Local Bending Moment Research Articles

Bending Moment Distribution along Swimming Fish

A dynamic analysts of body undulation was carried out for the saithe and an assumed eel-like swimmer. It was found that the three-dimensional unsteady waving plate theory results in a better momentum balance than the slender body theory. For subcarangiform swimmers the recoil effect requires that the envelope of the waving motion increases non-linearly close to an exponential function starting from a non-zero value at the head. The local bending moments necessary to produce such a movement pattern appear almost simultaneously (standing wave) within the middle segment. Within the following caudal segment the bending moment travels backward with a phase-velocity close to that of the undulatory wave. For both the eel and the saithe bending moments display a rostrally running wave within the rostral body segment. The phase coupling between moment and bending moments roughly agrees with the one observed between movement and muscle activity. Owing to the influence of hydrodynamic forces a phase shift between muscle activity and movement is necessary for both subcarangiform and anguilliform swimmers.

Combined Boundary Element/Finite Strip Analysis of Bridges

In the present study, the boundary element method is employed to analyze the top slabs of rectangular or skewed composite slab‐on‐girder and box‐girder bridges, while the finite strip method is used to analyze the girders. The boundary elements and the finite strips are connected by transition strips. One side of the transition strip coincides with the nodal line of the adjacent finite strip and has the same degrees of freedom; while on the opposite side, a number of nodes coincides with the nodes of the neighboring boundary elements. Within the transition strip the displacements are expressed in terms of the degrees of freedom of the finite strip nodal line and the boundary element nodes by their corresponding shape functions. In this way, a fully compatible connection between slab and girders is achieved. This combined analysis is very effective in calculating the local bending moments due to moving vehicle wheel loads.

Structural modeling of composite beams with induced-strain actuators

This paper presents an analytical-experimental investigation on structural modeling of coupled composite beams with distributed induced-strain actuators. Analysis based on Vlasov theory is developed to include distributed piezoelectric actuators, either surface mounted or embedded. Salient features of composite open-section beam analysis, like constrained warping and transverse shear deformation, were included. Induced-strain actuation was introduced in the constitutive relations of plate segment of the open-section composite beams. To evaluate the analytical predictions, several bending-torsion and extension-torsion coupled graphite-epoxy solid beams were fabricated using an autoclave molding technique. These were surface mounted with piezoelectric actuators. The actuators were excited to produce local bending moment and axial force on the beam, and the structural response was measured in terms of bending slope, induced twist, and surface strain. Good correlation between analysis and experiment was achieved. Because of the existence of a chordwise actuator moment, the induced twist of bending-torsi on coupled beams was significantly influenced by including the chordwise curvature of the plate segment of beam in the formulation. For [45]i4 solid beams, the chordwise bending of the plate segment of beam was found to increase the tip twist by about

Weldment Design for RHS Truss Connections. II. Experimentation

Laboratory-based investigations were conducted to assess the performance of and evaluate the design of weldments around the perimeter of rectangular hollow-section (RHS) web members at their connection to the chord member of a truss. Experimental work was carried out by subjecting a connecting weldment to a tension load, initially within an isolated connection specimen and then within a truss environment. These research projects entailed the testing of 29 isolated connections and two large-scale, 12.2-m (40.0-ft) and 12.0-m (39.4-ft) span, simply supported Warren trusses. The results of these tests have been used to evaluate international design recommendations for weldments and thereby produce preferred design approaches that utilize an effective-length concept for the weldment. For welded trusses, with gapped \IK\N- (or \IN\N-) or 50% overlapped \IK\N-connections, and comprising rectangular or square hollow structural section (HSS) members, it has been shown that the strength of the welded joint can be related reasonably well to the axial force in the connected web member. Any local or secondary bending moments in the connection are thereby accommodated in the design of the welds by means of a weld effective length.

Static Forces and Moments in a Grain Silo

The differential equation for elastic deformation of a cylindrical shell is formulated and solved. The particular solution is for grain pressure given by Jannsen's formula and includes frictional force of grain on the wall and the weight of the wall itself. If the bottom edge of the silo is restrained from radial displacement, localized circumferential compression, shear and bending moment develop.

Optimal correction of mass and stiffness matrices using measured modes

Discussion of Results The equations of motion were numerically integrated utilizing a total of 36 elements to define the geometry of the corer. The corer was allowed to free-fall for 3 s, at which time the global variables had the following values: u = 23.6 m/s, w = 2.3 m/s, 4 = 0.05 rad/s, 6 = 6.4 deg, ^=-0.8 m, Ze = 31.0 m. The corer assumed an elongated inverted-S shape. At ^ = 3 s, maximum bending moments occurred at the location of the step taper and at the junction between the afterbody and the upper portion of the barrel. The local element deflection, slope, and bending moment at these locations are given in Table 1 and are approximate due to the local variables being measured at discrete locations along the length of the corer. It is unlikely that the corer will actually experience such large bending moments during free-fall. However, it is intuitive that large bending moments will occur at the barrel/afterbody junction and may even become larger during penetration.

Limit loading of cylindrical shells subjected to local circumferential bending moments

Experiments have been carried out on twelve mild steel cylindrical shells each of which had a rigid radial square bar attached at its mid length. Strain and deformation patterns in the shell were measured when a hoop bending moment was applied to it through the attachment. Though some elastic stress distributions were obtained, the observations were mainly concerned with plastic deformations, the determination of plastic limit moments and the onset of instability. Measured deformation patterns were used to suggest a collapse mechanism from which a theoretical upper bound for the plastic limit moment was determined. Theoretical and experimental limit moments were compared for all specimens which had radius thickness ratios varying between 13·75 and 67·5, and attachment half width/cylinder radius ratios varying between 1 2·5 and 1 10·25 .

Localization of minor folds by major folds

Some naturally folded multilayer sequences show an association of major folds (which develop across the whole multilayer sequence) with localized minor folds (which are restricted to a few layers). The minor folds have highest amplitudes immediately adjacent to a major fold and attenuate rapidly away from that major fold. Analogous geometries have been duplicated in model experiments. Our mechanistic explanation for the initiation of growth of the localized folds uses an elastic beam analysis first put forward by Heteyni and assumes that an important effect of a developing major fold is to impart a localized bending moment on the layers under compression.

Equilibrium Method for Limit Calculation of Frames

Starting from the requirement that a hinge within a member must occur at a point of local maximum bending moment, it is shown that suitable equilibrium equations may replace differentiation of the mechanism equation for a frame. This is similar to the equilibrium method of yield line theory for slabs. There is considerable freedom of technique in establishing equations. Several examples are presented to explore the approach. A comparison is made with the standard approach wherever necessary.

Paper 2: Effect of Bending Moments on Nozzles with Forged Transition Pieces

An experimental study has been made of the elastic stress distributions arising in the vicinity of two transition rings of the type used to connect cylindrical ducts with large spherical pressure vessels. The effect of bending moments on the duct was considered and theoretical estimates of the stresses were made by modifying certain well-known analyses. Two of these methods gave results close to the experimental values in a region which included the position of maximum stress. This occurred near the weld between the spherical shell and the transition ring. In a further investigation it was found that, for the order of loads applied, the principle of superposition may be used to calculate the combined effect of a local bending moment and an internal pressure. When allowable bending moments at design pressure are calculated using a limiting stress concentration factor, the heavier transition piece is slightly superior to the other.

Localized Loads Applied to a Spherical Pressure Vessel through a Cylindrical Insert

A solution is obtained for the membrane and bending stresses in a thin spherical shell due to the action of a localized bending moment or radial load which is applied through a thin cylindrical insert, for example, a duct connection on a reactor pressure vessel. The stress distribution will be affected by the nature of the duct to vessel connection. In this paper attention is confined to the case of an unreinforced junction as sketched in Fig. 1. The solution is general in so far as it is reduced to a set of four simultaneous equations which can be solved readily when dealing with practical problems. As a numerical example, the case of the Hunterston reactor pressure vessel is considered, and it is shown how the localized stresses are affected by a change in duct thickness. Furthermore, these stresses are compared with those which would be induced in the sphere if the duct insert were rigid. It is found that in this practical example, the cylinder thickness has a significant effect on the calculated values for the stresses and displacements.