Effective Moment Of Inertia Research Articles

Effective Moment of Inertia of Reinforced Concrete and Reinforced Steel Fiber-Reinforced Concrete One-Way Slabs

Effective Moment of Inertia of Reinforced Concrete and Reinforced Steel Fiber-Reinforced Concrete One-Way Slabs

Proposition for the effective moment of inertia to determine the deflection in a composite slab

The objective of this work is to propose a mathematical expression for calculating the effective moment of inertia of a composite slab that utilizes steel formwork incorporated into the concrete, and consequently, to verify the deflection. The analysis of the behavior and strength of composite steel and concrete slabs covers several parameters, such as load-deflection curves, load-end slip curves, and load-steel strain curves. Among these parameters, the load versus deflection curve at the mid-span perform a crucial role in the evaluation and verification of deflection. Regarding the calculation of deflection, generally, the technical standards recommend that the moment of inertia of the composite section be given by the simple average of the moments of inertia of the uncracked and cracked sections. However, experimental investigations have shown that this procedure inadequately characterizes composite slab behavior, resulting in underestimated effective moment of inertia and reduced deflection, especially when subjected to higher loads. Using the results of experimental tests on a composite slab built with a specific steel sheeting carried out at the Structures Laboratory of the Federal University of Minas Gerais, this work evaluated several expressions suggested by technical standards and authors of scientific articles aiming to validate a proposal for determining the moment of effective inertia in composite slabs that adequately represents the behavior load versus deflection during the entire loading phase until collapse. From this evaluation it is possible to recommend the proposed equation for design verification in the case of the service limit state for excessive deformations.

Structural behavior of concrete slabs made of seawater sea sand and reinforced with GFRP reinforcement under flexural loading

Seawater sea sand concrete (SSC) structures reinforced with glass fibre-reinforced polymer (GFRP) reinforcing bars offer a promising alternative to conventional reinforced concrete, especially in the face of depleting clean water and river sand. However, comprehensive studies on the flexural performance and cracking behaviour of SSC structures reinforced with GFRP reinforcing bars are currently limited. This study delves into the influence of longitudinal reinforcement ratio on the flexural and cracking behaviour of SSC slabs reinforced with GFRP reinforcing bars under quasi-static loads, as well as the bond behaviour of GFRP reinforcing bar and SSC. The experimental program included 9 large-scale slabs and 30 pull-out specimens, revealing that the longitudinal reinforcement ratio significantly affects the flexural performance, particularly at higher load levels. Increased reinforcement ratio improved flexural stiffness, reduced deflection and crack width, enhancing load-carrying capacity and energy absorption. Although bond strength decreased at the serviceability load (up to 47%), a marginal reduction was observed at the ultimate state. The study proposes a semi-empirical equation for the effective moment of inertia of SSC slabs, accounting for the influence of reinforcement ratio on cracking moment and reduced bond strength of GFRP reinforcing bars. This equation aligns well with experimental results, demonstrating low error and coefficient of variation.

Analysing the influence of ground granulated blast furnace slag and steel fibre on RC beams flexural behaviour

This study examines the effect of Ground Granulated Blast Furnace Slag (GGBS) and steel fibers on the flexural behaviour of RC beams under monotonic loading. Various percentages of GGBS were used to substitute cement, namely 0%, 20%, 40%, 60%, and 80% and fibers were added to the concrete mix as 0%, 0.5%, 1%, and 1.5% of the volume of concrete. The load–deflection behaviour of GGBS-incorporated RC beams with fibers was compared with the control RC beam. Beams were tested under load control for 28 days and 180 days. The ultimate load of the GGBS-incorporated RC beam up to 40% cement replacement was found to higher than that of the control beam. The strength of concrete is reduced by 28% and 19% when cement was partially replaced by 80% of GGBS at 28 and 180 days, respectively, compared to control concrete without fibres. Further, the analytical load–deflection response of GGBS-incorporated RC beams was determined by using several codes of practice, namely, ACI 318-11(2011), CSA A23.3-04 (2004), EC-04 (2004), and IS 456 (2000). The Codal provisions were primarily based on the effective moment of inertia, Young’s modulus, and modulus of rupture, stiffness, and cracking. Average load–deflection plots obtained from experiments were compared with the computed load–deflection of analytical studies. It was found that the analytically predicted load–deflection behaviour is comparable with the corresponding average experimental load–deflection response. Moment curvature relations were also developed for RC beams.

Experimental and numerical investigation on the behavior of concrete sandwich slab panel for a structural system

This paper proposes a simplified methodology based on a concentrated plasticity model to develop numerical analysis of concrete sandwich slab panels for structural systems. Also, a proposal for the determination of experimental damage and its evolution within concrete sandwich panels is formulated. To validate the proposed methodology, an experimental study was carried out on full-scale slab panels to analyze the flexural behavior. Eight specimens were subjected to three- and four-point bending tests. A cycle loading protocol with unloading up to zero load was performed. These specimens, constructed with either one or two joined panels, were used to assess the group action. Mechanical properties for structural analysis—such as strength, stiffness, degree of composite action, and effective moment of inertia—were determined. The tested specimens exhibit significant stiffness degradation, indicating a notable evolution of damage even at small plastic displacements. The proposed methodology proves to be effective and reliable for predicting the behavior of concrete sandwich panels under bending moments. The numerical simulations performed show an adequate description of slab panel behavior until the ultimate load, regardless of its simplicity.

Flexural behavior of composite section of multiple full-culm bamboo beams with mortar infill bolted joints

Full-culm bamboo has several characteristics that make it an excellent alternative construction material due to its rapid growth rate, high strength-to-weight ratio, and high carbon sequestration. Thus, it becomes crucial to study the mechanical and structural performance of bamboo within an engineering framework, such as flexural behavior of multi-culm elements, since it is a key issue of typical elements of building such beams, joists, and others. While there is a general understanding of the composite section behavior in materials such as timber, steel and concrete, there is a lack of experimental evidence concerning bamboo in this regard. Therefore, an experimental program was undertaken by the Center of Research in Materials and Civil Works (CIMOC) at the Universidad de Los Andes in Colombia. Two- and three-culm elements of Guadua angustifolia Kunth from a Colombian plantation using a Bolted-Mortar Infill connections were tested in a bending setup. The gamma method, extensively employed in timber standards, was used to find the percentage of composite section for different number of shear connectors. Montecarlo simulations were performed to deal with uncertainty of the modulus of elasticity and the slip modulus (stiffness) of the Bolted-Mortar Infill connection. Additionally, a design factor FI was proposed that allows to find the ratio of increment of the effective moment of inertia of partially composite section for different connection configuration. Equations were derived and proposed for C and FI through linear regression.

Inertia Modulated Meta-Structure With Time-Varying Inertia Amplification

Abstract In this work, a new inertia modulated meta-structure is proposed to enable time-dependent inertia parameters, and thereby realize non-reciprocal wave propagation via spatiotemporal modulation. The designed cell structure is composed of an oscillatory disk and a mass that slides in a guide embedded in the disk frictionlessly with prescribed motion. Effective moment of inertia and damping coefficients of the rocking motion of the cell structure are rendered time-dependent due to the inertia and Coriolis forces of the periodically sliding mass, which allows us to implement the expected spatiotemporal modulation upon a super-cell. Non-reciprocal propagation behavior of the proposed meta-structure is verified via the theoretical solution of the dispersion relation as well as the dynamic response of a finite array. Effects of modulation parameters, including the frequency, amplitude, and phase, on the unidirectional propagation characteristic are thoroughly investigated.

Instability-driven family optimization of cold-formed steel lipped-channel cross-sections with strength and stiffness constraints

The objective of this study is to advance a solution scheme that can produce a family of optimized thin-walled cold-formed steel lipped-channel sections under combined compressive and flexural loading subjected to both strength and stiffness constraints. In this new study, the solution scheme is extended from previous work considering strength constraints only to include stiffness constraints to address the serviceability requirement as well for a more practical reflection of behavior whereby stiffness is reduced due to member instabilities. The stiffness constraint is driven by a novel method for estimating effective moment of inertia due to cross-section instabilities such as local and distortional buckling modes. A two-level optimization framework is utilized to produce a family of optimized sections. The first level focuses on individual member optimization of the P−M demand space as derived from current commercially available lipped-channel sections in the United States; the second level focuses on a new family of optimized sections capable of covering the same design space at a minimal family size. The results of the study show that a family of only 8 unique optimized sections can replace 186 commercially available sections and still achieve the same or improved performance in terms of both strength and stiffness compared to strength constraints only. The developed family of sections demonstrates that optimization techniques, employing complicated design constraints, have a great potential for improving cold-formed steel production on currently widely-used cross-section shapes such as lipped channels.

Effective moment of inertia of reinforced concrete slender beams with only tension reinforcement

For a reinforced concrete structure to be deemed satisfactory, it must satisfy both the ultimate and serviceability limits state criteria. Deflection is one of the major criteria to be satisfied under the serviceability limit state. This paper derived a model by modifying Olanitori’s model to obtain the effective moment of inertia for slender beams without compression reinforcement. The beam without compression reinforcement was subjected to a one-point load in order to determine the experimental effective moment of inertia. It was observed that the beam had an ultimate load of 83 kN. At a service load of 55.33 kN, the beam’s actual deflection was found to be 5.90 mm and the experimental effective moment of inertia, Ie(EXP) was 206.96 x104mm4. At a service load of 55.33 kN, the estimated deflections of the beam using the proposed model P, model 1, model 2, and model 3 were 3.32 mm, 2.60 mm, 1.33 mm, and 0.78 mm respectively, while the actual deflection was 5.09 mm for the beam. From these results, the proposed model predicts more accurately the deflection of the slender beam than the three other models.

Bond performance of spliced GFRP bars in pre-damaged concrete beams retrofitted with CFRP and UHPC

Fiber-reinforced polymer (FRP) reinforced concrete structures are inevitably subjected to extreme loads. The retrofitting of damaged FRP-reinforced concrete structures will become an important issue, especially with the gradual application of FRP bars in concrete structures. For structures that can be retrofitted, the structural performance is significantly affected by the bond of FRP bars in pre-damaged concrete. For this reason, this paper investigated the effectiveness of retrofit methods of carbon FRP (CFRP) sheet and/or ultra-high performance concrete (UHPC) at restoring the bond strength of glass FRP (GFRP) bars in pre-damaged concrete, and twenty spliced GFRP-reinforced concrete beams were tested under four-point loading. The beams were pre-loaded until bond failure occurred, and then retrofitted and reloaded to assess the restoration of the bond strength. The effects of retrofit methods, spacing of confining stirrups, GFRP bar diameter, and pre-loading type were investigated. The bond strength of the 20 mm and 28 mm diameter GFRP bars was increased by 4~138% and 4~234% after retrofitting with CFRP sheet and/or UHPC, respectively. The modified flexural strength model and modified effective moment of inertia addressing the adverse effect of partial fracture of glass fibers and concrete cracks predicted well the load-carrying capacity and deflection of the retrofitted specimens showing flexural failure, respectively.

Experimental and analytical study of high performance concrete beams reinforced with Basalt FRP bars

This research aims to investigate flexural behaviour of high performance concrete beams reinforced with Basalt Fibers Reinforced Polymers (BFRP) bars. Twelve half-scale concrete beams were tested under four-points bending. The experimental parameters are BFRP reinforcement ratios (0.58%, 0.87%, and 1.16%), and Polyvinyl alcohol (PVA) fibers ratios (0.0%, 0.5%, and 1.0%).The test results showed significant improvement in the load-carrying capacity of high performance concrete beams with PVA fibers compared to non-fibrous concrete beams, the improvements are 29% and 48% for PVA ratio of 0.5% and1.0% respectively. In the presence of PVA fibers, the ultimate strain of BFRP bars is higher than that recorded in the absence of PVA fibers. It confirmed the contribution of PVA fibers to the flexural strength of the concrete beams and the better use of the tensile strength of the BFRP bars. Furthermore, an analytical investigation based on strain compatibility method was carried out to predict the moment capacity and effective moment of inertia of PVA concrete beams reinforced with BFRP bars.

Flexural and deflection behaviour of synthetic fibre reinforced concrete beams reinforced with glass fibre reinforced polymers bars under sustained service load

Glass fibre reinforced polymers (GFRP) bars have attracted increasing interest as a promising alternative for conventional steel reinforcement for its contribution towards sustainability and significantly improving the flexural performance of structural members. To mitigate the excessive deflections and crack widths exhibited by the FRP reinforced concrete members, fibre reinforced concrete (FRC) is employed which improves the toughness and cracking capacity of members. However, available research on the structural performance of FRC has focused on metallic fibres. The research presented in this paper is aimed at experimentally evaluating the influence of synthetic fibres on the time-dependent flexural behaviour of FRC beams reinforced with GFRP bars. Eight simply supported beams with varying synthetic fibre contents and GFRP bar diameters (but same reinforcement ratio) were tested under sustained service load. Creep under compression, concrete shrinkage, cracking moment, and deflection behaviour over 90 days were monitored and analyzed. Investigation revealed that the inclusion of synthetic fibres reduced the concrete deformations under creep and shrinkage by up to 22% and 26% respectively, increased the cracking capacity by 27%, increased the effective moment of inertia by 75%, and also resulted in up to 43% lower deflections. Suitability of several codes to predict the deformations and deflections under short and long-term conditions was also evaluated through comparison of the prediction models to the experimental results. Model proposed by ACI 440.1R-15 was found to predict the instantaneous deflection in beams without fibres with reasonable accuracy, however in FRC-GFRP beams, all models tend to overestimate the deflection. Presented research highlights the need for further investigation on non-metallic fibres and their contribution towards improvement of residual and flexural performance of FRC members to improve the validity of existing analytical prediction models.

Implementation of GFRP-RC Code Provisions: Detailing for Deflection Criteria

The American Concrete Institute has developed a design standard for glass fiber–reinforced polymer (GFRP) RC members, dependent to their standard for steel-reinforced structural concrete. Design examples conforming to code language have been developed and their solutions examined to understand the impacts that code requirements have on the design of GFRP-RC members. The impacts include selecting member dimensions and reinforcement on the basis of serviceability requirements, rather than strength, and the related detailing issues involving bar cutoff points. As the design of GFRP-RC members is typically controlled by serviceability requirements, some reinforcement may be provided to satisfy deflection requirements. Cutoff points for such bars must be located differently than for steel bars, where the cutoff point is determined by strength requirements. A proposed method locates cutoffs by calculating the resulting maximum deflections as the cutoff point is varied. A second, approximate, approach locates cutoffs at points where continuing bars provide the same value for effective moment of inertia as that available from all bars at the critical section. The second method results in longer bar lengths but is more easily applied. Shear and crack control requirements should also be checked at cutoff locations.

Flexural performance predictions of prefabricated bridge deck panels connected with CFRP tendons and UHPC grout

The cracking moment and deflection of prefabricated bridge deck panels (PBDPs) with connections are the critical indexes to assess their crack resistance and reliability. This paper presented improved prediction models for estimating the flexural performance, especially cracking moment and deflection, of PBDPs connected with CFRP tendons and UHPC grout. Afterwards, comparisons between experimental data and predicted cracking moment, moment capacity, and moment-deflection curves showed desired agreement. In addition, a finite element (FE) model was established and its reliability was verified by the comparison of moment-deflection curves between the FE model, predicted results, and tests. A parametric study was conducted to evaluate the influence of design parameters on flexural performance. The results show that the existing equations in the literature for calculating the effective moment of inertia cannot accurately predict that of PBDPs with novel connections. The improved performance prediction models have reasonable accuracy for flexural performance, including cracking moments, flexural capacity, and moment-deflection responses. The diameter and initial stress of CFRP, as well as concrete strength, have a positive influence on the performance of PBDPs connected with the proposed connections under bending moment.

On the Stability of Solitons for the Maxwell-Lorentz Equations with Rotating Particle

We prove the stability of solitons of the Maxwell–Lorentz equations with extended charged rotating particle. The solitons are solutions which correspond to the uniform rotation of the particle. To prove the stability, we construct the Hamilton–Poisson representation of the Maxwell–Lorentz system. The construction relies on the Hamilton least action principle. The constructed structure is degenerate and admits a functional family of the Casimir invariants. This structure allows us to construct the Lyapunov function corresponding to a soliton. The function is a combination of the Hamiltonian with a suitable Casimir invariant. The function is conserved, and the soliton is its critical point. The key point of the proof is a lower bound for the Lyapunov function. This bound implies that the soliton is a strict local minimizer of the function. The bound holds if the effective moment of inertia of the particle in the Maxwell field is sufficiently large with respect to the “bar moment of inertia".

Analysis of lightweight composite sections with reinforced concrete infill with autoclaved aerated concrete (AAC)

The development of composite sections is of great importance in structural design, with the aim of reducing weight and deflection while limiting the effect on the composite section’s strength and durability. This paper examines the computational analysis of composite sections where reinforced concrete was replaced with autoclaved aerated concrete (AAC) in the compression zone. The first principles of concrete combined with Hook’s law were adopted to find a flexure, shear, equivalent modulus of elasticity, effective moment of inertia, and deflection. The results are discussed and investigated using the finite element models developed by ANSYS WORKBENCH software. We found that the proposed analytical model can effectively provide a solution for the composite cross-section. The comparison between the theoretical calculation of the first cracking loads and the finite element percentage ranges from 89 to 110%. The ratio of the computational calculation of the modulus of elasticity to the finite element results ranged from 0.91 to 1.06. The comparison between the theoretical calculation of the effective moment of inertia to the finite element percentage ranged from 92% to 118%. The ratio of the computational calculation deflection to the finite element ranged from 0.87 to 1.15.

ANN-based critical review of the effective moment of inertia of RC beams

ANN-based critical review of the effective moment of inertia of RC beams

Estimation of the Effective Moment of Inertia for Hybrid Concrete Beams Reinforced with Steel and FRP Bars

Estimation of the Effective Moment of Inertia for Hybrid Concrete Beams Reinforced with Steel and FRP Bars

Ultimate and Deflection Performance of Concrete Beams Strengthened in Flexure with Basalt-Textile-Reinforced Polymer Mortar

This paper presents an investigation into the ultimate and serviceability behavior of concrete beams strengthened in flexure with basalt-textile-reinforced polymer mortar (BTRM). The bond performance at the interface between the BTRM and concrete was studied by performing single shear tests, and the effectiveness of using an adhesion promoter and impregnated resin for bond enhancement was explored. The results suggested that using an adhesion promoter and impregnated resin can improve the interfacial stress transfer and ensure the tensile failure of the basalt textile in BTRM. Afterward, four-point bending tests were conducted to study the flexural performance of strengthened beams. It was found that the flexural strength of strengthened beams increased with the amount of textile, and the strength increase was more prominent for the strengthened beams with end anchorages. The increase in the failure force was up to 37% for the beam strengthened with five layers of the textile and an end anchorage. The calculated flexural strength exhibited a percentage error of no more than 7% compared to the test results. In addition, the Bischoff-I Equation can closely estimate the effective moment of inertia and provide an accurate prediction of deflection for strengthened beams.

Comparison of the Prediction of Effective Moment of Inertia of FRP Rebar-Reinforced Concrete by an Optimization Algorithm.

FRP (fiber-reinforced polymer)-reinforced concrete members have larger deflection than reinforced concrete members because of the low modulus of elasticity of the FRP bar. In this paper, we proposed a new effective moment of inertia equation to predict the deflection of FRP-reinforced concrete members based on the harmony search algorithm. The harmony search algorithm is used to optimize a function that minimizes the error between the deflection value of the experimental result and the deflection value expected from the specimen's specifications. In the experimental part, four GFRP (Glass Fiber-Reinforced Polymer)- and BFRP (Basalt Fiber-Reinforced Polymer)-reinforced concrete slab specimens were manufactured and tested. FRP-reinforced concrete slabs were reinforced with GFRP and BFRP rebars on spiral rib surfaces. The effects of the FRP reinforcement ratio and balanced reinforcement ratio (ρf/ρfb), the moment of inertia of the transformed cracked section and the gross moment of inertia (Icr/Ig), and the cracking moment and the maximum service load moment (Mcr/Ma) on the effective moment of inertia have been considered. The experimental results and predicted results of the flexural testing of concrete slabs reinforced with FRP rebars were compared, and the experimental results were in good agreement with the calculated values using the proposed effective moment of inertia equation.