Effective Moment Of Inertia Research Articles

Analysis of flexural concrete beams prestressed with basalt composite bars. Analytical-experimental approach

This present work describes the complex analysis of flexural concrete members prestressed with basalt fiber reinforced polymer (BFRP) bars considering consecutive phases of the loading applied. The aim of this research was to propose analytical approach for the prediction of effective prestress force that directly influence the serviceability limit state of prestressed concrete members, in particular to deflections. Proposed method considering prestress losses for deflection estimation is based on the concept of prestressed concrete laws within particular assumptions. The method is based on strain and curvature analysis, effective moment of inertia including decompression effect and early aging effects of both the concrete and BFRP. The instantaneous and time-dependent prestress losses, cross-sectional stress-strain, deflection and cracking behavior of concrete members reinforced with BFRP bars are described as an interrelated process. This complex approach allows to avoid disappearing of prestressing effect, such as camber or strain of decompression, as a base point and the principle of serviceability analysis of prestressed concrete members. Also, an experimental program was expanded with the purpose to evaluate the influence of prestress level for flexural stiffness of the real scale concrete beams prestressed with BFRP bars.

Flexural performance of FRP/steel hybrid reinforced engineered cementitious composite beams

Flexural performance of six groups of beams reinforced with hybrid steel and FRP bars, one group with steel bars, and a final group with FRP bars was investigated in this paper. Each group comprised two specimens having identical reinforcement, but one made of concrete and the other made of ECC. All test specimens had the same geometrical dimensions and loading arrangements. Test results showed that the load capacity, deflections and crack widths of hybrid reinforced beams are 1.19–1.37, 0.19–0.55 and 0.23–0.81, respectively, of those of FRP reinforced control beams; with the application of ECC, the load capacity, deflections and crack widths of ECC beams are 1.02–1.28, 0.49–0.97 and 0.30–0.88 times, respectively, those of concrete control beams. According to simplified constitutive models of materials, compatibility of strains and equilibrium of forces, four failure modes and their discriminants are put forward. Simplified formulas for cracking, yield and ultimate moments, as well as effective moment of inertia and crack width, of hybrid reinforced ECC specimens are also proposed. Predicted results calculated by the simplified formulas are well correlated with the test results, confirming validity of the developed simplified formulas for practical use.

Long-term deflections of FRP reinforced concrete beams

ABSTRACT Concrete beams reinforced with fiber-reinforced polymer bars (FRP) are becoming widely used. The sustained deflections due to creep and shrinkage for these beams control the design due to the low modulus of elasticity of FRP bars. The current work presents a successful finite elements modeling for tests on FRP reinforced concrete beams along with study for some factors influencing the long-term deflection such as the reinforcement ratio and the type and the level of sustained load. Increasing the FRP reinforcement ratio results in reduction in the total sustained load deflection. Similarly, for the reduction in the sustained load level. Carbon FRP reinforced beams have the least total long-term deflections. FRP design codes such as ACI 440.1 R-06 and CSA-S806-02 provide simple equations for calculating the sustained deflection based on multiplicative factors. Also, the literature gives other equation for creep and shrinkage deflections based on multiplicative coefficients. The three original methods and the same methods with their amendments are verified against experimentally calibrated finite element models. The ACI440.1 R-06 method modified with Bischoff’s effective moment of inertia is found to yield the best results. The current paper further modifies this method. The currently modified ACI440.1 R-06 with the effective moment of inertia as proposed by Bischoff is found to produce better accuracy for the calculations of the total sustained load deflections.

Parameter Effects of the Hydrostatic Propulsion Drive System on the Operation Accuracy of a Tamping Machine

A dynamic mathematical model of the hydrostatic propulsion drive system of a tamping machine is established in this study, and a simulation model is built in the AMEsim software environment using the mathematical model. Parameter effects of the hydrostatic propulsion drive system on the operation accuracy of the tamping machine are analysed. Simulation results show that the effective moment of inertia of the powertrain and the oil volumetric elastic modulus have obvious influences on the operation accuracy of the tamping machine, the effect of the total volume of the high-pressure circuit of the hydraulic system on the displacement accuracy is not obvious, but it has some influence on the velocity amplitude. The models established and results obtained in this work are of significance and instructive for design optimization and maintenance of tamping machines.

The New Australian Concrete Structures Standard AS 3600:2018 – Aspects of its Complexity and Effectiveness

Australian Standard for Concrete Structures AS 3600-1988, the first of the AS 3600 series, was published in March 1988. Since then, AS 3600 has been revised four times and published consecutively at between six to nine-year intervals as AS 3600-1994, AS 3600-2001, AS 3600-2009 and the latest, AS 3600-2018. The changes incorporated in AS 3600-2018 concern mainly the following topics: 1. Stress-block configuration for bending analysis and design of reinforced and prestressed members 2. Shear and torsional strengths of reinforced and prestressed members 3. Values of the strength capacity reduction factor,  for different member strengths 4. Effective moment of inertia for deflection calculations As part of a review, a summary of the relevant new design procedures and associated formulas have been prepared. Research worldwide on the mechanics and strength of concrete structures – a rather mature discipline – is sustaining a state of diminishing return. Australia is no exception. In particular, the modifications identified above have led to more complicated processes which require increased computational efforts. Academically, such added complexity may be considered as a disciplinary upgrade. Concrete engineering practitioners, on the other hand, deserve to be advised of the effectiveness, or worthiness, of such an advance. In each of the concerned topics and for practical problems, analysis and design calculations have been carried out using the updated specifications given in AS 3600-2018, as well as those existing in the superseded AS 3600-2009. Based on the analysis results and design outcomes, observations are made in regard to the complexity and effectiveness of this Australia‟s premier concrete structures code.

Analytical mechanics solution for measuring the deflection of strengthened RC beams using FRP plates

Partial-interaction due to sliding between the steel bars, adhesively attached FRP plates and their bordering concrete surface, accompanied with the detachment of the FRP plates due to intermediate crack (IC) debonding make the deflection of strengthened RC beams difficult to anticipate. Previous research and design rules on determining the deflection of strengthened RC beams using FRP plates have opted for a full-interaction moment-curvature design technique where the deflection was measured by either deriving average effective moment of inertia and using elastic deflection equations or integrating the curvature along the beam’s length. Therefore, IC deboning of the plate and the slip resulting from the formation and broadening of new cracks were not directly considered. In this study, a partial-interaction moment-rotation analysis of an adhesively plated beam segment was used to derive analytical equations for the rotation of individual crack faces. The analytical expressions were used to compute the rotation at a crack for a given moment; subsequently, the influence of each crack to the midspan deflection of the RC beams was calculated. As for the uncracked region of the beam, the deflection contribution was measured by integrating the curvature over the uncracked span. The deflection results from the mechanics solution seem to compare well with experimental results. The analytical mechanics solution accounts for the partial-interaction between the steel bars, externally bonded FRP plate and their bordering concrete surface, and also the detachment of the external plate through IC debonding. Further, due to its generic nature and non-reliance on empirical data, the mechanics solution can be adopted to forecast the deflection of strengthened RC beams with novel types of reinforcement materials.

ENTRAINMENT FACTOR OF INDIVIDUAL GLITCH FRACTIONAL MOMENT OF INERTIA

The superfluid in the inner crust of a neutron star is assumed to be the reservoir of momentum released in a pulsar glitch. Recently, due to crustal entrainment, it appears debatable whether the magnitude of the inner crust is sufficient to contain the superfluid responsible for large glitches. This paper calculates the fractional moment of inertia (FMI)(i.e. the ratio of the inner crust superfluid moment of inertia to that of the coupled components) associated with individual glitches. It is shown that the effective moment of inertia associated with the transferred momentum is that of the entrained neutrons. The FMI for glitches in three pulsars, which exhibit the signature of exhausting their momentum reservoir, were calculated and scaled with the entrainment factor. Some of the glitches require an inner crust superfluid with moment of inertia larger than the current suggested values of 7-10% of the stellar moment of inertia.

Prediction of Deflection of Reinforced Concrete Beams Strengthened with Fiber Reinforced Polymer.

The article analyses the calculation of the deflection of reinforced concrete beams strengthened with fiber reinforced polymer. This paper specifically focuses on estimating deflection when the yielding of reinforcement is reached. The article proposes a simple method for calculating deflection that was compared with the experimentally predicted deflection. The carried out comparison has showed that the proposed method is suitable not only for the strengthened beams but also for the reinforced concrete beams with a varying reinforcement ratio. The suggested calculation method is based on the effective moment of inertia, such as the one introduced in the ACI Committee 318 Building Code Requirement for Structural Concrete (ACI318). The development of deflection was divided into three stages, and equations for the effective moment of inertia were proposed considering separate stages. In addition, the put forward equations were modified attaching additional relative coefficients evaluating a change in the depth of the neutral axis.

Effective Moment of Inertia of Single Spanned Reinforced Concrete Beams with Fixed Beam-Column Joints

Effective Moment of Inertia of Single Spanned Reinforced Concrete Beams with Fixed Beam-Column Joints

Mass number and excitation energy dependence of the Θeff/Θrig parameter of the spin cut-off factor in the formation of an isomeric pair

The ratio of the effective moment of inertia to the rigid body moment of inertia (Θeff/Θrig) parameter of the spin distribution of the level density was determined for 61 nuclei covering the mass range of 44 to 200. The experimental data for 25 isomeric pairs were compared with the model calculations carried out with the TALYS code. The reduced χ2 values were calculated to describe the deviation of the experimental data from the model calculation as a function of the η=Θeff/Θrig parameter. A term ηd was introduced by calculating the Θeff/Θrig value from the low energy discrete levels of the nucleus. The η/ηd values seem to be independent of the mass number and the η values independent of the excitation energy. The mass number and (N-Z) dependences of the η values were studied. The η values for the odd mass nuclei show a characteristic exponential decrease as a function of the mass number or (N-Z). The η values for the even type of nuclei show more complicated behavior. The odd-even effect of Θeff/Θrig may change the calculated activation cross section significantly.

Wobbling motion in Lu within a semi-classical framework

The results obtained for Lu with a semi-classical formalism are presented. Properties like excitation energies for the super-deformed bands TSD1, TSD2, TSD3, in 165Lu, and TSD1 and TSD2 for 167Lu, inter- and intra-band B(E2) and B(M1), the mixing ratios, transition quadrupole moments are compared either with the corresponding experimental data or with those obtained for 163Lu. Also alignments, dynamic moments of inertia, relative energy to a reference energy of a rigid symmetric rotor with an effective moment of inertia and the angle between the angular momenta of the core and odd nucleon were quantitatively studied. One concludes that the semi-classical formalism provides a realistic description of all known wobbling features in Lu.

Service load deflection of tilt-up concrete wall panels

The suitability of using CSA A23.3-14 to compute service load deflection of slender concrete wall panels is evaluated. Calculation of deflection using an effective moment of inertia with a reduced cracking moment is reviewed for beams, slabs, and tilt-up wall panels. While the procedure adopted by A23.3 for computing deflection works reasonably well for beams and slabs with reinforcing ratios as low as 0.4%, computed values do not correlate well with existing tests on slender walls and can underestimate deflection significantly. Deflection of slabs with very low reinforcement ratios (less than 0.4%) is also likely to be underestimated. Revisions to A23.3 are proposed for computing deflection.

Steel and Concrete Elasto-Plastic Models at Bridges with Steel Beams Embedded in Concrete

Abstract For new railway bridges with short spans (L ≤ 35.00 m) superstructures with steel beams embedded in concrete are recommended or used, which can ensure the requirements of strength and stiffness in particular, regardless of velocity. They are built relatively easily compared to reinforced concrete structures or steel structures, they have high durability if designed, built and maintained correctly and don’t have high sensitivity to fatigue degradation in service. They are also used for road bridges when it is desired to achieve a reduced construction height. In all the design prescriptions used so far for structures with steel beams embedded in concrete, the calculation is a simplified one, made on a single insulated longitudinal beam of the deck, if certain conditions related to the geometry of the structure are met (obliquity, curvature). Simplifications are also made regarding the state of deformation of the decks made in this constructive solution by introducing an effective moment of inertia in the displacement calculation, as an average of the inertia moments of the cross section considered to be cracked and respectively un-cracked. The article aims to validate steel and concrete elasto-plastic models, based on an experiment from the technical literature, necessary for complex analyses of the percentage of concrete involved in the stiffness of the cross-sections, in case of bridges with steel beams embedded in concrete.

Numerical analysis of RC plane structures: a concentrated nonlinear effect approach

The present work aims to study the nonlinear behavior of reinforced concrete structures via Refined Plastic Hinge Method (RPHM). Pseudo-springs are used at the finite element ends, where the gradual loss of stiffness is determined by the combination of the normal force and bending moment (NM) in the cross section. The limiting of the uncracked, elastic and plastic regimes is done in the NM diagram. The concrete cracking is explicitly simulated with two approaches to calculate the effective moment of inertia of the cross section. The displacement-based formulation is referenced to the co-rotational system and coupled with continuation strategies to allow to overcome the possible critical points in the equilibrium paths. For validation of the numerical simulations, the results found with the proposed formulation are confronted with experimental and numerical data present in literature.

Effect of fiber reinforcing on instantaneous deflection of self-compacting concrete one-way slabs under early-age loading

The Early-age construction loading and changing properties of concrete, especially in the multi-story structures can affect the slab deflection, significantly. Based on previously conducted experiment on eight simply-supported one-way slabs this paper investigates the effect of concrete type, fiber type and content, loading value, cracking moment, ultimate moment and applied moment on the instantaneous deflection of Self-Compacting Concrete (SCC) slabs. Two distinct loading levels equal to 30% and 40% of the ultimate capacity of the slab section were applied on the slabs at the age of 14 days. A wide range of the existing models of the effective moment of inertia which are mainly developed for conventional concrete elements, were investigated. Comparison of the experimental deflection values with predictions of the existing models shows considerable differences between the recorded and estimated instantaneous deflection of SCC slabs. Calculated elastic deflection of slabs at the ages of 14 and 28 days were also compared with the experimental deflection of slabs. Based on sensitivity analysis of the effective parameters, a new model is proposed and verified to predict the effective moment of inertia in SCC slabs with and without fiber reinforcing under two different loading levels at the age of 14 days.

Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars

In this paper, the flexural behavior of partially fiber-reinforced high-strength concrete (FRHSC) beams reinforced with FRP bars was investigated. A total of 12 beams were tested under four-point bending. The effects of the thickness of FRHSC layer, steel fiber volume fraction and FRP reinforcement ratio were studied. The failure mode, flexural capacity, deflection, crack width and ductility of the tested beams were investigated. The results showed that adding steel fibers in tension zone is an effective way to overcome the large deflection and large crack width of FRP bar reinforced concrete beams and reduce the cost, however, the ductility of tested beams decreased with the addition of steel fiber into tension zone. The optimum thickness of FRHSC layer in FRP bar reinforced concrete beams was 0.57 times of the total depth of the beam. Higher FRP reinforcement ratio provided better flexural performance including higher flexural capacity, post-cracking stiffness and ductility and smaller crack width. A simplified calculation method for predicting the effective moment of inertia of fully and partially FRHSC beams reinforced with FRP bars was developed. The beam deflections calculated by the proposed method match well with the experimental results.

Prediction of effective moment of inertia for hybrid FRP-steel reinforced concrete beams using the genetic algorithm

Prediction of effective moment of inertia for hybrid FRP-steel reinforced concrete beams using the genetic algorithm

Theoretical and experimental analysis of two-culm bamboo beams

Guadua angustifolia is a species of bamboo native to South America. The aim of this study was to accomplish experiments and finite-element simulations to determine the stiffness of two-culm G. angustifolia beams, as typically used in the construction of low-rise buildings. Calculations were also accomplished to find the moment of inertia (i.e. effective) to assess beam deflections using a solid mechanics formula that includes bending and shear effects. First, full-scale tests of simple culms were performed with four different spans to find the axial and the circumferential–axial shear moduli. Next, full-scale tests of two-culm beams with two shear connectors located at L/6 from the supports were performed. There was a marginal increase of stiffness compared to that of two-culm beams without connectors. Finite-element simulations confirmed that the stiffness of two-culm beams with connectors is similar to that of two superimposed culms. Only the addition of cement mortar yielded an important increase of stiffness. Results indicate the need to reformulate the calculation of the effective moment of inertia of multiple-culm bamboo beams, as the value calculated using the parallel axis theorem is too large, and yields deflections substantially lower than those obtained experimentally.

Flexural behavior and a modified prediction of deflection of concrete beam reinforced with a ribbed GFRP bars

This study experimentally investigated the flexural capacity of a concrete beam reinforced with a newly developed GFRP bar that overcomes the lower modulus of elasticity and bond strength compared to a steel bar. The GFRP bar was fabricated by thermosetting a braided pultrusion process to form the outer fiber ribs. The mechanical properties of the modulus of elasticity and bond strength were enhanced compared with those of commercial GFRP bars. In the four-point bending test results, all specimens failed according to the intended failure mode due to flexural design in compliance with ACI 440.1R-15. The effects of the reinforcement ratio and concrete compressive strength were investigated. Equations from the code were used to predict the deflection, and they overestimated the deflection compared with the experimental results. A modified model using two coefficients was developed to provide much better predictive ability, even when the effective moment of inertia was less than the theoretical Icr. The deformability of the test beams satisfied the specified value of 4.0 in compliance with CSA S6-10. A modified effective moment of inertia with two correction factors was proposed and it could provide much better predictability in prediction even at the effective moment of inertia less than that of theoretical cracked moment of inertia.

Shear strength reduction due to introduced opening in loaded RC beams

The reduction of shear strength due to the introduction of an opening is an ongoing problem for reinforced concrete (RC) beams. Fifteen rectangular section (150mm × 300mm × 1650mm) specimens were tested and divided into six groups under three considerations: 1) opening dimensions and shape, 2) time needed to create an opening for a new or an existing building; 3) external and internal strength of the opening in RC beams. The results demonstrate that a reduction in stiffness occurs due to the presence of an opening. The stiffness reduces further when the opening is placed under loading because of the reduction in the effective moment of inertia due to formation cracks around the opening as a result of the opening process. The stirrups besides the opening resisted shear force with ratios between 35% and 65% from the yield strength of steel bars and must be considered for shear resistance. Finally, the initial proposal equation that calculates the resistance shear force taken by the vertical stirrups around the opening can serve as a guideline for the introduction of an opening in RC beams.