Showing papers on "Flexural rigidity published in 2005"

A method for flexural reinforcement of old wood beams with CFRP materials

Abstract: This paper presents a study on the reinforcement of existing wood elements under bending loads through the use of FRP materials. An analytical investigation was first conducted on the behavior of a generic FRP-reinforced wood section. This study, in turn, led to a numerical procedure based on non-linear wood properties, suitable for application in the design of FRP reinforcement of old, pre-existing wood beams under varying configurations of intervention layouts and materials. An experimental programme based on a four-point bending test configuration is proposed to characterize the stiffness, ductility and strength response of FRP-wood beams. Mechanical tests on the reinforced wood showed that external bonding of FRP materials may produce increases in flexural stiffness and capacity. The FRP composite material was made of High Tensile Carbon monodirectional reinforcing fabrics embedded in an epoxy resin matrix. This reinforcing method can be applied without necessitating the removal of the overhanging part of the pre-existing wood structure, thus maintaining the original historical structure. In addition, a beam non-linear model was proposed to predict ultimate load. At the end of this paper results of the experimental programme are presented and used for comparison with the numerical procedure.

Soft and Hard Adhesion

Abstract: The force needed to pull a cylindrical stud from a soft elastomeric film depends on their elastic and geometric properties. For a rigid stud and a thick elastomeric film, the pull-off stress (σ) depends on the elastic modulus (E) of the film and the radius (a) of the stud as σ ∼ (E/a)1/2 (soft adhesion). However, when the film is very thin, the pull-off stress is significantly higher than the case with thick films, and its value depends on the elastic modulus and the thickness (h) of the film as σ ∼ (E/h)1/2 (hard adhesion). Here, we study the pull-off behavior of a soft cylindrical stud, one flat end of which is coated with a high modulus thin baseplate. As the flexural rigidity of this baseplate is varied, we observe the transition between the two types of adhesion. We present a simple physical interpretation of the problem, which could be of value in understanding various biofouling and adhesive situations.

Rectangular Filament-Wound Glass Fiber Reinforced Polymer Tubes Filled with Concrete under Flexural and Axial Loading: Experimental Investigation

Abstract: This paper presents results of an experimental investigation on three beams and five short columns, consisting of glass fiber reinforced polymer concrete-filled rectangular filament-wound tubes (CFRFTs). The tubes included fibers oriented at 45 deg and 90 deg with respect to the longitudinal axis. Additional longitudinal fibers [0 deg] were provided in flanges for flexural rigidity. Beams included totally filled tubes and a tube partially filled with concrete, which had a central hole for reducing deadweight. The effect of reinforcement ratio was examined by using tubes of two different sizes. Flexural behavior of CFRFT was compared to concrete-filled rectangular steel tubes (CFRSTs) of similar reinforcement ratios. Short columns were tested under eccentricity ratios (e/h) of 0, 0.09, 0.18, and 0.24, where h is the section depth. Transverse strains were measured around the perimeter of concentrically loaded column to evaluate confinement effect. The study showed that CFRFT is a feasible system that could offer similar flexural strength to CFRST. The tube laminate structure and its progressive failure contribute to the slightly nonlinear behavior of beams. The CFRFT beam with inner hole had an overall strength-to-weight ratio, 77% higher than the totally filled beam, but failed in compression. Bulging of CFRFT columns has limited their confinement effectiveness.

Magnetorheological elastomer-based smart sandwich beams with nonconductive skins

Abstract: The field-dependent dynamic flexural rigidity of a simply supported sandwich beam with a soft core composed of a magnetorheological elastomer (MRE) part and non-MRE parts is studied in this paper. The skins of the sandwich beam are nonconductive such that there are no magnetoelastic loads applied to the skins during vibration. The orientation of the chain-like structures inside the MRE part is perpendicular to the skins such that the MRE part operates in shear mode. Due to such a configuration, the dynamic flexural rigidity of the sandwich beam can be controlled by applied magnetic fields due to the field-dependent shear modulus of the MRE part. Based on the Hamilton principle, a dynamic model of the proposed sandwich beam is developed. A simply supported beam excited by a vertical force, distributed uniformly in a narrow region around the center of the beam is simulated. The anti-resonant frequencies are found to change with the shear modulus of the MRE part up to 40%, while the resonant frequencies change only slightly. Although MRE is an extremely soft material with a zero-field shear modulus about 0.4 MPa, the results from the current research indicate that the sandwich configuration can well utilize the controllable properties of MRE to realize applicable semi-active devices with controllable stiffness.

Analysis of flexible bending behavior of woven preform using non-orthogonal constitutive equation

Abstract: Previous studies by Yu et al. [Yu WR, Pourboghrat F, Chung K, Zampaloni M, Kang TJ. Non-orthogonal constitutive equation for woven fabric reinforced composites. Composites Part A 2002;33:1095–1105; Yu WR, Zampaloni M, Pourboghrat F, Chung K, Kang TJ. Sheet hydroforming of woven FRT composites: non-orthogonal constitutive equation considering shear stiffness and undulation of woven structure. Compos Struct 2003;61:353–62; Yu WR, Zampaloni M, Pourboghrat F, Liu L, Chen J, Chung K, Kang TJ. Sheet forming analysis of woven FRT composites using picture-frame shear test and non-orthogonal constitutive equation. Int J Mater Prod Tech 2004;21(1/2/3):71–88] have illustrated the validity of the non-orthogonal constitutive relationship for predicting deformation behavior and changes in fiber angle in situations where woven preform was constrained by tools such as the die and blank holders. In the previous studies, the bending rigidity for out-of-plane deformation was assumed to be dependent on the in-plane stiffness; thereby the non-orthogonal constitutive equation being developed was based on the in-plane deformation geometry. The assumption for the bending rigidity was modified in this study by modeling the bending property using an asymmetric axial modulus. The asymmetric axial modulus was considered in order to utilize its ease in calculating bending rigidity from the in-plane stiffness, defining bilinear behavior over the range of tension to compression. The asymmetric factor, the ratio of compression and tensile modulus, for a woven preform was determined through simple cantilever deflection in the warp and weft directions, the validity of which was proven by conducting a cantilever deflection test and simulation in the bias direction. Finite element simulation of three-dimensional bending deformation was performed by using a non-orthogonal constitutive equation and the asymmetric axial modulus. The results show that the draped shape obtained numerically is in good agreement with the experiments in both overall deflected shape and projected contour. A shaping process was also simulated to show the usefulness of the current approach. By including the gravity and contact loading, successful prediction was made but a need was identified that extends linear asymmetric factor into nonlinear form in order to simulate large deformation in bending.

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Finite Element Method and Absolute Nodal Coordinate Formulation

Abstract: Three formulations for a flexible spatial beam element for dynamic analysis are compared: a finite element method (FEM) formulation, an absolute nodal coordinate (ANC) formulation with a continuum mechanics approach and an ANC formulation with an elastic line concept where the shear locking of the asymmetric bending mode is suppressed by the application of the Hellinger–Reissner principle. The comparison is made by means of an eigenfrequency analysis on two stylized problems. It is shown that the ANC continuum approach yields too large torsional and flexural rigidity and that shear locking suppresses the asymmetric bending mode. The presented ANC formulation with the elastic line concept resolves most of these problems.Copyright © 2005 by ASME

Doubly-anchored thermal actuator having varying flexural rigidity

Abstract: A doubly-anchored thermal actuator for a micro-electromechanical device such as a liquid drop emitter or a fluid control microvalve is disclosed. The thermal actuator is comprised of a base element formed with a depression having opposing anchor. A deformable element, attached to the base element at the opposing anchor edges, is constructed as a planar lamination including a first layer of a first material having a low coefficient of thermal expansion and a second layer of a second material having a high coefficient of thermal expansion. The deformable element has anchor portions adjacent the anchor edges and a central portion between the anchor portions wherein the flexural rigidity of the anchor portions is substantially less than the flexural rigidity of the central portion. The doubly-anchored thermal actuator further comprises apparatus adapted to apply a heat pulse to the deformable element that causes a sudden rise in the temperature of the deformable element. The deformable element bows outward in a direction toward the second layer, and then relaxes to a residual shape as the temperature decreases. The doubly-anchored thermal actuator is configured with a liquid chamber having a nozzle or a fluid flow port to form a liquid drop emitter or a fluid control microvalve, or to activate an electrical microswitch. Heat pulses are applied to the deformable element by resistive heating or by light energy pulses.

Elasticity and stability of a helical filament.

Abstract: We derive the general shape equations in terms of Euler angles for a uniform elastic rod with spontaneous torsion and curvatures and subjected to external force and torque. Our results based on an analytic formalism show that the extension of a helical rod may undergo a one-step discontinuous transition with increasing stretching force. This agrees quantitatively with experimental observations for a helix in a chemically defined lipid concentrate. The larger the twisting rigidity, the larger the jump in the extension. The effect of torque on the jump is, however, dependent on the value of the spontaneous torsion. In contrast, increasing the spontaneous torsion encourages the continuous variation of the extension. An "over-collapse" behavior is observed for the rod with asymmetric bending rigidity, and an intrinsic asymmetric elasticity under twisting force is found.

Evolution of flexural rigidity according to the cross-sectional dimension of a superelastic nickel titanium orthodontic wire.

Abstract: The present study compared bending in 10 archwires made from NiTi orthodontics alloy of two crosssectional dimensions. The results were based on microstructural and mechanical investigations. With conventional alloys, the fl exural rigidity was constant for each wire and increased largely with the crosssectional dimension for the same strain. With NiTi alloys, the fl exural rigidity is not constant and the infl uence of size was not as important as it should be. This result can be explained by the non-constant elastic modulus during the martensite transformation process. Thus, in some cases, treatment can begin with full-size (rectangular) wires that nearly fi ll the bracket slot with a force application deemed to be physiologically desirable for tooth movement and compatible with patient comfort.

Seismic performance of rectangular-shaped steel piers under cyclic loading

Abstract: The purpose of this experimental work is to investigate the seismic resistance characteristics of rectangular-shaped steel bridge piers commonly found in rigid frames, concerning the cross-sectional aspect ratios. To this end, seven specimens were tested under cyclic lateral loads. Six of them were under constant compressive axial load and one was under variable axial load. At first, the effects of web to flange aspect ratio ( W∕F ratio) on the differences between actual and estimated yield displacements, yield loads and flexural stiffness were examined. W∕F ratio of around 2.0 was found to offer minimum difference between those values. Secondly, the effects of W∕F ratio on ultimate strength, ductility, and energy dissipation capacity were determined. The highest strength was observed in columns with a W∕F ratio of about 2.0 while the highest ductility and cumulative energy dissipation capacity were in those with a W∕F ratio of around 1.60. Also, the effect of varying axial load on the strength was examin...

High-strength steel sheet having excellent bending rigidity and its production method

Abstract: PROBLEM TO BE SOLVED: To provide a high-strength steel sheet in which tensile strength TS in the 90° direction to the rolling direction is ≥590 MPa and bending rigidity in the 0°, 45° and 90° directions to the rolling direction is excellent, and to provide its production method. SOLUTION: The high-strength thin steel sheet having excellent bending rigidity has a microstructure having a ferrite phase of, by area, 60 to 90% and a martensite phase of 10 to 40%, and, in which the total area ratio of the ferrite phase and the martensite phase is ≥95%, also, the average grain diameter (d) α of the ferrite grains is 1.0 to 6.0 μm, the average grain diameter d M of the martensite grains is 0.5 to 3.0 μm, and d α /d M ≥1.5 is satisfied. In the high strength steel sheet, TS in the 90° direction to the rolling direction is ≥590 MPa, also, when, from each curve of stress σ-strain e on the outside of each bent part obtained by performing a three point bending test regarding the 0°, 45° and 90° directions to the rolling direction, the gradient (Δσ/Δe) of each curve in the case σis 200 MPa is calculated, the (Δσ/Δe)c in the 90° direction to the rolling direction is ≥230 GPa, and the (Δσ/Δe) on the average in the above three directions is ≥200 GPa. COPYRIGHT: (C)2007,JPO&INPIT

Flexural Strengthening of RC Beams Using Steel Reinforced Polymer (SRP) Composites

Abstract: Synopsis: This paper presents the application of a new generation of externally bonded composite material in flexural strengthening of reinforced concrete beams. The steel reinforced polymer (SRP) composite consists of high-carbon steel unidirectional Hardwire® fabrics embedded in epoxy resin, and offers high strength and stiffness characteristics at a reasonable cost. In this paper, the mechanical properties of SRP are evaluated and its application in flexural strengthening of RC beams is investigated. Six beams have been tested in three-point bending to study the effect of SRP retrofitting on flexural behavior, failure modes, and crack patterns. Test parameters include variation of the width of SRP sheets and the use of SRP U-wraps at both ends to prevent premature failure caused by delamination of the longitudinal sheet. Significant increase in flexural capacity, up to 53 %, and pseudo-ductile failure modes have been observed in the SRP-strengthened beams. Failure is governed primarily by concrete cover delamination at the tips of the SRP sheets or crushing of concrete at mid-span. It is also shown that the U-wraps have improved flexural stiffness by means of controlling diagonal crack width and providing anchorages to the longitudinal SRP sheets, which reduces their slip. Shear stress concentration near the cut-off point of the SRP sheet has also been investigated. An analytical model is proposed to predict the nominal strength of the SRP-strengthened beams.

Evaluating the Bending Rigidity of Flat Textiles with the Use of an Instron Tensile Tester

Abstract: The purpose of this work is to verify the possibility of using an Instron tensile tester for evaluating those mechanical properties of flat textile fabrics which are responsible for their handle properties. A method of evaluating the bending rigidity of woven fabrics was developed. The method consists in axially compressing samples fixed at both ends and placed in a vertical position, which leads to their buckling. The bending rigidity was determined on the basis of the critical maximum force occurring at buckling, and the curvature of the buckled sample which appears as result of the action of this force. The results obtained by this method were compared with those obtained with the use of the FAST system. The good compatibility of both these methods was proved by the correlation coefficients.

Analysis of bending properties of worsted wool yarns and fabrics based on quasi-three-point bending

Abstract: The bending behavior of worsted wool yarns and fabrics plays a crucial role in handling and performance of end-use textiles. Hence, the fabric/yarn bending properties were studied based on a quasi-three-point bending model by means of the theoretical modeling and the corresponding measuring method. By means of the formula and the measured curves, the curve of bending rigidity and the curvature of a fabric or a yarn can be calculated so as to characterize the bending behavior more precisely than in the previous work. All the experiments on the fabric/yarn bending rigidity have been conducted for both the worsted wool fabrics and the corresponding yarns procured from the fabrics, with the same apparatus bending evaluation system of fabric and yarn, which was developed independently. The measured results of bending rigidity and curvature curve show good correlation with the bending moment and the curvature relationship of the theoretical modeling, and the comparisons of bending rigidity among KES-FB...

Flexural Properties of Flexible Conductors Interconnecting Electrical Substation Equipment

Abstract: This paper presents the results of quasi-static bending tests on two different flexible conductors (cables) used to interconnect electrical substation equipment. The main objectives were to observe the flexural response of flexible conductors and to determine their moment–curvature relationships under axial tension. The results of the tests indicate that the force–displacement behavior of the conductors is linear-elastic with negligible hysteretic response. For most combinations of axial tension and lateral displacement, the flexural stiffness is very small, and tends toward the minimum possible flexural stiffness, corresponding to the situation where all the strands are slipping past each other, and are unable to transfer any shear force. Only for very large axial tension values does the flexural stiffness approach the maximum possible flexural stiffness, corresponding to the situation where all the strands are able to transfer longitudinal shear forces over one another, and the conductor section acts as...

Modelling and classification of tubular joint rigidity and its effect on the global response of CHS lattice girders

Abstract: In engineering practice, tubular connections are usually assumed pinned or rigid. Recent research showed that tubular joints may exhibit non-rigid behavior under axial or bending loads. This paper is concerned with establishing a new classification for tubular joints and investigating the effect of joint rigidity on the global behavior of CHS (Circular Hollow Section) lattice girders. Parametric formulae for predicting tubular joint rigidities are proposed, which are based on the finite element analyses through systematic variation of the main geometric parameters. Comparison with test results proves the reliability of these formulae. By considering the deformation patterns of respective parts of Vierendeel lattice girders, the boundary between rigid and semirigid tubular connections is built in terms of joint bending rigidity. In order to include characteristics of joint rigidity in the global structural analysis, a type of semirigid element which can effectively reflect the interaction of two braces in K joints is introduced and validated. The numerical example of a Warren lattice girder with different joint models shows the great effect of tubular joint rigidities on the internal forces, deformation and secondary stresses.

Nonlinear EI Equation for Slender Reinforced Concrete Columns

Abstract: The ACI Building Code permits the use of a moment magnifier approach for the design of slender reinforced concrete columns. This approach was introduced into design practice to eliminate the need for extensive calculations, based on the solution to a differential equation, to compute second-order bending moments in columns. The moment magnifier approach is influenced by the critical buckling load P c . The computation of P c is strongly influenced by the effective flexural stiffness El, which varies due to the nonlinearity of the concrete stress-strain curve, creep, and cracking along the length of the unsupported column. This study was conducted to examine the influence of different variables on El used for the design of slender, tied, rectangular reinforced concrete columns in braced frames under short-term loads and also to examine the existing ACI El equations. Over 11,000 isolated square reinforced concrete columns, each with a different combination of specified properties of variables, in symmetrical single curvature bending, were simulated to generate the stiffness data. A new nonlinear design equation to compute El of reinforced concrete columns was then developed from the simulated stiffness data and is proposed as an alternative to the existing ACI design equations for El.

Deflector mirror with regions of different flexural rigidity

Abstract: A deflector mirror is disclosed that includes a mirror substrate configured to vibrate in a reciprocating manner on beams as a torsional rotary shaft so as to deflect a light beam emitted from a light source. The mirror substrate includes multiple regions in each of portions thereof extending from the torsional rotary shaft to respective ends of the mirror substrate, the regions being different in flexural rigidity.

Improvement of capacity in bending by the use of FRP layers on RC beams

Abstract: Carbon‐filled plastic bands are more extensively used for strengthening the permanently exploited curved elements. As a result, the bending rigidity of the element is increased and the crack formation process is changed. Investigation of these problems is carried out basing on the model of laminated material, in which the mechanical properties of separate layers may have discreete different values depending on the external load volume. Practical calculations are made by numerical methods which make it possible to follow up the origin of the crack formation in the concrete, by taking into account its non‐linear deformation character. The work deals with the analysis of the beam strengthening specific character under unloaded and loaded conditions. Testing of the results is performed by using 2 m long reinforced concrete beams strengthened with carbon‐filled plastic bands.

On optimum thin-walled closed cross section

Abstract: This paper deals with the problem of finding a minimum area thin-walled closed cross section with prescribed constant thickness and flexural rigidity. The cross section is supposed to be double symmetrical with respect to the Cartesian reference system (x0y), where 0 is the centroid of the cross section, and subjected to a bending moment M. The vector M is taken to be non-coincident with the x or y axis. This means that to represent the flexural rigidity both Ix and Iy moments of inertia are required. The function describing the centerline of the thin-walled closed cross section is taken as unknown.

Bending Analysis of Nonlinear Material Fibers with a Generalized Elliptical Cross-section:

Abstract: The bending moment-curvature relation was derived for generalized elliptical cross-section fibers made of nonlinear material and particular values were found to agree with those already obtained for elliptical cross-section and rectangular cross-section. The bending shape factors, the relation between bending rigidity and linear density were explicitly determined. The bending stress-strain relation of the generalized elliptical cross-section fibers was also derived.

Finite element model creation method of structure, and simulation method of structure

Abstract: PROBLEM TO BE SOLVED: To provide a model creation method which is a finite element model creation method of a structure having a reinforcing layer with a reinforcing material embedded in a base material, and matches not only rigidity in the in-plane direction but also flexural rigidity in the out-of-plane direction of a model with those of an actual reinforcing layer, and also to provide a simulation method of a structure using it. SOLUTION: A base material model element 20 with a base material represented by a finite model is created; a reinforcing layer model for duplicating a reinforcing layer by adding, to the model element 20 as model elements of the reinforcing layer, at least two laminated virtual reinforcing model elements 22 each provided with Young's modulus as a material constant, separated from each other and having a separation distance freely set; and the distance between the model elements 22 formed in parallel with each other is so adjusted that flexural rigidity in the out-of-plane direction in the reinforcing layer model coincides with the flexural rigidity in the out-of-plane direction of the reinforcing layer. Stress and distortion of a structure is analyzed by using the created reinforcing layer model. COPYRIGHT: (C)2005,JPO&NCIPI