Local Bending Stresses Research Articles

Measurement of Tensile Properties using Filament Wound Ring Specimens

In this study, the tensile properties of a filament wound ring specimens were evaluated by split disk test and compared to the theoretical values obtained by the rule of mixtures. The circumference-wound ring specimens were prepared from 4 types of material systems. The research results showed that the measured strengths of the composite systems were considerably lower than the theoretical values due to the local bending stresses around the split disk edges. For the measurement of elastic moduli of the filament wound ring specimens, the effect of friction on the strain of the ring must be taken into account. But the effect of friction between the split disk fixture and the ring specimen can be eliminated by averaging the moduli for loading and unloading state with maintaining the same crosshead rates. The measured elastic moduli of ring showed very good agreement with the theoretical values.

Approximate method for the optimum design of ring and stringer stiffened cylindrical panels and shells with local, inter-ring, and general buckling modal imperfections

The PANDA2 computer program for minimum-weight design of stiffened composite panels is expanded to handle optimization of ring and stringer stiffened cylindrical panels and shells with three types of initial imperfections in the form of buckling modes, any combination of which may be present: local (buckling between adjacent stringers and rings), inter-ring (buckling between rings with stringers bending with the panel skin), and general (buckling in which both stringers and rings bend with the panel skin). Stresses and buckling load factors of the imperfect panels are computed with use of the assumption that the amplitudes of the buckling modal imperfections grow hyperbolically with increasing load factor according to the formula AMP(i) = EIG(i) (EIG(i) − 1), in which AMP(i) is a factor to be multiplied by the initial buckling modal imperfection and EIG(i) represents the critical load factor for the ith type of buckling mode ( i = 1 = local buckling, i = 2 = inter-ring buckling, i = 3 = general buckling). Buckling load factors corresponding to local, inter-ring, and general buckling of the imperfect panel are computed with use of the maximum radius of curvature that develops in whatever portion of the panel (between stiffeners, inter-ring, overall) is being considered in the calculations and including redistribution of stress resultants over panel skin and stiffener cross-sections caused by prebuckling bending. Stress constraints in the optimization problem are computed including local, inter-ring, and general bending stresses generated by the growth of the initial local, interring, and general imperfections. These bending stresses are added to the stresses from other sources (thermal, in-plane loading, normal pressure, curing, redistribution of membrane stresses from overall prebuckling bending of the imperfect panel). Minimum-weight designs for various imperfect unstiffened and stiffened cylindrical shells derived by PANDA2 are evaluated with use of the STAGS general-purpose finite element code. The agreement of results from PANDA2 and STAGS appears to qualify PANDA2 for the preliminary design of imperfect, stiffened, composite cylindrical shells.

LOCAL STRESS STATE DEFINITION OF STRUCTURAL ELEMENTS USING HOLOGRAPHIC INTERFEROMETRY

Abstract A method has been developed for local stress strain state definition of thin walled construction elements. Holographic interferograms of the normal components of the displacement vector of the studied element surfaces are used to determinate of local bending stresses in the elements. Some experimental results including local bending state definition ahead of the crack in the elements are represented.

Plastic Collapse at Lap Joints in Pressurized Cylinders under Axial Load

Circular steel silos and tanks are often constructed from rolled‐steel plates with welded or bolted lap splices. Where the lap runs horizontally around the silo circumference, the lap connection causes a local eccentricity in the line of vertical thrust in the shell wall. This eccentricity induces high local bending stresses and circumferential membrane stresses, which are detrimental to the strength of the structure. Although elastic buckling of the shell wall may be the critical failure mode for thin lap‐jointed cylinders under axial load with no or small internal pressure, axisymmetric plastic collapse is the likely failure mode when the internal pressure is high, especially for relatively thicker cylinders. This paper presents a detailed study of the axisymmetric collapse behavior and strength of lap‐jointed cylinders under combined axial compression and internal pressure and establishes easy‐to‐use design equations for such shells.

The Ultrafine Structure of Carbon Fibers

High resolution phase contrast microscopy has been used to study the ultrafine structure of Morganite I and Thornel high modulus carbon fibers. Both are commercial fibers processed at 2800° to 3000°C, the former made from a polyacrylonitrile and the latter from an cellulose (rayon) precursor. Graphitizing is combined with stretching in order to align the basal planes parallel to the fiber axis to secure the high modulus. The ultrafine structures of these fibers have previously proved elusive.The fibers have been looked at in two ways. Since they are irregular in shape it was found possible to direct the electron beam normal to the fiber axis and image the basal planes viewed edge-on at the periphery of a fiber. The image disappears as one moves into the thicker region, so that only the structure near the surface is accessible. The second approach was to fracture the fiber by applying local bending stresses.

A photoelastic evaluation of the influence of closure and other effects upon the local bending stresses in cracked plates

Two sets of photoelastic experiments employing stress freezing were performed in order to evaluate closure and precatastrophic extension of cracks in plates under cylindrical bending. Data were compared with the Hartranft-Sih theory in order to obtain quantitative results. It was found that crack closure on the compressive side of the plate produced somewhat larger local elastic stresses on the tensile side of the plate for straight through cracks than predicted by the mathematical model. When precatastrophic extension was allowed on the tension side of the plate, accompanying stress relaxation neutralized the stress intensification effect of closure. For short, nearly square cracks, three-dimensional effects appeared to reduce the stress intensification effects due to closure.

Flexural waves scattering at a through crack in an elastic plate

The diffraction of a plane flexural wave by a through-the-thickness crack in an elastic plate is examined by application of Mindlin's theory of flexural motions of plates. In his theory, which takes into account the rotatory inertia and shear effects, an incident flexural wave passing through the crack is scattered into three types of flexural waves. By combining the incident and scattered waves, the complete stress distribution around the crack can be calculated. However, in the application of the theory of crack propagation, it is only necessary to determine the intensity of the moment distribution in a small region surrounding the crack tip. It is found that this intensity decreases as the circular frequency of the input wave is increased. In other words, the magnitude of the local bending stresses is always lower in the dynamic case than in the static case. Defined in the paper is a dynamic moment-intensity factor whose critical value may be used to determine the onset of crack extension in brittle materials. Moreover, the present investigation also covers the problem of a cracked plate vibrating at steady state.

Shells with zero bending stresses

Shells in general, when subjected to external loads, develop bending as well as membrane stresses. If the middle plane of the shell is a surface of revolution and the applied loads are radially symmetrical about the axis, the membrane stresses are readily calculated provided the bending stresses are small enough to be ignored. When the bending stresses are taken into account, the problem becomes very much more complicated. It may, however, be relatively easy to design the shell in such a way that bending stresses are entirely absent. The paper describes shells which will be free from bending stresses when the applied load is any uniform axial force. Consideration is given to shells of varying thickness, but particular attention is paid to shells whose thickness is uniform. The possibilities of providing boundary rings to prevent local bending stresses in the vicinity of the end sections is also investigated.

The Stresses in a Pressure Vessel With a Flat Head Closure

Abstract This paper presents the results of computations for determining the stresses in a cylindrical pressure vessel with a flat head closure. The accurate bending theory of shells is used to evaluate the local bending stresses in the neighborhood of the junction of the flat head and the cylindrical body. Tables show the magnitudes of the shear stress, the circumferential stress, and the axial stress as multiples of pd/2t. For the axial and circumferential stresses, the tables show the magnitude and sense of the stress on the internal and external surfaces of the vessel. The locations where these stresses are critical are also determined. Curves are given showing the maximum stresses as functions of the diameter-thickness ratio of the shell and of the thickness ratio of head to shell body. The range of calculation includes most vessel sizes encountered in practice. Tables of influence numbers for the cylinder and the flat head are presented. These tables can be utilized in problems in which other elastic structures are attached to either member. The paper includes a discussion of the mathematical procedure.

Stresses in a Pressure Vessel With a Conical Head

Abstract This paper presents the results of computations for determining the stresses in a pressure vessel with a conical head. The accurate bending theory of shells is used to evaluate the local bending stresses in the neighborhood of the junction of the conical head and the cylindrical body. Tables show the magnitudes of the shear stress, the circumferential stress, and the axial stress at the junction as multiples of pd/2t. For the axial and circumferential stresses, the tables show the magnitude and sense of the stress on both the internal and external surfaces of the vessel. Additional results show the magnitude and location of the maximum stress (of each of the three types) in the cylinder. Curves are given showing the maximum stresses for values of cone apex angle, ratio of conical head thickness to cylinder thickness, and ratio of cylinder diameter to cylinder thickness which will include most of the vessels encountered in practice. Tables of influence numbers for the conical head are presented. These can be utilized in many problems which require attaching a conical shell to some other elastic structure. A discussion of the mathematical procedure is contained in an Appendix.