Saint-Venant Theory Research Articles

Thin curvilinear beams of minimum weight

The problem of minimizing the weight of thin curvilinear beams whose state of stress is described by the Saint-Venant theory, is considered. The elastic state of the beam is analyzed and the influence of the shape of the cross-section on the state of stress studied. It is assumed that every point of the beam must satisfy some condition of the strength of material. Solutions of concrete problems are given for beams of varying configuration. Problems of minimum weight of beams and bars described by the equations of the elementary theory of bending, were discussed in /1–3/.

On transient creep bounds for Saint-Venant pure bending problems

The field equations governing primary and secondary creep, with the inclusion of elastic strains, in the Saint-Venant theory of pure bending are reduced to a single equation in the tensile stress. It is shown how, from this equation, the limiting or steady-state stresses can be obtained. This equation is then used to derive inequalities which describe the shape of the stress profile at all times, and from which bounds on stresses and displacements are easily obtained. The inequalities, which are similar to those of[1], are established using new arguments which greatly simplify the analysis for the case of primary creep.

Upper and lower bounds for the shear stress in the Saint-Venant theory of flexure

Upper and lower bounds are derived for the shear stress as it is determined by Saint-Venant's theory of flexure, and used to establish the asymptotic character of the classical Strength of Materials formula in the limit of vanishing thickness.

Torsion of Bars with Polygonal Cross-Sections

The term Polygonal Cross-Section is given for a non-circular but continuosly curved cross-section. This profile is produced by the lathe tool which is reciprocated laterally, and synchronized with the revolution of main spindle. And the standard type of the profile is produced by the simple harmonic motion of the tool. We can use a pair of polygonal shaft and boss for the power transmission coupling. First of all, in this report, we touch on the theoretical analysis of the torsion of the bars with this profile. The shear stress, twisting moment and twist angle in the torsion of this bar are calculated approximately on the basis of Saint Venant theory. Next, some results of experiment are presented. It is shown that the analytical results agree satisfactorily with the experimental ones and can be used as the design formula.

Vibrations and Stability of Plates Under Initial Stress

Equilibrium of plates, under initial stresses uniformly distributed across plate thickness; equations derived by B.de SAINT-VENANT by considering isolated plate element; paper presents generalization of Saint-Venant theory and establishes more inclusive theory of plates under initial stress, analogous to R.D.MINDLIN plate theory, by retaining in equations of motion effects of transverse shear deformation and rotatory inertia.

Note on Torsion With Variable Twist

Abstract In a recent paper (1) the author considered anew the problem of determining corrections to the Saint Venant theory of torsion, induced by restraint against warping at the end section of the beam. The present note is intended to furnish some further discussion of these earlier results.

Influence of Secondary Inertia Terms on Natural Frequencies of Rotating Beams

Abstract The equations of small motion of a straight cantilever beam attached to the rim of a rotating disk are determined assuming the Bernoulli-Euler theory of bending and the Saint Venant theory of torsion are valid, the mass and elastic axes coinciding and retaining all inertia terms. Influence of the secondary inertia terms on the fundamental torsional and lateral frequencies is then examined at two angular settings for a uniform beam having a length to disk-radius ratio in the range usually encountered in gas-turbine buckets and axial-flow compressor blades.

The flexure and torsion of aeolotropic beams

Many writers have studied special cases of the Saint-Venant torsion and flexure problem for an isotropic beam of constant cross-section. An excellent summary of this work has been given by Stevenson (4) who also greatly extended the field of application of the theory by showing that the general Saint-Venant problem can be reduced to the solution of boundary problems involving six simple ‘canonical’ flexure functions. Miss Rosa Morris (2, 3) has applied the Saint-Venant theory, as extended by Stevenson, to the solution of the flexure and torsion problem for beams possessing two fairly general types of cross-section, her results including many previous solutions as special cases.

A Theorem on the Shearing Stress in Beams with Applications to Multicellular Sections

The methods in use for the calculation of the flexural shearing stress in wing beams of multicellular section are rigorously examined by means of the Saint-Venant theory of flexure and torsion. I t is shown that the line integral of the shearing stress around a cell does not, in general, vanish as has been supposed. I ts value is found in a simple form. The effect on the magnitude of the shearing stress is calculated for several examples and found small for certain one-, two-, and three-cell sections. Solutions of the flexural shear stress problem are given for rectangular cell sections of one, two, three, and any number of equal cells, with flange areas.

On the Shearing Stress in the Structure of a Ship when Inclined

When a ship is inclined to the upright, the shearing stress in the ship's structure cannot be found at once. The shearing force should be resolved into two components parallel to the principal axes of the cross-section. The shearing stress at any point on the cross-section can then be found by taking the algebraic sum of the effects produced by the component shearing forces. One of the components acts on the ship as when she is upright, and the other as when inclined to 90°. The shearing stress at the up rightcondition can be found by the usual method, but, when inclined to 90°, the cross-section of the ship is not symmetrical about the principal axis parallel to the component shearing force, and we are not accustomed to compute the shearing stress on such section. In this paper, the distributions of the shearing stress on some simple cross-sections of vessels when inclined to 90° are found from the approximate theory of thin sections deduced from Saint-Venant's theory of flexure. Observing these results some reasonable assumptions are made for computing the shearing stress on the more complicated cross-section as a ship's section when she is inclined to 90°. Thus the distribution of shearing stress on the cross-section of a ship when inclined is found.The result of the calculation on an ordinary two decked steamer shows that, when the angle of inclination is 30° to 45°, the shearing stresses at the side of deck plating and inner bottom plating are more than 10% greater than those when upright, and, when inclined, though the neutral axis passes through bilge plating, the shearing stress at this part is not much greater than that when upright. It is also observed that, at the centre of deck plating, bottom plating, and inner bottom plating, the shearing stresses are nearly equal to those at the sides, but, as these are only for the angle of inclination near 90°, an actual ship will not be subjected to such stresses. Therefore, roughly speaking, for ordinary merchant ships, the calculations of shearing stresses when inclined are not necessary if they are made for the upright condition. However, the method of calculation suggested in this paper may be helpful when computing the shearing stress in some cases dealing with ships of special type.