When considering reinforced concrete design, “Bond” refers to the adhesion or the shear stress that is occurring between the concrete and the steel in a loaded member. This bond is the reason that makes the steel and concrete as a single unit without the cause of any slip. The assumption is simple beam theory that the plane sections remain plane after bending will be only satisfied if there is no kind of slip between the steel and the concrete.
Local Bond is defined as the magnitude of the bond stress at any point on the structural element between the reinforcement and the concrete. As shown in the figure below, the value will vary depending on the variation of bending moment along the section of the element.
Fig.1: Bond Stress – Local Bond; This stress is flexural in nature. The variation of tension with the change in the moment is shown.
Now, in order to support the full development of tension in the steel that is placed at the mid-section of the beam, it is required to be anchored on both the sides of the section. This will help to attain full tension capacity of the reinforced steel by the beam structure. Now the average stress that is acting along the anchorage length is called as the average anchorage bond. The average value is taken for design as the value of the local bond will vary along the length of the anchorage. The figure-2 shows the anchorage bond stress.
|Fig.2: Anchorage Bond Stress|
Development length in tension can be defined as the length or an extension that has to be provided on either side of the point of maximum tension in the steel in order to stop the chances of exceeding of average bond stress. When this has to be ensured in compression steel, we call it as Development length in Compression.
When mild steel bars were used, it was necessary to consider both the local bond and the development length in routine design checks. But when the use of high bond bars came, more importance was given to the development length of the local bond. This is because in high bond bars mechanics is more complex and undergo not only adhesion but also the mechanical locking due to the presence of projection on it. These are shown in figure-3. The development length is given by Ld . The calculation of development length varies with different codes.
|Fig.3: Nature of Bond in smooth (a) and (b) deformed reinforcement bars|
The local bond or the flexural bond is specified with respect to any point in any location of the R.C.C member. It is defined as the rate of change of the tension in steel at the given point in the R.C.C member. When the mild steel smooth reinforcement bars are considered, the local bond have great importance. The magnitude of the flexural bond at a point can be calculated by the following expression.
Considering a distance dx over the length of the R.C.C beam, let T be the increase in tension as from the figure-1. Then we have,
T = dM/jd eq.1
If u is the local bond stress and ∑O is the perimeter of the steel that is provided, then corresponding tension acting at perimeter is u * (∑O)
The tension acting in distance dx is,
u * (∑O) * dx eq.2
Equating eq.1 and eq.2 we get,
u * (∑O) * dx = dM/jd,
The mechanism of the bond between the reinforcement bars and the concrete will vary for the mild smooth bars and the deformed bars (Figure-3). Hence the above local bond stress is not valid for ribbed steel bars. The projection for the deformed bars is designed such a way that the local bond stresses are not taken place. Hence this is not calculated for ribbed bars.
The reinforcement anchorage is due to the:
- Ø Concrete and Steel adhesion
- Ø Concrete shear strength
- Ø Ribs interlocking with the concrete
This is prominent is the high bond bars. The codes recommend that the average bond stress which is developed along the full length of the bar surface which is placed in the concrete must be safe for ultimate loads also. The below is the value of bond stress for plain bars which are in tension. This is as per Indian Code IS: 456-2000. The Clause is 22.214.171.124- Table 10.2
Fig.4: A picture shot of Table.10.1 from IS:456-2000
The length of the bar that is necessary in order to attain the full strength of the reinforcement bar is called as the development length Ld. The figure -5 shows the development length provision and its necessity.
Fig.5. The need for extending the bar by a distance of d beyond the theoretical cut-off point
The expression for Ld is derived by considering the yield strength in tension as 0.87fy
(Taking 0.87fy as steel design strength for compression)
When actual reinforcement that is provided is greater than the theoretical one, the actual stress is less than the full stress. Hence the development length required may be reduced by the following relationship.
This principle is followed in the design of footings and other short bending bars where the bond is considered very critical. The bond requirement can be satisfied by considering small sized bars or more steel. Always keep in mind that the Ld is calculated from the point of maximum stress. IS 456 gives simple rules for the Ld provision compared to other codes like BS and ACI.
The steel reinforcement for both tension and compression will be extended beyond the theoretical length. This length extended will be equal to the effective depth of the structural element d or 12 times the diameter of the bar – whichever is greater is considered. This length is called as the anchorage length La . The need for an extension is explained in the figure-5. Any formation of diagonal cracks will result in the steel force that is corresponding to X and not Y. This value of La will be part of the Ld development length.