Shear Strengthening of Concrete Members - Strengthening Design of Reinforced Concrete with FRP - page 161

1.21 × 0.684 × 2.032

k v = = 0.327 < 0.75

468 × 0.011

20.043 × × 12 × 4943 × 0.327 × 0.011 × 6.44

f Ψ= × 0.85 = 8.37 k

12

VVVV =++ψ = 9.54 k + 8.37 k = 17.91 kV > = 15.28 k N.G.

n c s f f exp

The ACI 440 model overestimates the shear capacity with FRP in this case. One
main reason could be the size effect. The model of Khalifa et al. (1998) was cali-
brated against typical beam cross sections, while this beam is on the smaller side.

Example 6.4: Analysis

Al-Sulaimani et al. (1994) tested 16 reinforced concrete beams deficient in shear
and strengthened in flexure and/or shear using GFRP plates. The control beam
was designated as CO, and one of the strengthened beams was designated as SO.
The strengthened beam had side-bonded transverse strips that were 20-mm wide
at 50-mm on center covering the entire sides of the shear spans. The geometric
and material parameters of the strengthened beam are given in Figure 6.6.

f'c = 37.7 MPa, fy = 450 MPa
GFRP plate: f fu = 200 MPa, E f = 15.65 GPa, ε fu = 0.01278, t f = 3 mm

Solution:

The unstrengthened beams have their steel stirrups provided not in accordance
with ACI 318-11 (spacing = 200 mm > d /2).

d =+= 76 37 113 mm = d fv

f

37.7
6

c

V = bd = ××= 150 113 17,345.6N = 17.35 kN

c w

6

ϕ 6-mm stirrups at 200 mm o.c.

56.55 ×× = 450 113

V s = 14,377.5N 14.38 kN =

200

VVV =+= 31.73 kN < V = 34.5kN .K. n c s exp

P/2 P/2

150 mm

400 mm

400 mm 400 mm

37 mm

2 φ 6

150 mm

76 mm

3 φ 12

20 mm strips at
50 mm c/c

37 mm

1200 mm

φ 6 mm@200 mm c/c

Beam SO

FIGURE 6.6 Example 6.4 showing the beam section and profile.