Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 139

where A vf is the area of shear friction reinforcement perpendicular to the
plane of shear and f vf is defined as

f vf = E f ε vf ≤ f fu (4.113)

Unless tests demonstrate otherwise, the recommended value for ε fv is 0.003.
According to ACI 318-11, μ is the coefficient of friction. For the com-
mon case of normal weight concrete placed against hardened concrete
surfaces:

μ = 0.6 (if the surface is not intentionally roughened)

μ = 1.0 (if the surface is intentionally roughened)

This formulation of shear friction provides a resistance considerably
lower than what steel reinforcement can deliver. Hence, other param-
eters, such as compressive axial force transferred across the plane, or
other devices and mechanisms, such as shear keys, may be considered to
enhance the strength. In this case, the recommended total nominal shear
strength is:

( )

2

( )

2

V = A f µ +µ+ P V ′ (4.114) n u n

vf vf

where P u ≥ 0 is the compressive axial force acting simultaneously with the
transferred shear. V ′ n is the shear strength provided by other mechanisms.
If P u < 0 (tensile force), then

( )

2

2

V = A f µ + V ′

+µ

P (4.115) n n u

vf vf

The reason that the contributions of reinforcement and other mech-
anisms are not considered to be directly additive is the relatively large
deformations that are required to mobilize the normal force provided by
reinforcement. Therefore, the presence of another mechanism may render
the other partly ineffective. Finally, as always, Equation (4.86) has to be
verified and other cases of shear design (ϕ = 0.75). An example of the appli-
cation of this design is presented in Chapter 5 for the case of a shear wall
(Example 5.6).

4.10.7 Shear stresses due to torsion
The basic safety relationship at the ultimate limit state can be written as

ϕ T n ≥ T u (4.116)