Principal stress

Welding is a primary source of residual stresses principally because of large temperature differences between the weld bead and the rela-... 

The containment shell is analyzed for individual and various combinations of loading cases of dead load, live load, prestress, temperature, and pressure. The design output includes direct stresses, shear stresses, principal stresses, and displacements of each nodal point. Stress plots which show total stresses resulting from appropriate combinations of loading cases are made and areas of high stress identified. If necessary, the modulus of elasticity is corrected to account for the nonlinear stress-strain relationship at high stresses. Stresses are then recomputed if a sufficient number of areas requiring attention exist. 

When stress components are referred to axes rotated through that value of 9 compared with the original axes, the shear stress components vanish, and we have defined the principal axes of stress. Principal axes of strain are defined similarly. In Figure A1.2 extensional stresses o, Oyy are plotted along the OX axis, and shear stresses 0 y = Oy are plotted along the OY axis. 

Bulk Modulus Volume changes are produced only by normal stresses. For example, consider an element loaded with only normal stresses (principal stresses) as shown in Fig. 2.16(b). The change in volume can be shown to be (for small strains). 

The results of an experimental research activity aimed at the system setup of the Stress Pattern Analysis by Measuring Thermal Emission used to measure the sum of the principal stresses of the free surface are presented. 

The thermoelastic law, valid only within the elastic range of isotropic and homogeneus materials, relates the peak to peak temperature changes to the peak to peak amplitude of the periodic change in the sum of principal stresses. 

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

The calibration curve of each rosetta strain gauge was so obtained and ftg.5 shows the sum of the principal stresses at the measuring points versus pressure inside the vessel. Further tests were carried out to obtain the calibration factor and to check that it remained constant on the whole scan area of the test surface. This was achieved through additional measurements using the SPATE system on fixed points on the surface located very close to the applied rosetta strain gauges. This procedure gave the following results ... 

Fig.5 Sum of the principal stresses at the measuring points versus pressure inside the vessel.

The calculation was carried out using the ANSYS F.E.M. code. The pressure vessel was meshed with a 4 nodes shell element. Fig. 18 shows a view of the results of calculation of the sum of principal stresses on the vessel surface represented on the undeformed shape. For the calculation it was assumed an internal pressure equal to 5 bar and the same mechanical characteristics for the test material. 

Fig. 18 FEM Analysis, sum of the principal stress distribution on the vessel surface on the deformed shape of it for a pressure equal to 5 bar.

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

Elastic Behavior. In the following discussion of the equations relevant to the design of thick-walled hoUow cylinders, it should be assumed that the material of which the cylinder is made is isotropic and that the cylinder is long and initially free from stress. It may be shown (1,2) that if a cylinder of inner radius, and outer radius, is subjected to a uniform internal pressure, the principal stresses in the radial and tangential directions, and <7, at any radius r, such that > r > are given by... 

Fig. 1. Principal stresses acting on small element of cylinder waU at radius, r, when the cylinder is stressed elastically by internal pressure, (3).

Equations 1 to 3 enable the stresses which exist at any point across the wall thickness of a cylindrical shell to be calculated when the material is stressed elastically by applying an internal pressure. The principal stresses cannot be used to determine how thick a shell must be to withstand a particular pressure until a criterion of elastic failure is defined in terms of some limiting combination of the principal stresses. 

Fig. 11. Principal stresses induced in a cylinder of / = 2 by a temperature gradient of 100°C (a) maximum temperature at outside surface (b) maximum...

The principal advantage of plastic dmms and liners is their resistance to corrosion. This aspect of their performance requires the lading to be investigated in terms of capacity for chemical attack on the dmm. Stress-cracking tests should be performed in all instances where the compatibiUty of jading and dmm material has not been estabUshed (6). 

A bursa, a sac filled with fluid located around a principal joint, is lined with a synovial membrane and contains synovial fluid. This fluid minimizes friction between the tendon and the bone, or between tendon and ligament. Repeated small stresses and ovemse can cause the bursa in the shoulder, hip, knee, or ankle to swell. This swelling and irritation is referred to as bursitis. Some patients experience bursitis in association with tendonitis. Bursitis can usually be reheved by rest and in some cases by using antiinflammatory medications. Some orthopedic surgeons also inject the bursa with additional medication to reduce the inflammation. 

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