotonically applied force into hysteretic energy dissipation under the cyclic forces.

Experimental Study on the Flexural Behavior of I-Shaped Laminated Bamboo Composite Beam as Sustainable Structural Element

Laminated bamboo (LB) is considered a promising environmentally friendly material due to its notable strength and advantageous lightweight properties, making it suitable for use in construction applications. LB I-beams are a prevalent component in bamboo structures due to their ability to fully utilize their material properties and enhance efficiency when compared to beams with rectangular solid sections, while the characteristics of connections should be further studied. This paper presents an experimental investigation of the flexural behavior of I-shaped LB beams that are connected using self-tapping screws and LB dowels. Compared with glued beams of the same size, the findings of the study reveal that the primary failure modes observed in those two types of components were characterized by the separation of the component and web tensile fracture. The screw beam and dowel beam exhibited a reduced ultimate capacity of 43.54% and 30.03%, respectively, compared to the glued beam. Additionally, the ultimate deflections of the screw beam and dowel beam were 34.38% and 50.36% larger than those of the glued beam, respectively. These variations in performance can be attributed to the early breakdown of connectors. Based on design codes, it can be observed that the serviceability limits were in close proximity, whereas the ultimate strains of the top and bottom flanges were significantly lower than the ultimate stresses experienced under uniaxial loading conditions. As a result of the slip and early failure of connectors, the effective bending stiffness estimated by the Gamma method achieved better agreements before elastic proportional limit. Therefore, in future investigations, it would be beneficial to enhance the connector and fortify the flange as a means of enhancing the bending characteristics of an I-shaped beam.

Design and Analysis of Leaf Beam Single-Translation Constraint Compliant Modules and the Resulting Spherical Joints

Abstract A wire beam is a single-translation constraint along its axial direction. It offers many applications in compliant mechanisms, such as being a transmitting/decoupling element connected to a linear actuator and being a fundamental constitutive element to design complex compliant joints and mechanisms. It is desired to find an alternative leaf beam single-translation constraint to equal a wire beam in order to improve the manufacturability and robustness to external loading. In this paper, we propose and model a new single-translation constraint compliant module, I-shape leaf beam design, to compare with a corresponding L-shape leaf beam design reported in the literature. Two spherical (S) joints using three I-shape leaf beams and three L-shape leaf beams, respectively, are then analytically modeled and analyzed. Three key geometric parameters are adopted to thoroughly assess four performance indices of each S joint, including stiffness ratio, rotation radius error, coupling motion, and parasitic motion. It shows that the I-shape leaf beam–based S joint performance indices are generally 10 times better than those of the L-shape leaf beam–based S joint. For each S joint, the optimal parameters are found under the given conditions. Finally, experimental tests are carried out for a fabricated S joint prototype using the I-shape leaf beams, the results from which verify the accuracy of the proposed analytical model and the fabrication feasibility.

The Italian Guidelines for special inspections of post-tensioned concrete bridges: review and case study

Post-tensioned (PT) concrete bridges are structural systems characterized by intrinsic fragility. The assessment of their health condition is very difficult due to their nature, which prevents the detection of degradation in PT elements through conventional investigation methods and/or visual inspections. For this reason, the Italian Guidelines for the maintenance of existing bridges envisage special inspections to assess the condition of the post-tensioning system. According to the dedicated Guideline, the special inspection procedure consists of four steps. First there is Step O, which identifies the number and location of PT samples to be investigated based on the historical•critical review of available documentation and the visible defects in the post-tensioned members. Then, in Step 1 a preliminary analysis of the identified PT elements is performed, identifying the presence and location of active defects and grout voids, as well as the probability of corrosion of the reinforcement through non-destructive tests. In Step 2, the analysis of defects becomes more accurate, determining the probability of corrosion and estimating the level of stress in the concrete and in post-tensioned cables through locally destructive tests. Step 3 is applied if the outcome of Step 2 is uncertain and involves the experimental analysis of the overall structural response of the bridge. Eventually, in case the presence of damaged PT elements is confirmed, a load assessment of the structure is performed. The objective of this study is to evaluate the effectiveness of the investigation method proposed by the Italian Guidelines, highlighting its strengths and potential weaknesses. The procedure is applied to the Dora Riparia River Bridge, located in Avigliana (Turin) on provincial road SP197. The bridge consists of seven spans, 21.4 m long, and is characterized by a simply supported static layout; each span has four post-tensioned I-shape beams and four post-tensioned diaphragms.

Rotation Capacity of I-Shaped Beams with Concrete Slab in Buckling-Restrained Braced Frames

Rotation Capacity of I-Shaped Beams with Concrete Slab in Buckling-Restrained Braced Frames

Global Resistance Methods for the Design of Fiber-Reinforced Concrete (FRC) Beams with Material Nonlinear Finite Element Analysis

This article explores the application of the global resistance methods (GRMs) on the design of hybrid glass fiber-reinforced polymer (GFRP) and steel fiber-reinforced concrete (SFRC) beams. Addressing challenges posed by GFRP-reinforced beams, this study aims to assess the impact of material uncertainties on the behavior of such hybrid beams. The investigation involves the experimental testing of I-shaped SFRC beams, which are used to develop and validate nonlinear finite element analysis (NLFEA) models. These models incorporate material non-linearities while minimizing uncertainties related to modeling assumptions. Through the application of GRM, the study evaluates the global resistance safety factor, offering insights into the structural performance of hybrid reinforcement SFRC beams. Ultimately, this research seeks to facilitate a transition from traditional localized approaches to more accurate and comprehensive analyses for the design of hybrid reinforcement SFRC beams, contributing to the advancement of structural engineering by promoting safer, more resilient, and sustainable construction systems.

Elastic local buckling coefficients of I-shaped beams considering flange–web interaction

Since using high–strength and high–performance steels has become a more common structural design practice in building and bridge construction, there is an increased potential for designing extremely thin-walled I-shaped beam members to enhance the efficiency of the steel beam design. For a more accurate design approach for these thin-walled I-beam members, particularly when they are near noncompact limits, it is necessary to explore more rational methods for determining the elastic local buckling strength of I-beams. This study aimed to investigate the local buckling behavior and strength of I-shape structural sections by considering flange-web interactions through three-dimensional finite element analysis. The goal was to provide a more reasonable estimation of local buckling strength under uniform bending. To evaluate the local buckling behavior of flange and web panels and explain it reasonably, this study adopted the ratio of flange-web slenderness (λf/λw) and height-to-width ratio (H/bf) of I-shaped beams which can affect buckling mode shapes and local buckling strength of I-shaped beams induced by flange local and web bend bucklings. Finally, this study presented design equations for both flange local and web-bend buckling coefficients considering λf/λw and H/bf. It was expected that the presented local buckling coefficients (kf) for flanges and webs could lead to a more reasonable design, as compared to the existing AISC design provisions.

Flexural behavior of open-web composite slab with I-shaped steel bottom chord and vertical flat webs

Traditional composite floor truss systems with top and bottom chords and web trusses have encountered difficulties in system erection, installation, and the passage of utilities. In order to address these challenges, this study introduces a novel open-web composite floor system that only consists of a bottom chord and vertically placed flat web elements. These vertical web members are essentially short I-shaped steel elements and are connected to the I-shaped steel beam bottom chord and concrete slab through steel top plates and shear connectors, forming an innovative composite floor system. This paper presents the results of static loading tests conducted on two specimens with distinct web members, evaluating deformation, cracking characteristics, ultimate bearing capacity, failure mode, and stress and strain distributions. The findings indicate that the new composite floor system offers good flexural performance. Furthermore, finite element models of the composite floor system have been developed to analyze the influence of the web element’s geometry on the composite slab’s ultimate bearing capacity. This study also develops a theoretical calculation method for determining the internal force, elastic deflection, and ultimate bearing capacity of the composite floor system. The theoretical calculation results regarding the failure mode and ultimate load capacity align closely with the experimental values, and the deformation calculation formula can be used to estimate the deformation curve shape and elastic deflection of the floor system.

Experimental study on seismic behavior of cover-plate connections between steel beams and high strength steel box columns

As one of the beam-to-column fully restrained connections that could shift the plastic hinges of the beam away from the face of the column, cover-plate reinforced connections are expected to be a practical choice for high strength steel frame seismic applications. Five cover-plate reinforced and one unreinforced welded flange-bolted web connection specimens combined with Q355 steel I-shaped beams and Q460 or Q690 steel box columns were designed according to Chinese codes and tested under cyclic loads at full scale. Failure modes, including local buckling of the beam, complete joint penetration (CJP) weld fracture, and column web fracture, were reported. The strength, stiffness, deformation, and energy dissipation features were analyzed. The four cover-plate connections met the AISC requirements for special moment frames (SMF) with maximum story drift angles greater than 0.06 rad and exhibited satisfactory seismic behavior. According to the test results, a limit on the ratio of the diaphragm plate to column plate thickness should be considered when the electroslag welding (ESW) process is used in high strength box columns. The strong panel zone designed with a panel zone resistance ratio (γpz) greater than 1.20 was recommended for box columns with steel strength no less than 690 MPa. Additionally, other design implications of the results were discussed.

An Optimal Selection of the Clamping Fixture for Manufacturing an I-Shaped Composite Beam

In this paper, the influence of the different clamping zones of a web on the vibration of I-shaped composite beams is discussed. This current study is divided into two steps. In the first step, according to the different clamping spacings, through vibration simulation analysis, the optimal clamping spacing was selected. In the second step, the optimal new fixture was designed by means of different clamping positions and shapes. The analysis also reveals that a reduction in the clamping space does not contribute to a reduction in vibration. A newly selected fixture was designed based on the results that were delivered by the finite element model analysis of the L fixture in the upper and lower. Based on static analysis, the improved fixture was able to significantly reduce displacement, stress, and strain compared with the original one. By using dynamic analysis, modes, the frequency response, and random analyses, we found that the improved fixture could enhance the natural frequencies of the structure and reduce vibration displacement and acceleration during manufacturing. From the 2000 Hz sweep, the peak values of the power spectral density of displacement and acceleration went down by about 100 and 10 times, respectively.

Prediction of shear behavior of glass FRP bars-reinforced ultra-highperformance concrete I-shaped beams using machine learning

This study focuses on using various machine learning (ML) models to evaluate the shear behaviors of ultra-high-performance concrete (UHPC) beams reinforced with glass fiber-reinforced polymer (GFRP) bars. The main objective of the study is to predict the shear strength of UHPC beams reinforced with GFRP bars using ML models. We use four different ML models: support vector machine (SVM), artificial neural network (ANN), random forest (R.F.), and extreme gradient boosting (XGBoost). The experimental database used in the study is acquired from various literature sources and comprises 54 test observations with 11 input features. These input features are likely parameters related to the composition, geometry, and properties of the UHPC beams and GFRP bars. To ensure the ML models' generalizability and scalability, random search methods are utilized to tune the hyperparameters of the algorithms. This tuning process helps improve the performance of the models when predicting the shear strength. The study uses the ACI318M-14 and Eurocode 2 standard building codes to predict the shear capacity behavior of GFRP bars-reinforced UHPC I-shaped beams. The ML models' predictions are compared to the results obtained from these building code standards. According to the findings, the XGBoost model demonstrates the highest predictive test performance among the investigated ML models. The study employs the SHAP (SHapley Additive exPlanations) analysis to assess the significance of each input parameter in the ML models' predictive capabilities. A Taylor diagram is used to statistically compare the accuracy of the ML models. This study concludes that ML models, particularly XGBoost, can effectively predict the shear capacity behavior of GFRP bars-reinforced UHPC I-shaped beams.

Additive Manufacturing of Body-Centered Cubic Metamaterials with Novel I-Shaped Beam Lattice Towards Enhanced Mechanical Properties

The recent advancement of additive manufacturing paves the way to achieve the highly complex design of metamaterials. Mechanical metamaterials are promising materials for high-yield industrial applications since they demonstrate superior mechanical behaviors that cannot be found in natural materials. Designing metamaterials is crucial to ensure enhanced mechanical performances. The objective of this research is to explore different metamaterial lattices utilizing a numerical approach in order to obtain higher mechanical strength. This research employs a Mechanics of Structure Genome (MSG) method to design a novel I-shaped beam with reinforcement lattice metamaterials to attain higher mechanical properties. Three cross-sectional shapes including circular, Ibeam, and Ibeam with reinforcement and their corresponding Body-Centered Cubic (BCC) metamaterials, have been designed applying the MSG modeling approach. The Stereolithography (SLA) based additive manufacturing process is leveraged to fabricate the designed metamaterials. A standard compressive test is performed to characterize the mechanical properties. The test results reveal a remarkable improvement in the mechanical behaviors of the proposed I-shaped beam with reinforcement (Reinf Ibeam). The Reinf Ibeam demonstrates higher energy absorption capacity, stiffness, and strength compared to the other two metamaterials. A 40.57% increased energy absorption/weight ratio, 140% higher stiffness/weight ratio, and 74% larger yield strength/weight ratio are obtained for the Reinf Ibeam in comparison with circular beam lattice metamaterial.