Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 144

Table 4.9 Coefficients Bi i
c (in.)

B 1 B 2 B 3

0.787 −23.43 15.38 0.4660

1.18 −104.68 58.45 0.2821

1.58 −159.79 87.28 0.2437

2.00 −2159.93 1995.44 0.02800

2.36 −13582.44 13347.56 0.0055

Note: 1 in. = 24.5 mm

where f ′c is the concrete compressive strength, ε c1 is the strain correspond-
ing to f f′c and equal to 0.0025, and ε cu1 is the ultimate strain equal to 0.002.
The typical elastic-brittle stress-strain relationship is, instead, assumed for
the FRP. The ultimate usable FRP tensile strength is the smaller of the reduced
strength due to fire, computed per Equation (4.120), and the maximum stress
developable by the end anchorage in zones not directly exposed to fire. Based
on the work by Katz and Berman [43], it is assumed that for temperatures
exceeding 122°F (50°C) the bond between concrete and FRP reinforcement
becomes negligible. For this reason, in computing the maximum developable
tensile stress, Nigro et al. recommend considering only the length of the end
anchorage whose temperature does not exceed 122°F (50°C). The following
equation provided by the Italian CNR Guidelines [44] is proposed.

l − l

ddfi tT Tcr ,,, >

(4.124)

f =

fd t ,

0.1 ⋅ d

where l d is the design development length, l d,i,t,T>Tcr is the embedment length
of a bar with a temperature exceeding 122°F (50°C), d is the bar diameter.
The development length l d,i,t,T>50C is proposed to be computed as
follows:

(

)

(

)

(

)

Bc

l = B cBct + ⋅ (4.125)

3

dfitTTcr ,,, > 1 2

where t is the fire exposure time, c is the concrete cover in in., and
the coefficients B i (c) are computed based on thermal analysis results and
reported in Table 4.9.
An application of this method is further discussed in Chapter 6 (Step 10).

REFERENCES

1. J. K. Wight and J. G. MacGregor. Reinforced concrete mechanics and design,
6th ed., Englewood Cliffs, NJ: Prentice Hall (2012).

2. ACI Committee 318. Building code requirements for reinforced concrete, ACI
318-11. American Concrete Institute, Farmington Hills, MI. (2011).