Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 106

4.7 ANCHORAGE AND DEVELOPMENT LENGTH

Development length of straight bars. The development length, if d , of FRP
straight bars is defined in ACI 440.1R-06 as the bond length necessary
to develop the minimum of if fu , the design tensile stress; if if , as defined in
Equation (4.40); or if fe as defined in Equation (4.39). if d is given by the fol-
lowing equation:

if

fr

α − 340

if ′

c

if = d (4.59)

d b

C
d

13.6 +

b

if

fr

α − 340

0.083 if ′

c

or if = d in SI units

d b

C
d

13.6 +

b

where d d is the bar diameter, C is the lesser of the cover to the center of
the bar or one-half of the center-on-center spacing of the bars being devel-
oped, and α is a factor to account for the bar location. α is taken equal
to 1.5 for bars with more than 12 in. (300 mm) of concrete cast below,
otherwise α is taken equal to 1.0. For the case of columns, α is always
equal to 1.5.
ACI 440.1R-06 recommends the following criterion for development of
positive reinforcement at points of inflection and simple supports:

φ M

V

n

if ≤ + if

a (4.60) d

u

where M n is the effective nominal bending moment capacity at the critical
cross section, V u is the factored shear force at that section, and if a is the
embedment length (a) beyond the center of the support or (b) at a point of
inflection. For the latter, if a is the larger of the effective depth of the member
or 12 d b .
Development length of bent bars. Because of the constituents (i.e., ther-
mosetting resin) and manufacturing method (i.e., pultrusion), it is difficult,
if not impossible, to create bends at the end of a long FRP bar. Bent bars are