Page 357 - Civil Engineering Formulas

288 CHAPTER ELEVEN

P v

R

S

C
FIGURE 11.12 Radial pressure, P v , on the wall of a curved conduit
is resisted by compressive thrust C.

carried by the steel. The ring compression is an axial load acting tangentially
to the conduit wall (Fig. 11.12). For conventional structures in which the top
arc approaches a semicircle, it is convenient to substitute half the span for the
wall radius. Then,
S
C P v (11.32)
2
Allowable Wall Stress

The ultimate compression in the pipe wall is expressed by Eqs. (11.34) and
(11.35) that follow. The ultimate wall stress is equal to the specified minimum
yield point of the steel and applies to the zone of wall crushing or yielding.
Equation (11.34) applies to the interaction zone of yielding and ring buckling;
Eq. (11.35) applies to the ring-buckling zone.
When the ratio D/r of pipe diameter—or span D, in (mm), to radius of gyra-
tion r, in (mm), of the pipe cross section—does not exceed 294, the ultimate
wall stress may be taken as equal to the steel yield strength:
F b F y 33 ksi (227.4 MPa) (11.33)
When D/r exceeds 294 but not 500, the ultimate wall stress, ksi (MPa), is given by
2
D
F b 40 0.000081 (11.34)
r
When D/r is more than 500,
4.93 10 6
F b (11.35)
(D/r) 2