Page 106 - Handbook of Materials Failure Analysis

4 Shear Strength Model 101

4.1 INTACT CONCRETE AND AGGREGATE INTERLOCK RESISTANT
CONTRIBUTIONS
The shear-resistant contributions due to concrete are given according to the follow-
ing criterion:

D ¼ 0 ! V C ¼ V i
(5.17)
0 < D < 1 ! V C ¼ V a
One of most used approaches to account for aggregate interlock is by reducing the
transversal elasticity modulus by a factor that depends, essentially, on the diagonal
opening cracks [39,40]. The opening crack measurement is approximated using the
main tensile strain value, ε 1 . Therefore, the updated value of transversal elasticity
modulus is calculated assuming a penalization parameter, μ, for which the value
is in between 0 and 1. This parameter depends on the value of ε 1 and allows updating
Gas μG.
As the damage variable at a given point is a function of its main strain state, as
previously presented, strain ε 1 also governs directly the reduction on concrete trans-
versal stiffness. Thus, intact concrete and aggregate interlock strength contributions
are assessed by the integration of shear stresses along the cross-section of reinforced
concrete finite elements as follows:
Z h
2
V i ¼ Gγ dy
xy
h
2
Z h (5.18)
2
V a ¼ 1 Dð ÞGγ dy
xy
h
2
in which h is the cross-section height.
Therefore, by using convenient Mazars’ damage parameters, A T ,B T ,A C and B C ,
based on experimental analysis, for instance, aggregate interlock is automatically
represented as the transversal mechanical stiffness reduction is consistently modeled
using damage D.
4.2 DOWEL ACTION STRENGTH CONTRIBUTION
The dowel action refers to a shear strength complementary mechanism attributed to
reinforced cracked concrete. This shear-load transfer mechanism occurs when cracks
grow and cut across longitudinal reinforcements, providing an increase into the
mechanical shear strength. Then, the crack lips transfer shear stresses to reinforce-
ments. As a result, a local bending and shear at reinforcements are observed. The
dowel action can increase significantly the structural shear strength as well as the
post-peak ductility of some structural elements, such as beams with few or no shear
reinforcements.
In the proposed nonlinear model, reinforcements are modeled as beams over an
elastic foundation composed by concrete. Therefore, the dowel action behavior
may be affected by several factors, such as reinforcements position along the