PGSplice  3.0
Precast-prestressed Spliced Girder Bridges
Flexural Resistance Factor

A generalized version of the flexure resistance factor defined in AASHTO LRFD 5.5.4.2.1 is used in this software. The resistance factor is a linear interpolation between the resistance factors for compression controlled and tension controlled sections. A linear interpolation is also made for partial prestress ratio between reinforced concrete and prestressed sections.

This article illustrates the derivation of the generalized resistance factor for flexure equation.

Given:

et.png
= Net tensile strain in extreme tension steel at nominal resistance
dt.png
= Distance from extreme compression fiber to the centroid of extreme tension steel
phi_trc.png
= Resistance factor for a reinforced concrete tension controlled section
phi_tps.png
= Resistance factor for a prestressed tension controlled section
phi_c.png
= Resistance factor for a compression controlled section
phi_t.png
= Resistance factor for a partial prestressed tension controlled section
PPR = Partial prestress ratio
ResistanceFactorGraph.png

The net tensile strain is

net_tensile_strain.png
(Eq. 1)

The resistance factor for a partially prestressed tension controlled section is

PPR.png
(Eq. 2)

From the graph above, the resistance factor can be computed as

Eqn1.png
(Eq. 3)

Substituting Eq. 1 into Eq. 3 we get

Eqn2.png
(Eq. 4)

Simplify

Eqn3.png
(Eq. 5)

Substituting Eq. 2 into Eq. 5 gives

Eqn4.png
(Eq. 6)