Prestressed Concrete - Design of Reinforced Concrete - page 594

compression to the centroid of the tensile reinforcement. Should the reaction introduce
compression into the end region of a prestressed member, sections of the beam located at
distances less than h /2 from the face of the support may be designed for the shear com-
puted at h /2 where h is the overall thickness of the member.

V u v u

b w d

The Code (11.4.1) provides two methods for estimating the shear strength that the
concrete of a prestressed section can resist. There is an approximate method, which can be
used only when the effective prestress force is equal to at least 40% of the tensile strength
of the flexural reinforcement f pu , and a more detailed analysis, which can be used regard-
less of the magnitude of the effective prestress force. These methods are discussed in the
paragraphs to follow.

Approximate Method
With this method, the nominal shear capacity of a prestressed section can be taken as

c 700 V u d
M u

V c 0.6 f b w d (ACI Equation 11-9)

The Code (11.4.1) state s t hat regardless of the value given by this equation, V c need
not be taken as less than nor may it be larger than In this expression,
V u is the maximum design shear at the section being considered, M u is the design moment
at the same section occurring simultaneously with V u , and d is the distance from the ex-
treme compression fiber to the centroid of the prestressed tendons. The value of V u d / M u is
limited to a maximum value of 1.0. (At sections near the ends of members where pre-
stressing forces may not have been fully developed or transferred, V c may not be larger
than the values given in ACI Sections 11.4.3 and 11.4.4.)

c b w d , c b w d .

2 f 5 f

More Detailed Analysis
If a more detailed analysis is desired (it will have to be used if the effective prestressing
force is less than 40% of the tensile strength of the flexural reinforcement), the nominal
shear force carried by the concrete is considered to equal the smaller of V ci or V cw , to be
defined here. The term V ci represents the nominal shear strength of a member provided by
the concrete when diagonal cracking results from combined shear and moment. The term
V cw represents the nominal shear strength of the member provided by the concrete when
diagonal cracking results from excessive principal tensile stress in the concrete. In both
expressions to follow, d is the distance from the extreme compression fiber to the centroid
of the prestressed tendons or is 0.8 h , whichever is greater (Code 11.4.2.3).
The estimated shear capacity V ci can be computed by the following expression, given
by the ACI Code (11.4.2.1):

c b w d V d V i M cr c b w d V ci 0.6 f

M max

but need not be taken as less than 1.7 f

(ACI Equation 11-10)