DESIGN - Prestressed Concrete Transmission Pole Structures - page 44

where A psi and f sei are the area and stress of the i th strand, respectively.
Trial and error iteration of the location of the neutral axis c is used to
solve for the depth of the stress block, such that equilibrium between
tension and compression is satisfi ed.

Ultimate Moment Capacity Equation: The ultimate moment capac-
ity of a pole section is given as the sum of the moments of tensile and
compressive forces with respect to the neutral axis:

n

∑ 1

( )

φ Me Af = + cC 1 − K (4-4)

n i psi sei c

i =

where e 1 is the capacity reduction factor.

Note A psi , f sei , and c are previously defi ned, c (1

= d 1 − c and φ

K ) is the distance of
the centroid of the reduced compressive concrete area (pressure line) from
the neutral axis, d i is the distance of the i th strand from the extreme com-
pressive fi ber, and e i is the distance of the i th strand to the neutral axis.
The quantity e i A psi f sei is positive when the i th strand is located below the
neutral axis (tension zone) and negative when it is located above (com-
pression zone). In the case of braced H-frames and guyed structures, the
formula for the ultimate moment capacity should incorporate the effect
of the applied axial loads.
The capacity reduction factor (which is also known as the strength
factor

−

) is typically taken as 0.9. However, if a Manufacturer can demon-
strate consistency in the quality and predictability of the manufactured
pole, a

φ

φ of up to 1.0 can be used with consent from the Purchaser.

Cracking and Zero Tension Moment Capacity

Cracking Moment: Cracking starts when the tensile stress in the
extreme fi ber of the concrete reaches its modulus of rupture. The cracking
moment can be computed by elastic theory to predict the behavior of
poles.
For a symmetrically reinforced prestressed concrete pole section, a
uniform stress P/A g results from the effective prestress P acting on the
gross sectional area A g . Because of the external moment M , the section
area is subject to the extreme tensile stress My t / I g , where y t is the distance
from the centroidal axis to the extreme tensile fi ber and I g is the gross
moment of inertia of the section. The cracking moment may be calculated
using the following relationship:

fI
y

PI
Ay

rg g

M = +

(4-5) cr

t gt