Stress theories

Subsection A This subsection contains the general requirements applicable to all materials and methods of construction. Design temperature and pressure are defined here, and the loadings to be considered in design are specified. For stress failure and yielding, this section of the code uses the maximum-stress theory of failure as its criterion. 

By definition, a brittle material does not fail in shear failure oeeurs when the largest prineipal stress reaehes the ultimate tensile strength, Su. Where the ultimate eompressive strength, Su, and Su of brittle material are approximately the same, the Maximum Normal Stress Theory applies (Edwards and MeKee, 1991 Norton, 1996). The probabilistie failure eriterion is essentially the same as equation 4.55. 

Whitney and Pagano [6-32] extended Yang, Norris, and Stavsky s work [6-33] to the treatment of coupling between bending and extension. Whitney uses a higher order stress theory to obtain improved predictions of a, and and displacements at low width-to-thickness ratios [6-34], Meissner used his variational theorem to derive a consistent set of equations for inclusion of transverse shearing deformation effects in symmetrically laminated plates [6-35]. Finally, Ambartsumyan extended his treatment of transverse shearing deformation effects from plates to shells [6-36]. 

For brittle materials such as glass or cast iron, the maximum shear-stress theory is usually applied. 

Maximum principal stress theory which postulates that a member will fail when one of the principal stresses reaches the failure value in simple tension, or. The failure point in a simple tension is taken as the yield-point stress, or the tensile strength of the material, divided by a suitable factor of safety. 

Maximum shear stress theory which postulates that failure will occur in a complex stress system when the maximum shear stress reaches the value of the shear stress at failure in simple tension. 

The maximum shear stress theory is often called Tresca s, or Guest s, theory. 

The maximum shear-stress theory has been found to be suitable for predicting the failure of ductile materials under complex loading and is the criterion normally used in the pressure-vessel design. 

The maximum intensity of stress allowed will depend on the particular theory of failure adopted in the design method (see Section 13.3.2). The maximum shear-stress theory is normally used for pressure vessel design. 

If the maximum shear stress theory is taken as the criterion of failure (Section 13.3.2), then the maximum pressure that a monobloc vessel can be designed to withstand without failure is given by ... 

Manning (1947) has shown that the maximum shear strain energy theory of failure (due to Mises (1913)) gives a closer fit to experimentally determined failure pressures for monobloc cylinders than the maximum shear stress theory. This criterion of failure gives ... 

The fractures on a plane surface, created by the collisions of hard spherical particles at low-impact velocities, may form a conical crack according to the Hertzian quasi-static stress theory. In a multiple-impact situation, the conical cracks meet those extending from neighboring impact sites, and then the brittle material becomes detached. Once appreciable damage is done, the cracking mechanism may be altered because the particles no longer strike on a plane surface nevertheless the brittle removal continues by the successive formation and intersection of cracks. 

High light intensity may have decreased the concentration of secondary metabolites if the plants were stressed by the high irradiance (see the environmental stress theory, Section IV.D). The plants grown at 100% of surface irradiance probably received high doses of ultraviolet radiation as well as photosynthetically active radiation. Ultraviolet radiation can stress Dictyota ciliolata, leading to decreased concentrations of secondary metabolites.183... 

The basic character of non-fluidized gas-particle flow is the existence of contact pressure (or stress) among particles and between particles and the pipe wall. Both theoretical analyses and experimental results (Terzaghi, 1954 Johanson and Jenike, 1972 Li and Kwauk, 1989) showed that the pressure of the interstitial fluid in particulate material neither compresses nor increases the shear resistance of the particulate material. After Walker (1966) and Walters (1973), Li and Kwauk (1989) analyzed the stresses in a vertical pneumatic moving-bed transport tube by using the stress theory of particulate media mechanics and Mohr circles, shown in Figs. 19 and 20, and gave the following stress ratios at any point in the flow field ... 

Departing from the maximum shear stress theory of plastic flow R. H. Lance and D. N. Robinson [6] developed yield conditions for fiber reinforced eomposite materials. The authors of [6] assumed that the material could flow plastically if (i) the shear stress on planes parallel to fibers, and in a direction perpendicular to them, reaches a critical value or... 

Lance, R.H. and Robinson, D.N., (1972), A maximum shear stress theory of plastic failure of fiber-reinforced materials. J. Mech. Phys. Solids, 19,49. 

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