7. What are the other stresses against which the design of piping is safe guarded?
A. Principal stress.
B. Shear stress.
Apart from the stress which is normal to the surface of the crystal as mentioned in question No. 4, the grains would have been oriented in the pipe wall in all possible orientations. The above stresses (axial, circumferential and radial stress) have stress component in direction normal to faces of randomly oriented crystal. Each crystal thus fac es normal stresses. One of these orientations must be such that it maximizes one of the normal stresses. Normal stresses for such orientation (maximum normal stress orientation) are called principal stresses and are designated as S1 (maximum), S2 and S3 (minimum).
Principal stresses are way of defining the worst case scenario as far as the normal stresses are concerned.
In addition to the normal stresses, a grain can be subjected to shear stresses as well. These stress act parallel to the crystal surface. The shear stresses occur if the pipe is subjected to torsion, bending etc. Just as there is an orientation for which normal stresses are maximum, there is an orientation which maximizes shear stress. The maximum shear stress in a 3-D state of stress c an be shown to be as:- max= (S1- S3)/2 i.e. half of the difference between the maximum and minimum principal stresses.
8. What does the solid mechanics states regarding the normal stresses?
Solid mechanic states that the sum of the three normal stresses for all orientation is always the same for any given external load as:- SL+ SH + SR = S 1 + S2 + S3
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9. Which component of normal stress is considered negligible?
In most pipe design cases, the radial component of normal stresses (SR) is negligible as compare to the other two component (SH and SL).
10. What are the theories of failure?
Imp ortant theories in common use are:-
A. Maximum Stress Theory or Rankine Theory.
B. Maximum Shear Theory or Tresca Theory.
C. Octahedral Shear Theory or Von Mises Theory.
11. What is maximum stress theory?
According to this theory, failure occurs when the maximum principal stress in a system (S1) is greater than the maximum tensile principal stress at yield in a specimen subjected to uniaxial test. In uniaxial test, the applied load give rise to axial stress (SL) only and hoope’s stress (SH) & radial stress (SR) as well as the shear stress are absent. In a specimen under uniaxial tension test at yield the following holds.
SL= SY, SH= 0, SR= 0S1 = SY, S2 = 0, and S3 = 0.
The maximum tensile principle stress at yield is thus equal to the conventionally reported yield stress (load at yield / cross – sectional area of specimen)
The rankine theory thus says that the failure occurs when the maximum principal stress in a system (S1) is more than the yield stress of the material(SY).
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