Page 280 - Buried Pipe Design

Rigid Pipe Products 251

M (t/2) M (t/2) (M/b) (t/2)
(5.3)
3
3
I bt /12 t /12

t
M 0.318F r i † (5.4)
2
where M moment
F load
I moment of inertia of wall
r i internal radius
b length of specimen thickness
t wall thickness

Equation (5.3) can be written as follows:

6 (0.318) (F/b) (r i t/2)
(5.5)
t 2
For external loading only, at failure, the stress is the strength, some-
times called the modulus of rupture (MR). The three-edge bearing load
to cause failure (three-edge bearing strength W) is F/b lb/ft. Thus,

6 (0.318) (W lb/ft) (1 ft/12 in) [(d i t)/2]
MR
t 2
or
0.0295W (D t)
MR (5.6)
t 2
The hoop stress h in a cylinder may be calculated as follows:

PD
h (5.7)
2t
Knowledge of h , MR, and t will allow calculation of w and p through
the use of Eqs. (5.1) or (5.2) and (5.6) and (5.7). By solving Eq. (5.7) for
P and Eq. (5.6) for W, one may substitute into Eqs. (5.1) and (5.2) to
obtain
MRt 2 2t/D p

w (5.8)
0.0795 (D t) 2t/D

† This is the maximum moment in a closed ring loaded with diametrically opposite con-
centrated loads. See a text on the mechanics of materials for details.