Experimental Tests to Study the Influence on the Shear Behavior of Fibers of Different Characteristics - On Shear Behavior of Structural Elements Made of Steel Fiber Reinforced Concrete - page 115

With fR3 and rho without limitation
With fRm and rho without limitation

With fR3 and rho with limitation

With fRm and rho with limitation

1.40

NEITHER
FIBERS
NOR
STIRRUPS

65/40 BN 45/50 BN 80/50 BN 80/30 BP 80/40 BP WITH STIRRUPS

1.30

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

Fig. 6.13 Shear safety margins according to MC2010. Note rho ( ˁ ) = longitudinal reinforcement

ratio; where ˁ max =2%

concrete strength when varying from 55 to 90 MPa. The linear dependency for high
strength concretes is very high (see dashed red line), with a value r 2 0.85 for both

cases, using f R3 and using f Rm . For medium strength concretes the approximation to
a straight line is worse than for high strength concretes, but the correlation is
slightly better when f Rm (r 2 = 0.71) is used instead of f R3 (r 2 = 0.64). In a few words,
after seeing Figs. 6.11 and 6.12 , it seems that parameter represent much better the
tendency of the experimental shear value (with a coef

≈

cient of correlation, r 2 , close
to the unit, thus, points follow approximately a straight line) for different levels of
compressive strength, when f Rm is used instead of f R3 . Therefore, f R3 residual

strength may not be the most adequate parameter to de ne the shear capacity, as the

average crack width along the failure crack will be smaller.
For low strength concretes shear capacity is reduced, so is reasonable the
compression strength limitation (f ck ≤

60 MPa) according to the EHE-08 [ 14 ]. Only

some points are out of this tendency.
The shear safety margin (SM) obtained as V test /V theo (the shear test value divided
by the shear theoretical value) was used as a reference parameter to compare the
results obtained from the analyzed beams (see plot in Fig. 6.13 ). Theoretical shear
values were calculated by means of the formulation of the

rst complete draft of

Model Code 2010 [ 12 ]. Beams without bers were calculated by applying the most

accurate form (Level III of Approximation), which permits the calculation of ʵ x and

directly calculates the corresponding inclination of the compression stresses ( ʸ ).

Level III of approximation was based directly in the equations of the Modi ed

Compression Field Theory (MCFT) [ 15 ]. The beams with bers were calculated by