Background Knowledge - Strengthening Design of Reinforced Concrete with FRP - page 23

2.3 SHEAR DESIGN OF RC BEAMS
In addition to flexural failure of beams, which is typically ductile in nature and pro-
vides warning signs of large deflections as well as increased and widened flexural
cracks with continuous yielding of primary steel, beams may fail in shear or diagonal
tension, which is a sudden brittle failure posing more threat than flexural failure.
Furthermore, accurate prediction of shear failure is difficult to achieve because the
mechanisms involved are not all completely understood. Similar to strategies to
protect against flexural failure, concrete beams are typically reinforced with shear
reinforcement (stirrups), which are uniformly distributed along the beam profile in
a vertical or inclined orientation to provide bridging of diagonal tension cracks and
control or delay shear failure, such that flexural failure takes place first. Accordingly,
ACI 318-11 specifies a lower strength reduction factor for shear (ϕ = 0.75) compared
to tension-controlled flexural failure (ϕ = 0.9). Reduced shear resistance must exceed
factored shear demand:

φ≥ VV

n (2.24) u

but

VVV
n

=+ (2.25)

c s

thus

VVV
u

≤φ +φ

(2.26)

c s

where in the case of shear and flexure only
ϕ = 0.75

V =λ (see Figure 2.14) f bd (2.27)

c c w

Vd
M

Vd
M

u u

V =λ+ 1.9 f 2500 ρ bd ≤λ 3.5 f bd and ≤ 1.0 (2.28)

c c w w c w

u u

while in the case of shear, flexure, and axial compression.

N

u

(see Figure 2.15) (2.29)

V =+ λ 21 fbd

c cw

2000 A

g