Showing papers on "Flexural rigidity published in 2004"

Effect of column stiffness on braced frame seismic behavior

Abstract: Steel concentrically braced frames are generally designed to resist lateral force by means of truss action. Design consider- ations for columns in these frames are therefore governed by the column axial force while column bending moment demands are generally ignored. However, if the columns cannot carry moments, then dynamic inelastic time-history analyses show that a soft-story mechanism is likely to occur causing large concentrated deformations in only one story. Such large concentrations of damage are not generally seen in real frames since columns are generally continuous and they possess some flexural stiffness and strength. This paper develops relationships for column stiffness and drift concentration within a frame based on pushover and dynamic analyses. It is shown that continuous seismic and gravity columns in a structure significantly decrease the possibility of large drift concentrations. An assessment method and example to determine the required column stiffness necessary to limit the concentration of story drift is provided.

Free Vibration Analysis of Rotating Blades With Uniform Tapers

Abstract: A spectral finite element method (SFEM) is proposed to develop a low-degree-of-freedom model for dynamic analysis of rotating tapered beams. The method exploits semi-analytical progressive wave solutions of the governing partial differential equations. Only one single spectral finite element is needed to obtain any modal frequency or mode shape, which is as accurate or better than other approaches reported in the literature for straight or uniformly tapered beams. The minimum number of such spectral finite elements corresponds to the number of substructures, that is, beam sections with different uniform tapers, in a rotating beam to capture the complete system dynamic characteristics. The element assembly procedure is accomplished in the same fashion as the conventional finite element approach. Results are for a number of examples such as a straight beam and beams with uniform taper or compound tapers. Overall, for a rotating blade system, our SFEM provides highly accurate predictions for any modal frequency using a single element or very few elements corresponding to the number of uniform taper changes in the blade system. Nomenclature EI (x) = beam bending flexural stiffness EI 0 = reference beam bending flexural stiffness L = beam length M(x) = beam bending moment m(x) = beam mass per unit length m0 = reference beam mass per unit length R =o ffset length between beam and rotating hub T (x) = beam axial force due to centrifugal stiffening V (x) = beam shear force W(x) = beam bending mode shape function w(x, t) = beam transverse displacement α = beam mass per unit length constant βi = beam bending flexural stiffness constant, i = 1, 4 η = nondimensional axial force µ = nondimensional natural frequency � = beam rotation speed ω =e xcitation frequency

Relationship between axial and bending behaviors of the human thoracolumbar vertebra.

Abstract: Study Design. The authors studied the mechanical behavior of vertebrae through the use of finite element analyses. Objectives. To determine the relation between axial and bending rigidity, and to determine the geometric and densitometric factors that affect this relation. Summary of Background Data. Metrics of vertebral body mechanical properties in bending nave not been established despite evidence that anterior bending loads play a significant role in osteoporotic vertebral fracture. Methods. Voxel-based finite element models were generated using quantitative computed tomography (QCT) scans of 18 human cadaveric vertebral bodies, and both axial and bending rigidities of the vertebra were computed. Both rigidity measures and their ratio were correlated with vertebral geometric and densitometric factors obtained from The QCT scans. Results. Bending rigidity was moderately correlated with axial rigidity (r 3 = 0.69) and strongly correlated with the product of axial rigidity and vertebra anteroposterior depth squared (r 2 = 0.88). The ratio of bending to axial rigidity was independent of bone mineral density (P = 0.20) but was moderately correlated with the square of vertebral depth (r 2 = 0.69). Conclusions. Vertebral anteroposterior depth plays an important role in bending rigidity. The scatter in the correlation between bending and axial rigidity suggests that some individuals can have vertebrae with a normal axial stiffness but an abnormally low bending stiffness. Because whole-bone stiffness is indicative of bone strength, these results support the concept that use of more than one metric of vertebral strength, for example, compres sion and bending strengths, may improve osteoporotic fracture risk prediction.

Flexural Stiffness of Reinforced Concrete Columns and Beams: Analytical Approach

Abstract: The present ACI code 318-02 provisions on effective stiffnesses of beams and columns are reviewed. Factors influencing moments of inertia of beams and columns are discussed. The primary variables considered are: the reinforcement ratio, the axial load ratio, the eccentricity ratio, and the compressive strength of concrete. On the basis of a parametric study, simple formulas are proposed to determine the effective stiffnesses of reinforced concrete columns and beams. The proposed stiffness expressions are applicable for all levels of applied loading, including both service and ultimate loads. The analytical results show that the flexural stiffness assumption in the current ACI code procedure for design of slender columns using the moment magnifier method (Eq. 10-11 and 10-12) is extremely conservative. Recommendations are made concerning stiffness assumptions in the analysis of reinforced concrete frames under lateral loads.

Bending Rigidity of Interfaces in Aqueous Phase-Separated Biopolymer Mixtures

Abstract: Using equations for the interfacial properties for a two-phase multicomponent system, we present a new model for the interfacial tension and bending rigidity for liquid-liquid interfaces between semidilute polymer phases. Using this model, we calculate the interfacial thickness and the bending rigidity for two different gelatin/dextran systems and a gelatin/gum arabic system using experimentally determined values for the interfacial tension. The bending rigidity of such systems has been unaccessible experimentally until now. For the gelatin/dextran systems, which are both near-critical, the interfacial thickness is very large (1000 nm) close to the critical point, where the interfacial tension is very low. Further from the critical point, the interfacial thickness decreases to a value in the order of the size of the biopolymers (100 nm). For the gelatin/gum arabic system, which is off-critical, we found the interfacial thickness to be constant, in the order of the size of the biopolymers. For the gelatin/dextran systems, the scaling relation between the interfacial tension and the interfacial thickness was investigated. The exponents were found to be approximately 1.7 for the two systems, which is in agreement with the exponent 2 of the scaling relation ~ 1/2. The accompanying bending rigidities for these near-critical gelatin/dextran systems were found to be approximately constant, with a value of 500 kbT. The bending rigidity for the gelatin/gum arabic system, which is off-critical, was in the order of 25 kbT. These high values for both the interfacial thickness and the bending rigidity for the near-critical systems may be of significance for interface-related phenomena in aqueous phase-separated biopolymer mixtures, in particular in cases where the bending contributions dominate the stretching contributions to the interfacial energy.

Effect of Bending Rigidity on the Capstan Equation

Abstract: A tensioned fiber or yam in contact with a circular body is analyzed. In the model, a fiber is considered as a linear elastic and inextensible beam. An exact mathematical model is derived and the analytical solution is obtained. Both the beam-body contact and two noncontact regions are analyzed. From the equilibrium equation of force and bending moment, the derived model has three compatible ordinary differential equations, and one algebraic equation from the Euler beam theory with four unknown parameters. From the solutions, the relationship between incoming and outgoing tension is obtained, and we call this the modified capstan equation. The results show the correction connecting the capstan equation and its applications. For example, in a typical case, the capstan equation underestimates the effect of bending rigidity, which renders the only physically possible situation of tension in a real capstan to be the equilibrium of inclined tension. Moreover, the sensitivity of the tension ratio on the variati...

X-ray surface scattering investigation of Langmuir films: Phase transitions and elastic properties

Abstract: We have investigated Langmuir films at the water surface using grazing-incidence diffuse X-ray scattering. We show that beyond structural parameters like the film thickness and density, diffuse scattering also gives access to phase transitions and elastic properties (surface tension and bending rigidity). We find that the surface tension measured with X-rays is consistent with the Wilhelmy plate measurements, at least for tilted phases. The bending rigidity is found to be on the order of 20–30kBT whatever the phase. The underlying molecular mechanisms are discussed using different models.

Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation

Abstract: In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method.

Flexural stiffness of selected corrugated structures

Abstract: Top-to-bottom compression strength of a corrugated fibreboard box is partly dependent on the load-carrying ability of central panel areas of the box. The ability of these central panel areas to resist a bending force from loading may increase the stacking strength of the box. The difference in the compression strengths of boxes that have identical dimensions and were fabricated with identical components but different flute types, is primarily caused by flexural stiffness of the box panels. Top-to-bottom compression strength of boxes can be accurately predicted by flexural stiffness measurements and edge crush test (ECT) of the combined boards. This study was carried out to analyse the flexural stiffness, to measure bending force and bending deflection by a four-point bending test for various corrugated fibreboards, and to provide the major constructional factors which play a role in improving the compression strength of the box. Copyright © 2004 John Wiley & Sons, Ltd.

Analyzing Fabric Buckling Based on Nonlinear Bending Properties

Abstract: A fabric is a flexible material that it is highly affected by its own weight, which causes large deflections. The relationship between the bending moment and the curvature is nonlinear. This study presents a model for fabric buckling by considering the flexibility of the fabric as well as its nonlinearity in bending. The bending rigidity of the fabric is considered to be a function of its curvature to take into account the fabric's nonlinear bending properties. Based on Timoshenko's elastica theory and the Bernoulli-Euler theorem, geometric nonlinearity is also taken into account. Kawabata pure bending test results are applied to the governing equation. The values from the model. are compared with the experimental data. The results show a clear distinction from the linear model, where the nonlinear method coincides well with the experimental values. From data evaluated by the numerical analysis method, the critical buckling load is calculated.

Cyclic Bending Tests to Determine Fully Ductile Section Slenderness Limits for Cold-Formed Circular Hollow Sections

Abstract: This paper determines new section slenderness limits suitable for design and construction of seismic resisting structural systems. It describes an experimental investigation of the cyclic inelastic flexural behavior of cold-formed circular hollow section (CHS) beams. Controlled-rotation, symmetrical cyclic bending tests were performed on different sizes compact CHS with section slenderness D/t ranging from 13 to 39. With continuous cycling, the growth of ovalization caused a progressive reduction in the bending rigidity of the tube and eventually an instability occurred. The CHS beams exhibited stable hysteresis behavior up to local buckling and then showed considerable degradation in strength and ductility depending upon the D/t ratio. Seismic capacity parameters are presented, including strength, stiffness, hysteresis loops and modes of failure for each specimen. Peak moments obtained in the cyclic tests were compared with those obtained in monotonic tests published previously and also with design momen...

Flexural Stiffness of Reinforced Concrete Columns and Beams: Experimental Verification

Abstract: The current ACI code 318-02 provisions on effective stiffnesses of beams and columns have been reviewed in a companion paper, in which simple formulas are proposed to determine the effective stiffnesses of reinforced concrete columns and beams, based on an analytical parametric study. Analytical axial load-bending moment diagrams of slender columns for a given initial eccentricity (M/P ratio), obtained using the proposed stiffness assumptions, are compared in this paper with numerous published test data and are found to be in good agreement. The proposed stiffness expressions are applicable for all levels of applied loading, including both service and ultimate loads. Analytical and experimental results show that the flexural stiffness assumption in the current ACI code procedure for design of slender columns using the moment magnifier method (Eq. 10-12 and 10-18) is extremely conservative.

Nonlinear dynamic analysis of RC frames using cyclic moment-curvature relation

Abstract: Nonlinear dynamic analysis of a reinforced concrete (RC) frame under earthquake loading is performed in this paper on the basis of a hysteretic moment-curvature relation. Unlike previous analytical moment-curvature relations which take into account the flexural deformation only with the perfect-bond assumption, by introducing an equivalent flexural stiffness, the proposed relation considers the rigid-body-motion due to anchorage slip at the fixed end, which accounts for more than 50% of the total deformation. The advantage of the proposed relation, compared with both the layered section approach and the multi-component model, may be the ease of its application to a complex structure composed of many elements and on the reduction in calculation time and memory space. Describing the structural response more exactly becomes possible through the use of curved unloading and reloading branches inferred from the stress-strain relation of steel and consideration of the pinching effect caused by axial force. Finally, the applicability of the proposed model to the nonlinear dynamic analysis of RC structures is established through correlation studies between analytical and experimental results.

Torque rod structure

Abstract: An object of the invention is to increase the bending rigidity and torsional rigidity, as well as compression strength and tensile strength, of a torque rod by adding improvements to the rod portion of the torque rod. According to the invention, the torsional rigidity is improved 2 to 3 times in terms of a ratio to conventional rib shapes. The torque rod includes a pair of built-in rubber bushings formed to surround a pair of cylindrical sleeves, and a rod portion for joining the two rubber bushings. The cross section of the middle of the rod portion is quadrangular, with a pair of opposed sides of the quadrangle expanded outward. The cross section of the rod portion is hollow, honeycomb-shaped or of rib construction. In the figures, referential numerals (11, 12), (20) and (21) indicate inner sleeves, a torque rod, and a hollow portion, respectively.

The seismic shear of ductile cantilever wall systems in multistorey structures

Abstract: The distribution of seismic base shear demand among ductile flexural cantilever walls, comprising the lateral load resisting system of a multistorey building, is studied. It is shown that the base shear force demand depends on the sequence of hinge formation at the wall bases, and this in turn depends on the relative wall lengths. Hence, the routine elastic approach in which the shear forces are allocated per relative flexural rigidity or (when some consideration is given to plastic hinge formation) to moment capacity at the wall base, may appreciably underestimate the shear force demand on the walls, particularly the shorter (usually the more flexible) ones. A simple procedure yielding the results of ‘cyclic’ pushover analysis is proposed to predict the peak seismic wall forces for a given total base shear when plastification is confined to the wall base. The effects of plastic hinges developing at higher floors on (1) shear distribution among the walls and (2) the in-plane floor forces are also considered. Two numerical examples are presented to demonstrate the main points made. Copyright © 2004 John Wiley & Sons, Ltd.

Flexural Stiffness of Reinforced Concrete Columns and Beams: Experimental Verification

Abstract: The current ACI code 318-02 provisions on effective stiffnesses of beams and columns have been reviewed in a companion paper, in which simple formulas are proposed to determine the effective stiffnesses of reinforced concrete columns and beams, based on an analytical parametric study. Analytical axial load-bending moment diagrams of slender columns for a given initial eccentricity (M/P ratio), obtained using the proposed stiffness assumptions, are compared in this paper with numerous published test data and are found to be in good agreement. The proposed stiffness expressions are applicable for all levels of applied loading, including both service and ultimate loads. Analytical and experimental results show that the flexural stiffness assumption in the current ACI code procedure for design of slender columns using the moment magnifier method (Eq. 10-12 and 10-18) is extremely conservative.

Behavior of Concrete-Filled Hollow Structural Section Beam Columns to Seismic Shear Displacements

Abstract: An experimental program to study seismic resistance of concrete filled hollow structural section (HSS) columns using normal- and high-strength concrete, respectively, is described. 24 concrete filled, 203-mm steel hollow-structural section, beam-column specimens were tested under constant axial compressive load and cyclic horizontal displacement. Lines of action of the horizontal displacements were either square, normal to a conventional axis, or across a diagonal. The investigation included determination of strength capacity, ductility, and flexural stiffness of concrete filled steel tube (CFT) beam-columns for compact and slender HSS sections. All HSS CFT columns tested showed excellent hysteretic behavior. Maximum moments occurred at drifts of 2-3% and ultimate drift ratios exceeded 7%. No local buckling before yielding was observed. Moment capacities of HSS CFT columns loaded with the plane of bending across the diagonal were only slightly less than those loaded with the plane of bending parallel to a square side, reducing the need for elaborate procedures to calculate moment capacities at orientations between 0 and 45 deg.

Numerical and experimental study of auxetic closed-cell foams

Abstract: The procedures of fabrication and testing of auxetic foams with closed cells based on foaming a liquid substance and by joining microspheres are discussed. Physically , to obtain an auxetic structure, bending rigidity of elastic rods, plates and shells should strongly depend on the initial curvature. The cells of small size are found mostly to hold their original shape. Large ones show relatively low rigidity , and would get deformed similarly to thin-walled shells when compressed with a possibility of losing stability. Thus, the volumetric compression of a foamed material is mainly realized at the expense of decreased free volume of large cells. Separation of cells according to deformation levels is found to cause auxetic elastic behavior in converted closed cells foams. Technologically, to obtain this auxetics we proposed a two-stage process. It includes the formation of concave cell structure by a permanent volumetric compression of the initial material just after foaming in the solidification state under the action of a liquid or gas. High plasticity of foam materials in this stage allow s us to obtain the re-entrant structure of cells. To obtain a material with non-convex cells we used mostly a gas or liquid under pressure as a forming instrument. After cooling the foam material shows the property of elastic (reversible) deformation. I he homogeneity and isotropy of Poisson's ratio of obtained auxetics are caused by a uniform distribution of the gas or liquid pressure on the sample surface. Some problems of Poisson's ratio minimization for foam materials we have solved by the finite element analysis.

Evaluating The Effects Of Combined Freezing AndThawing And Flexural Fatigue Loading Cycles OnThe Fracture Properties Of FRC

Abstract: In cold climate regions, the life span of concrete structures can be significantly reduced if the mechanical properties of critical components of a structure are affected by the deterioration caused by simultaneous fatigue loading and freezing and thawing cycles. This makes the residual mechanical properties of the constitutive concrete material an important design consideration, after years of exposure in such a climate. The objective of the research program was to evaluate the residual mechanical properties of plain and Fiber Reinforced Concrete (FRC) (hooked-end steel, corrugated steel, and polyolefin fibers) exposed to several combinations of freezing and thawing cycles and flexural fatigue loading cycles. The residual mechanical properties (flexural strength, flexural stiffness, and flexural toughness) and the flexural fatigue resistance of the conditioned plain and FRC specimens were compared to the properties of unconditioned companion specimens to quantify the level of damage caused by each conditioning combination and to determine whether the addition of fibers could reduce the level of damage caused by conditioning. In general, the results indicated that the flexural strength, stiffness, and toughness of plain concrete and both steel and polyolefin fiber reinforced concrete, after exposure to a combination of 300 freezing and thawing cycles followed by 2 million cycles of flexural fatigue loading, 10-40% or 10-45% of the 90-day flexural strength, is greater than or approximately equal to the lowest residual flexural strength, stiffness, and toughness of specimens exposed to 300 freezing and thawing cycles or 2 million flexural fatigue loading cycles (between the same stress range). Interestingly, for all specimens, the residual flexural strength, after flexural fatigue loading at a stress range between 10-45% of the 90-day flexural strength value, was higher than specimens exposed to a stress range between 10-40% of the 90-day flexural strength. The applications of freezing and thawing cycles on all specimens (plain concrete and FRC) prior to flexural fatigue loading cycles resulted in higher flexural fatigue endurance limit than unconditioned specimens. D. P. Forgeron & J.-F. Trottier High Performance Structures and Materials II, C.A. Brebbia & W.P. De Wilde (Editors) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-717-5

Planar display panel

Abstract: PROBLEM TO BE SOLVED: To provide a planar display panel which can be bent, wherein a display part is prevented from being destroyed or deteriorated when the panel is bent. SOLUTION: The planar display panel 10 has the display part 11 and a non-display part 12 positioned separately within the display face, wherein a bending preventive layer 14 having the longitudinal elastic constant higher than that of the other material constituting the display part 11 is formed or the like at the display part 11, thereby the bending rigidity of the display part 11 is set higher than the bending rigidity of the non-display part 12. COPYRIGHT: (C)2006,JPO&NCIPI

Effective flexural stiffness for linear seismic analysis of concrete walls

Abstract: A trilinear bending moment – curvature model is used to develop a general method for determining the effective flexural stiffness of concrete walls for use in linear seismic analysis. The method ac...

Torsion beam type suspension structure

Abstract: PROBLEM TO BE SOLVED: To provide a torsion beam type suspension structure exerting excellent absorbing performance relative to torsion torque without degrading flexural rigidity of a torsion beam. SOLUTION: This torsion beam type suspension structure comprises left and right trailing arms 1 oscillatingly supported on a vehicle body at one end while rotatably supporting a wheel at the other end, and the torsion beam 4 connecting the left and right trailing arms 1, 1. The torsion beam 4 is inserted in through-holes 5a, 5b formed in the trailing arm 1, and is fitted in the through-hole 5a on the outer side in the vehicle width direction of the trailing arm 1. Moreover, the trailing arm and the torsion beam are fixed around there by welding 6, and the torsion beam 4 is contacted and engaged with the through hole 5b on the inner side in the vehicle width direction from this fixing section. Thus, a torsion deformation amount is increased without degrading the flexural rigidity of the torsion beam 4. COPYRIGHT: (C)2005,JPO&NCIPI