Showing papers on "Timoshenko beam theory published in 1968"

Beam Shear Strength Prediction by Analysis of Existing Data

Abstract: AN EMPIRICAL METHOD WHICH COMBINES THE TECHNIQUES OF DIMENSIONAL ANALYSIS AND STATISTICAL REGRESSION ANALYSIS IS APPLIED TO EXISTING SOURCES OF REINFORCED CONCRETE BEAM SHEAR TEST DATA. FOR BEAMS WITH A/D ABOVE 2.5, THE METHOD HAS PRODUCED FAILURE STRESS PREDICTION EQUATIONS WHICH ARE GIVEN FOR BOTH CRACKING AND SUDDEN DIAGONAL TENSION SHEAR. THESE EQUATIONS HAVE A LOW PERCENTAGE OF PREDICTION ERROR FOR A WIDE RANGE OF BEAM PROPERTIES AND TEST SOURCES. THE HIGH, BUT VARIABLE, SHEAR FAILURE STRESS OF SHORT BEAMS HAS A LOWER BOUND GIVEN BY THE SLENDER BEAM PREDICTION EQUATIONS. FURTHER, SHORT LATERAL STUB BEAMS, WITHOUT TOP AND BOTTOM LOAD AND SUPPORT BLOCK PRESSURES, APPEAR TO HAVE SLENDER BEAM BEHAVIOUR. /AUTHOR/

On the Accuracy of Timoshenko's Beam Theory

Abstract: The deflection and rotation which appear in Timoshenko's beam theory may be defined either (a) in terms of the deflection and rotation of the centroidal element of a cross-section or (b) in terms of average values over the cross-section. By consideration of an example for which a theoretically exact solution is available it is shown that the Timoshenko equations may be much more accurate if the latter definition is adopted. The example considered is the vibration of a simply-supported beam of narrow rectangular cross-section. The accuracy of the Timoshenko theory depends on the slenderness ratio of the beam, but even when the depth of the beam is equal to the length the Timoshenko theory differs from the exact solution by less than 3.5% provided definition (b) is adopted. Far larger errors occur if definition (a) is used, the most serious error being associated not with shear deformation but with the moment-curvature relation.

Steady State Vibration of Damped Timoshenko Beams

Abstract: A method for the analysis of the steady state vibration of damped Timoshenko beams is presented. The usual four differential equations of the Timoshenko Theory are increased to eight differential equations with the addition of damping in the form of complex modulii. These equations are solved by numerical integration and, therefore, no restrictions need be placed on the longitudinal variation of the beam cross-section or the forcing function. The solution gives the beam response at all values of the forcing frequency and polar-plots are used for the determination of the resonant frequencies. To illustrate the wide applicability of the method the behavior of three beams, typical of those encountered in practice, is studied. The results of these examples show the importance of considering shear deformation when determining resonant frequencies and the great effect that the damping coefficient has on the magnitude of the response at resonance.

Buckling of Naturally Curved and Twisted Beams

Abstract: A set of linear differential and boundary equations are derived, consistent with classical beam theory, to assist in the static buckling analysis of arbitrarily curved and loaded thin rods. Methods for accommodating different external load behaviors during buckling deformations are examined. Several examples from well-known linear buckling theories are treated, and a general numerical solution scheme for computer application is presented.

The effect of ship stiffness upon the structural response of a cargo ship to an impulsive load

Abstract: : The purpose of the study is to set up a computer program to investigate the dynamic effects resulting from an impulsive loading on a ship and to determine how these effects tend to vary with the stiffness of the hull girder. The hull is treated as a Timoshenko beam and the solution is obtained by finite difference technique. Two codes are written: an implicit one, which is more efficient for short durations, and an implicit one, which is superior for long durations of impulse. Application is made to a dry cargo ship. Limited analysis of her response to a unit impulse indicates that, in general, reduced hull rigidity tends to be beneficial. (Author)

Creep of a cracked reinforced beam.

Abstract: Conventional cracked reinforced concrete beam theory is extended to include general linear viscoelastic behavior of the matrix (concrete) material in compression. An analytical formulation is developed which leads to a single governing equation on the position of the neutral axis. Although it has not been possible to obtain a general closed solution, some important properties of the solution of this nonlinear, Volterra-type integral equation are established. The relationship of this theory to a popular approximate procedure, known as the effective modulus method, is discussed. The nonlinear integral equation is resolved numerically, and results are shown for several cases of interest.

Experimental Study of Nonprismatic Folded Plates

Abstract: An experimental study was conducted on two aluminum nonprismatic folded plate structural models. The stresses, moments, and deflections predicted by a theory for the analysis of long nonprismatic folded plate structures, which is an extension of ordinary folded plate theory, are compared to the experimental results obtained from the model study. Model 1 is made of eight triangular plates with a span to maximum depth ratio of about three. Model 2 is made of eight trapezoidal plates with a span to maximum depth ratio of about four. The predictions by the theory are shown to be in good agreement with the experimental results for both models. It is also shown that elementary beam theory is inaccurate in predicting the behavior of interior plate elements in regions where large differences exist between the depths of adjacent plates.

The response of beam and slab bridges to moving forces

Abstract: THE DYNAMIC RESPONSE OF A HIGHWAY BRIDGE UNDER MOVING LOADS IS USUALLY STUDIED BY TREATING THE BRIDGE AS A BEAM SUCH A TREATMENT WOULD BE SATISFACTORY IF THE SPAN/WIDTH RATIO OF THE BRIDGE IS LARGE HOWEVER, A MAJORITY OF HIGHWAY BRIDGES MAY HAVE SPANS COMPARABLE TO THE WIDTHS FOR SUCH BRIDGES, THE BEAM THEORY IS NOT ADEQUATE AND A SUITABLE TWO- DIMENSIONAL THEORY WILL HAVE TO BE ADOPTED TO CONSIDER THE INFLUENCE OF THE TRANSVERSE FLEXIBILITY OF THE BRIDGE ON ITS RESPONSE IN THIS PAPER THE DYNAMIC RESPONSE OF SIMPLE-SPAN BEAM AND SLAB HIGHWAY BRIDGES SUBJECTED TO A MOVING CONCENTRATED FORCE IS STUDIED THE HIGHWAY BRIDGE IS TREATED AS AN ORTHOTROPIC PLATE, AND THE NORMAL MODE METHOD IS USED IN THE RESPONSE ANALYSIS NUMERICAL RESULTS ARE PRESENTED FOR TYPICAL CASES IN THE FORM OF AMPLIFICATION SPECTRA AND HISTORY CURVES /AUTHOR/

Static tests of reinforced concrete beams: development of iterative analysis procedure and tests of beams reinforced with steel, aluminum, and fiber glass, with and without helical compressive reinforcement

Abstract: A GENERAL ITERATION ANALYSIS PROCEDURE IS OUTLINED FOR ESTIMATING THE FLEXURAL STRENGTH, THE MOMENT ROTATION, AND THE LOAD-DEFLECTION CHARACTERISTICS OF REINFORCED CONCRETE MEMBERS WITH ARBITRARY CROSS SECTION AND ARBITRARY REINFORCEMENT (BUT SYMMETRICAL ABOUT THE PLANE CONTAINING THE APPLIED LOADS). THE METHOD IS BASED ON THE TRADITIONAL ASSUMPTIONS MADE IN ELEMENTARY BEAM THEORY AND ON THE ACTUAL STRESS-STRAIN RELATIONS OF THE REINFORCEMENT AND CONCRETE AS DETERMINED IN STANDARD TESTS BUT DOES NOT SPECIFY COMPRESSIVE STRAIN FOR CONCRETE. RESULTS OF TESTS ON 11 SIMPLY SUPPORTED BEAMS OF 6-FT SPAN REINFORCED WITH SINGLE OR MULTIPLE LAYERS OF HIGH-STRENGTH STEEL, ALUMINUM, AND FIBER-GLASS RODS, BOTH WITH AND WITHOUT HELICAL CONFINING REINFORCEMENT IN THE COMPRESSION ZONE, ARE DESCRIBED AND COMPARED WITH ANALYTICAL RESULTS. AGREEMENT OF THEORY AND EXPERIMENT WAS CONSIDERED SATISFACTORY IN THE MAJORITY OF TESTS. /AUTHOR/

A cylindrically orthotropic elastic thick ring.

Abstract: : A Fourier series analysis is presented for the static problem of a plane elastic, cylindrically orthotropic, thick ring subjected to two equal and opposite forces applied to its outer surface at opposite ends of a diameter. Using this solution, it is possible to compute the response in regions not near the points of application of the loads. It is shown that technical beam theory becomes very inaccurate as the material becomes more and more orthotropic. (Author)

The dynamics of a beam of changing cross section

Abstract: : An investigation has been carried out to determine the response of a cantilever beam having a time-varying cross section, to a prescribed harmonic displacement at its support. The assumption of classical beam theory leads to a set of ordinary differential equations of the Mathieu type. A general solution to these non-homogeneous equations is developed and programmed for the IBM 7040 digital computer. The strong dependence of the lateral motion to the frequency of the support displacement and to the frequency of the changing cross section is investigated for a wide range of ratios of these frequencies. (Author)