Literature Survey on Shear in FRC Beams - On Shear Behavior of Structural Elements Made of Steel Fiber Reinforced Concrete - page 32

was incorporated in the Final Draft of the Model Code 2010 [ 2 ]. It includes the
shear contribution of bers as an enhancement of the concrete contribution by

modifying the longitudinal reinforcement ratio considered by EC2. As it increases,
the longitudinal reinforcement limits the growth of shear-critical crack, allowing a
greater transfer of stresses (whether tensile or shear). The proposed equation is
based on FRC performance (residual post-cracking strength), which is the more
signi cant index for FRC structural design. It can be easily applied and transferred

into practice [ 50 ].
The formula of MC2010 for FRC is based on the results obtained in the Ph.D.
thesis of Minelli [ 79 ]:

" # b w d

1 = 3

0 18

c c n

: f Ftuk

f ctk

V c ¼ 100 q l 1 þ 7 : 5 f ck þ 0 : 15 r cp ð 3 : 28 Þ

where:
γ c is the partial safety factor for the concrete without

bers;

ʾ is a factor that takes into account the size effect

and it is equal to:

q

200
d

n ¼ 2

d (mm) is the effective depth of the cross-section;

ˁ l is the reinforcement ratio for longitudinal rein-

forcement equal to: q l ¼

A s

bd 0

: 02;

A sl (mm 2 )

is the cross-sectional area of the reinforcement
which extends ≥ l bd + d beyond the considered

section;

f Ftuk (MPa) is the characteristic value of the ultimate residual

tensile strength for FRC, by considering

w u = 1.5 mm;

f ctk (MPa) is the characteristic value of the tensile strength

for the concrete matrix;

f ck (MPa) is the characteristic value of cylindrical compres-

sive strength;

˃ cp = N Ed /A c < 0.2

· f cd (MPa) is the average stress acting on the concrete cross-

section, A c (mm 2 ), for an axial force N Ed (N), due
to loading or prestressing actions (N Ed > 0 for
compression);

b w (mm) is the smallest width of the cross-section in the

tensile area.