Showing papers on "Flexural rigidity published in 1972"

Reinforced concrete members with cyclic loading

Abstract: Theoretical moment-curvature relationships for reinforced concrete members with cyclic loading are derived using stress-strain curves for steel and concrete. The theoretical curves compare well with test results and illustrate the variation in flexural stiffness due to the Bauschinger effect of the steel and to the presence of open cracks in the compression zone of the concrete which may eventually close. These cracks mean that for large portions of the moment-curvature curves after the first yield excursion the moment of resistance is provided by a steel couple alone. During this part of the cyclic loading the main role of the concrete is to prevent buckling of the steel. For beams with a marked difference between the top and bottom steel areas and for columns the moment-curvature loops show a pinching in effect and the loop area is significantly smaller than that of the commonly used elastoplastic idealization.

The Deformations and Stresses in Floating Ice Plates

Abstract: In the past, the analyses of floating ice plates subjected to static or dynamic loads were based on the theory of a thin homogeneous plate, although in actual floating ice plates Young's modulus may vary strongly with depth. Recently,A. Assur concluded, on the basis of a heuristic argument, that the solutions obtained for homogeneous plates may be used for floating ice plates, if a modified flexural rigidity is used. The purpose of the present paper is to study this question, by establishing a mathematically consistent formulation for the dynamic plate equation, utilizing Hamilton's Principle in conjunction with the three dimensional theory of elasticity. It is proven that for a variable Young's modulus and a constant Poisson's ratio the resulting formulations for plates and beams are the same as those for the corresponding homogeneous problems, if a modified flexural ridigity is used; thus confirmingAssur's conclusion. It is shown that the stress distribution is not linear and that the stress formula\(\sigma _{\max } = M{{z_0 } \mathord{\left/ {\vphantom {{z_0 } I}} \right. \kern- ulldelimiterspace} I}\) used by a number of investigators for the determination of the carrying capacity of a floating ice plate, as well as for the computation of failure stresses from tests on floating ice beams, is not applicable. Correct formulas are derived, corresponding stress distributions are presented and the consequences of the findings discussed.

Flexural rigidity and elastic constant of cilia.

Abstract: 1. The flexural rigidity of the large abfrontal cilia of Mytilus has been measured with a flexible glass micro-needle. 2. The same cilium has similar values to the flexural rigidity irrespective of the phases of beat cycle (including the recovery phase) and of the direction of force applied. 3. The values of 3-13 x 10-9 dyne. cm2 have been obtained for the flexural rigidity of compound cilia of various sizes; 2-3 x 10-10 dyne.cm2 for that of the component cilia. 4. The Young9s modulus of the microtubule is estimated to be 5-9 x 1010 dyne/cm2 on the basis that the outer doublet microtubules are tightly connected with one another.

27—the bending and creasing of multicomponent viscoelastic fibre assemblies. part i: general consideration of the problem

Abstract: The problems involved in making a mechanical analysis of bending deformations in textile fabrics are discussed. It is suggested that progress can be made by making simplifying assumptions concerning the geometry of fabric structure and deformation and using energy considerations to calculate forces and moments. Certain simple examples are given of the usefulness of this approach. A foundation is laid for the construction of a computer model that will, it is hoped, simulate the viscoelastic bending and creasing behaviour of textile fabrics from a knowledge of the bending and torsional viscoelastic properties of the constituent fibre(s) and their relative geometrical arrangement.

Lateral vibration and stability relationship of elastically restrained circular plates.

Abstract: = radius of the plate = £/i/[12(l — v)], flexural rigidity of the plate = Young's modulus of material = thickness of plate = rotational spring constant = radial load per unit length of circumference = buckling load per unit length of circumference = [_ppha/D']' characteristic value of frequency = characteristic value of frequency without radial load = deflection of plate = polar coordinates = nondimensional coordinate defined by r/a = mass density of plate material = frequency of oscillation, rad/sec = Poisson's ratio = nondimensional boundary restraint factor defined by ka/D = nondimensional radial load defined by Ra/D

On the Rigidity of the α-Helix as Measured by Dielectric Studies

Abstract: The persistence length and flexural rigidity of the α-helix of poly(γ-benzyl-L-glutamate) have been found to be 1000±100A and 4±04×10−19 dyn/cm2, respectively, from a dielectric study in m-cresol Since the electric dipole moment of the α-helix is expected to be proportional to the end-to-end distance, flexural rigidity can be estimated in the theoretical framework of the stiff-chain model The effect of side-chain moment is also discussed

An instrument for measuring rheological properties by bending. Application to food materials of plant origin.

Abstract: A new instrument, the MITEX MK II Bending Tester, is described as a means of measuring the following rheological properties of solid foods: bending moment, curvature, bending rigidity, modulus of elasticity, curvature set and bending moment loss. Equations applicable to bending and results of measurements on samples of celery, carrot, apple and potato are presented. Changes of the modulus of elasticity in relation to the time of exposure of sample strips to the ambient atmosphere, and graphical and mathematical treatment of the data for estimating a total ‘adjusted time’ (age) of a particular sample are discussed.

Bending Rigidity of an Inflated Circular Cylindrical Membrane of Rubbery Materials

Abstract: A system of linear constitutive equations is presented for a class of deformation of membranes of rubbery materials characterized by smallness of strains and superimposed upon a known state of finite deformation. The equations are applied to an inflated circular cylindrical membrane subjected to pure bending. In the analysis, the wrinkling of the membrane is taken into account. The numerical results indicate that the bending rigidity of the inflated circular cylindrical membrane increases as the internal pressure increases, and that it is preserved substantially even after the wrinkling occurs if a relatively high internal pressure is applied.

Moment-rotation relation between column and slab

Abstract: A METHOD IS PRESENTED FOR OBTAINING LIMITS TO THE ROTATIONAL STIFFNESS OF FLAT FLOOR PLATES AT A COLUMN-- SLAB JUNCTION. THE METHOD IS BASED ON THE ELASTIC THEORY OF ISOTROPIC THIN PLATES AND ACCOUNTS FOR THE COLUMN CROSS SECTIONAL CONFIGURATION AT THE COLUMN-- SLAB INTERFACE, AS WELL AS THE FLOOR PLATE'S BOUNDARY CONDITIONS. THE FLEXURAL STIFFNESS OF THE SLAB AT A COLUMN--SLAB JUNCTION IS REPRESENTED BY A MOMENT- ROTATION COEFFICIENT AS USED IN BEAM AND FRAME ANALYSIS. MOMENT-ROTATION COEFFICIENTS FOR SEVERAL CASES OF SQUARE PLATES ON CENTRAL SQUARE COLUMNS ARE EVALUATED. THE DISTRIBUTION OF MOMENT IN THE SLAB DUE TO AN APPLIED MOMENT AT THE COLUMN--SLAB JUNCTION IS STUDIED. A NUMERICAL EXAMPLE IS INCLUDED TO SHOW THE APPLICATION OF THE PROPOSED METHOD. /AUTHOR/

Flexural stiffness properties of asphalt concrete at low temperatures with discussion

Abstract: THE MODULUS OF RUPTURE AND MODULUS OF ELASTICITY OF A PAVING MIXTURE CHANGE CONSIDERABLY WITH DIFFERING GRADES AND TEMPERATURE SUSCEPTIBILITY OF THE ASPHALTS USED IN THE MIX. THE MODULUS OF RUPTURE IS A MEASURE OF THE TENSILE STRENGTH OF THE MIXTURE AND THE MODULUS OF ELASTICITY IN FLEXURE IS A MEASURE OF THE STIFFNESS. THE GREATER THE STIFFNESS MODULUS, THE GREATER THE THERMAL STRESS DEVELOPED IN THE PAVEMENT BY TEMPERATURE CHANGE. THE MIXTURE SHOULD BE DESIGNED AND AN ASPHALT GRADE SELECTED TO HAVE A HIGH MODULUS OF RUPTURE TO INSURE ADEQUATE TENSILE STRENGTH, BUT A LOW STIFFNESS MODULUS SO THAT THE MIXTURE WILL BE PLIABLE RATHER THAN STIFF AND BRITTLE. TO DETERMIINE THE EFFECT OF ASPHALT CEMENT VISCOSITY ON THE STIFFNESS OF MIXTURES AT LOW TEMPERATURES, BEAMS WERE FABRICATED FROM ASPHALT CEMENTS OF THREE DIFFERENT PENETRATION GRADES AND WERE DESIGNATED AS 40/50, 85/100, AND 200/300. THE RHEOLOGICAL PROPERTIES FOR EACH ASPHALT CEMENT WERE DETERMINED. THE ASPHALT PAVING MIXTURE BEAMS WERE ALSO TESTED IN FLEXURE AT MINUS 35 F, MINUS 5F, AND PLUS 25 F, TO DETERMINE HOW THE STIFFNESS MODULUS AND MODULUS OF RUPTURE VARIED WITH ASPHALT CONSISTENCY AND TEMPERATURE. RESULTS OF THE FLEXURE TESTS ARE RECORDED IN TABULAR FORM. REGRESSION ANALYSIS WAS APPLIED TO DEVELOP A MATHEMATICAL MODEL OF THE RELATIONSHIP BETWEEN STIFFNESS, TEMPERATURE, AND ASPHALT VISCOSITY. THE FOLLOWING CONCLUSION ARE REACHED: THE FLEXURAL STIFFNESS AND MODULUS OF RUPTURE AT LOW TEMPERATURE APPEAR TO BE SUITABLE CONTROL TESTS FOR USE IN DESIGNING ASPHALT PAVING MIXTURES AND SHOULD BE USED AS DESIGN CRITERIA. A DESIGN LIMIT OF 250,000 PSI FOR FLEXURAL STIFFNESS SHOULD BECOME PART OF THE MIX DESIGN PROCEDURE. THE MINIMUM TEMPERATURE FOR A PROPOSED MIX CAN BE DETERMINED AND COMPARED WITH EXPECTED FIELD TEMPERATURES. ALONG WITH THIS, A MINIMUM OF 800 PSI AT MINUS 5 F FOR THE MODULUS OF RUPTURE SHOULD BE PART OF MIX DESIGN PROCEDURE TO INSURE ADEQUATE TENSILE STRENGTH TO RESIST CRACKING. THE ASPHALT CEMENT WITH THE LOWEST VISCOSITY THAT CAN MEET HIGH TEMPERATURE STABILITY REQUIREMENTS SHOULD BE USED. IF HIGH TEMPERATURE STABILITY REQUIREMENTS CANNOT BE MET, A LESS DESIRABLE ASPHALT WILL HAVE TO BE CHOSEN AND SOME CRACKING EXPECTED. AS AN EXAMPLE, THE TYPICAL MIDCONTINENT 85/100 ASPHALT HAS A MINIMUM DESIGN TEMPERATURE OF MINUS 17 F. TO REACH MINUS 20 F WITHOUT CRACKING REQUIRES A 115 PENETRATION ASPHALT. A DISCUSSION IS INCLUDED WHICH DEALS WITH VARIOUS QUESTIONS CONCERNING THIS STUDY.

31—the handle and bending behaviour of fabric laminates

Abstract: Certain aspects of the handle of fabric laminates are related to properties of the component fabrics. Particular attention is paid to a theoretical prediction of the bending stiffness of a laminate from the bending and tensile properties of its components. This theoretical stiffness is a minimum value; if, in practice, the observed stiffness is much greater than this, it may generally be assumed that excess of adhesive or of melted foam is the cause. The paper also reports work on other features of the bending behaviour, such as the degree of recovery from bending, and on the shearing behaviour. The work is concluded by a brief study of some faulty laminates.

Analysis of bending stiffness variation at cracks in continuous pavements

Abstract: DISCONTINUITIES EXERT SIGNIFICANT INFLUENCE ON THE BENDING RIGIDITY OF STRUCTURAL MEMBERS. THE EFFECT OF TRANSVERSE CRACKS ON THE BEHAVIOR OF CONTINUOUSLY REINFORCED CONCRETE PAVEMENTS IS STUDIED, AND THE RESULTS SHOW THAT THE PERCENT REDUCTION IN BENDING STIFFNESS AT CRACK LOCATIONS RANGES BETWEEN 80 AND 90 PERCENT OF THE ORIGINAL UNCRACKED VALUE. BY SIMULATING THIS EFFECT ON THE DISCRETE-ELEMENT MODEL, A SENSITIVITY STUDY WAS PERFORMED ON THE PARAMETERS CONSIDERED IN THE DESIGN OF CONTINUOUSLY REINFORCED CONCRETE PAVEMENTS. THESE COVERED THE PRACTICAL RANGE OF EACH OF THE FOLLOWING VARIABLES: SLAB BENDING STIFFNESS, MODULUS OF SUBGRADE REACTION, AND CRACK SPACING. FROM THE ANALYSIS OF VARIANCE, THE MOST SIGNIFICANT VARIABLES, WHICH EXPLAINED AROUND 90 PERCENT OF THE VARIATION IN DEFLECTION AND PRINCIPAL MOMENT (STRESS) RESPONSES, WERE SLAB BENDING STIFFNESS AND MODULUS OF SUBGRADE REACTION. CRACK SPACING SHOWED A MINOR EFFECT ON SLAB BEHAVIOR. THE ORTHOGONAL POLYNOMIAL BREAKDOWN INDICATED THAT IN A LOGARITHMIC MODEL, THE LINEAR EFFECT OF BOTH SUBGRADE MODULUS AND SLAB BENDING STIFFNESS IS HIGHLY SIGNIFICANT. FURTHERMORE, INTERACTIONS BETWEEN THESE TWO DESIGN VARIABLES DO OCCUR, INDICATING THAT VARIATIONS IN DEFLECTIONS AND PRINCIPAL MOMENTS ARE NOT DEFINED BY THE MAIN EFFECT OF DESIGN VARIABLES ALONE. THE INFLUENCE OF THE WIDTH OF THE CRACK ON THE BEHAVIOR AND PERFORMANCE OF CONTINUOUSLY REINFORCED CONCRETE PAVEMENTS IS HIGHLY SIGNIFICANT. SLAB DEFLECTIONS INCREASE DRASTICALLY AS CRACK WIDTH INCREASES, WHILE NO SIGNIFICANT CHANGE IN PRINCIPAL MOMENTS IS ENCOUNTERED. /AUTHOR/

Stiffness of Reinforced Concrete Plates

Abstract: A general formulation for the in-plane and flexural stiffnesses of isotropically and nonisotropically reinforced concrete plates is presented. The stiffness of plates is related quantitatively to the relative orientation of the reinforcement with respect to the applied forces, the combination of the applied forces and the amounts of reinforcement in the two orthogonal directions. By rotating the reinforcement from 0° to 45° with respect to the axes of the applied forces the in-plane or flexural stiffness may be decreased to one-half or less. The investigation did not support conventional theories to calculate flexural stiffness such as those in the 1971 ACI Building Code. In general, the ACI Code Equations considerably overestimate flexural stiffness. Results of this investigation can be used to calculate bending moments, deflections and effectiveness of reinforcing bars in cracked concrete sections.

Flexural behavior of reinforced-concrete sandwich composites

Abstract: An experimental investigation was carried out to examine the flexural behavior of rectangular sandwich composites and to determine appropriate structural applications for such constructions. The sandwich cores were composed of nonpermeated, expanded aluminum honeycomb and the facings consisted of concrete mortar. Appropriate theories that predict the behavior of such composites were presented and compared to experimental data. All specimens had facing thicknesses of 1 in., core thicknesses of 1 in., 2 in. and 3 in.; core-cell size of 1/8 in. and 3/8 in.; while four different core foil gages were considered for each cell size. The lower facing was either plain concrete mortar or reinforced with steel wires. The large cell-size specimen displayed better bond characteristics and produced better and more stable experimental data. Reasonable agreement was found between the observed and computed flexural stresses. The deflections at midspan were in good agreement with the theoretically predicted deflections in all of the specimens, with or without reinforcement. Regardless of cell size, density, core thickness or reinforcement, the observed midspan and quarterspan deflections of the top facing were approximately twice the deflections at the corresponding locations on the lower facing. The ultimate loads increased as the core thickness and the core density increased. The influence of flexural rigidity of the core can be neglected.

Effect of cracks on bending stiffness in continuous pavements

Abstract: TRANSVERSE CONTRACTION JOINTS IN RIGID PAVEMENTS WERE LONG CONSIDERED ESSENTIAL TO PREVENTING PAVEMENT DAMAGE FROM VOLUME-CHANGE STRESSES. CONTINOUSLY REINFORCED CONCRETE PAVEMENT HANDLES THESE STRESSES IN ANOTHER WAY. IT ALLOWS THE PAVEMENT TO DEVELOP A REGULAR PATTERN OF VERY FINE RANDOM CRACKS. IN PREVIOUS ANALYSIS OF SUCH PAVEMENTS, IT HAS BEEN EXTREMELY DIFFICULT TO EVALUATE THE EFFECT OF CRACKS ON THE LOAD CARRYING CAPACITY AND SUBSEQUENT PERFORMANCE OF THE SLAB. THIS PAPER PRESENTS AN ANALYTICAL LOOK AT THE PROBLEM OF TRANSVERSE CRACKING IN CONTINUOUSLY REINFORCED CONCRETE PAVEMENTS. THE INFLUENCE OF THESE CRACKS ON THE LONGITUDINAL BENDING RIGIDITY WAS STUDIED BY USING BASIC MOMENT-CURVATURE RELATIONS. A RELATION WAS DEVELOPED THAT EXPRESSES THE AVERAGE MOMENT OF INERTIA DUE TO THE EFFECT OF THE CRACK AS A FUNCTION OF MATERIAL PROPERTIES AND SLAB GEOMETRIC CHARACTERISTICS. RESULTS SHOWED THAT A SIGNIFICANT DROP OF 80 TO 90 PERCENT IN THE BENDING RIGIDITY IS ENCOUNTERED AT CRACK LOCATIONS. FURTHERMORE, THE DEVELOPMENT LENGTH BOND IDEA WAS USED TO SPECIFY THE SLAB PORTION AFFECTED BY THE DISCONTINUITY. A PROCEDURE TO SIMULATE THIS EFFECT BY USING THE DISCRETE-ELEMENT METHOD OF SLAB ANALYSIS IS OUTLINED. THE PROCEDURE IS GENERAL AND SIMPLE TO USE.