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:

	= Net tensile strain in extreme tension steel at nominal resistance
	= Distance from extreme compression fiber to the centroid of extreme tension steel
	= Resistance factor for a reinforced concrete tension controlled section
	= Resistance factor for a prestressed tension controlled section
	= Resistance factor for a compression controlled section
	= Resistance factor for a partial prestressed tension controlled section
PPR	= Partial prestress ratio

The net tensile strain is

(Eq. 1)

The resistance factor for a partially prestressed tension controlled section is

(Eq. 2)

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

(Eq. 3)

Substituting Eq. 1 into Eq. 3 we get

(Eq. 4)

Simplify

(Eq. 5)

Substituting Eq. 2 into Eq. 5 gives

(Eq. 6)