196
6 Two-Dimensional Problems in Elasticity …
(a)
(c)
(b)
(d)
Fig. 6.12 Closed ring subjected to loads
fixed at the section BB and at section AA subjected to an axial load
P
2
and bending
moment M A . Here the magnitude and the sign of the moment M A are unknown.
Now, taking the moments of the forces that lie to the one side of the section, then
we get,
M mn = −M A +
P
2
(R − x)
But from Figure, x = R cos θ
∴ M mn = −M A +
P
2
(R − R cos θ )
6 Two-Dimensional Problems in Elasticity …
(a)
(c)
(b)
(d)
Fig. 6.12 Closed ring subjected to loads
fixed at the section BB and at section AA subjected to an axial load
P
2
and bending
moment M A . Here the magnitude and the sign of the moment M A are unknown.
Now, taking the moments of the forces that lie to the one side of the section, then
we get,
M mn = −M A +
P
2
(R − x)
But from Figure, x = R cos θ
∴ M mn = −M A +
P
2
(R − R cos θ )