2.1.2 Mechanical description of one-way shear force transfer in
2.1.2.4 Mechanisms of shear transfer in cracked concrete
The presence of a crack in a beam induces a redistribution of stresses. Very few or no tension can be transferred through a crack, which is incompatible with the elastic stress distribution shown in Figure 2.1.
Some changes occur in the way the structure bears the bending moments. From now on, the tension in the bottom is transferred by the steel only through the cracks and by steel and concrete (tension stiffening) between two cracks. The compressive zone is slightly affected by the displacement of the neutral axis due to the change of stiffness of the beam at cracking.
However, the changes in shear transfer in the web are the most complicated. After cracking, six shear transfer mechanisms can be distinguished and are described below in Figure 2.8. In these drawings, local truss models inspired by Muttoni et al. (2008) are used. Through the understanding of these different shear transfer actions, conclusions were drown and have been applied in the design procedure developed in this thesis work.
(a) (b)
Figure 2.8 Shear transfer mechanisms in reinforced concrete (a) cracking pattern, (b) direct arch action, (c) shear forces in the uncracked concrete teeth, (d) interface shear transfer, (e) residual tensile stresses through the cracks, (f) dowel effect, (g) truss action: vertical stirrups and inclined struts, (h) tensile stresses due to (c), (d), (e) and (f), (i) final cracking pattern
(a) (b)
(c) (d)
(e) (f)
(i) (g)
B
(h)
A
Concrete strut Concrete tie
Steel tie
(b) Direct arch action
The direct arch action is a process to transfer a load to a support without directly using the vertical tension or shear capacity of the material. The only transfer process is direct compression in the concrete struts and tension in the flexural reinforcement as shown in Figure 2.9.
Figure 2.9 The unique static equilibrium in beams with flexural reinforcement only, according to plasticity theory, neglecting the tensile capacity of concrete, (a) point load, (b) distributed load (Muttoni et al. 2008) The direct arch action is very attractive due to its apparent simplicity. However, the designer should not forget that the capacity of a structure to develop such a stress distribution is limited. Three reasons were distinguished:
- Close to the support in a slender beam, the directions of the compressive arch and the tension tie become very antagonists. Hence, strain incompatibilities may arise that the material is not able to scatter.
- The prismatic compressive strut drawn in Figure 2.9 is an idealised vision.
Actually, the strut will transfer forces to its surrounding by shear action and thus will widen. In order to respect strain compatibilities, tensile stresses will appear perpendicular to the strut. These stresses can lead to cracks which reduce the capacity of the strut.
- A direct concrete arch cannot fully form if the beam is cracked. In the case of a cracked beam, more sophisticated way to transfer shear forces occur and are described below.
The shear transfer of forces by direct arch action is predominant in deep elements like pile caps. The magnitude of the shear transfer of forces by direct “arch action” was shown to be in good agreement with the geometry of the element. For example in Eurocode2, the ratio a/d as defined in the Figure 2.10, is used. It is usually considered that arch action contribution to the overall shear force transfer becomes low for a/d>2.5.
(a) (b)
Figure 2.10 Examples were a significant part of the shear force is transferred by direct arch action, according to Eurocode 2
(c) Shear forces transferred in the uncracked concrete teeth
The uncracked zone of the beam between inclined shear cracks transfers vertical shear forces like in an uncracked beam, namely by orthogonal compressive and tensile stress fields in the web. This shear transfer action is often called cantilever action because the concrete teeth can be seen as bent between the compressive and tensile chords. The contribution of the cantilever action in the overall shear resistance is of increasing importance for beams with high uncracked web height, in prestressed beams and deep beams where crack control is assured for example.
(d) Interface shear transfer
A portion of the vertical shear capacity is provided by forces opposed to the slip direction along the cracks, vci in Figure 2.11.
Figure 2.11 Forces at crack interface
Depending on the situation forces at crack interface can be called aggregate interlock or shear friction. Indeed, these two last expressions point out that the ability to transfer forces along the crack is not only dependant on the material properties, but on the crack geometry as well. Muttoni et al. (1996) distinguished “micro interlocking”
and “macro interlocking” depending on the crack width. Therefore, the more general denomination: “interface shear transfer” is often used nowadays to name the transfer of forces that can occur at a crack interface.
The vertical component of the friction force contributes to the shear capacity of the member.
(e) Residual tensile stresses
It was shown recently that residual tensile forces can be transmitted through narrow cracks. Residual tension is significant for thin cracks 0.05 mm < w < 0.15 mm, these kind of cracks usually occur in thin beams with good crack control. It is not the case in deep members like pile caps, where cracks control is poor and cracks are wide due to size effects.
(f) Dowel action of the longitudinal reinforcement
Dowel action is the transfer of forces by shearing of the flexural steel. Dowel action requires relative displacement of two neighbouring concrete “teeth” in order to shear the flexural steel. This action generates compression and tension in the concrete around the bars. The dowel action of the longitudinal reinforcement is neglected in most compressive field approaches and in the strut-and-tie method. It is often considered that the displacements required to activate the capacity of the flexural bars in shear are too large to occur before failure of the beam. The CEB-FIP Model Code (CEB-FIP90, p115) suggests that a relative displacement between two neighbouring
“concrete teeth” of 0,10 times Φ, the diameter of the steel bars, is required to fully activate the dowel action.
It is considered that dowel action will be negligible in pile caps because the displacements are limited and flexural bars with large diameters are used.
(g) Shear stresses carried by truss action in beams with transverse reinforcement
In a slender beam with vertical or inclined shear reinforcements, the main way to transfer shear forces is by combination of compression in inclined compressive struts and tension in the stirrups, the so-called truss action as illustrated in Figure 2.12.
Figure 2.12 Free body diagram at the end of the beam (ACI 318-08)
For slender elements with stirrups, shear transfer of forces by combined tension in stirrups and compression in the web is overriding. For instance, this is the only shear transfer mechanism considered in the “variable inclination method” used in Eurocode.