Consider a thin-walled vessel with radius r, thickness h, and r>>h. When the ves
ID: 1858720 • Letter: C
Question
Consider a thin-walled vessel with radius r, thickness h, and r>>h.
When the vessel is pressurized with pressure P, pulled laong its axis with force F, and torqued along its axis with moment M, the stress field is approximately (in cylindrical coordinates):
(sigma) = -P / 2 0 0
0 Pr / h M / (2(pi)rh)
0 M / (2(pi)rh) Pr / (2h) + F / (2(pi)rh)
e(r), e(theta), e(z)
Let
F = 10 N
P = 2 kPa
M = 1.5 N*cm
r = 1.2 cm
h = 0.9 mm
What are the principal stresses? Max compression? Max tension? Max Shear Stress?
Explanation / Answer
by putting the values given we get the stress tensor in numerical values.
principal stresses are eigenvalues of stress tensor.
so the principal stresses for the given condition are -1 kPa, 26.6359 kPa, 28.1031 kPa
Max tension is 28.1031 kPa(highest positive principal stress)
Max compression is 1 kPa(negative principal stress of highest magnitude)
Max Shear Stress(28.1031+1)/2= 14.55 kPa..........(ans)