Seismic Retrofit of Lap Splices in Nonductile Square Columns Using Carbon Fiber-Reinforced Jackets

ACI Structural Journal, Nov/Dec 2006 by Harries, Kent A, Ricles, James R, Pessiki, Stephen, Sause, Richard

The bond stress-slip behavior, shown in Fig. 1, may be characterized by four regions:

Region 1-Initially, the lugs penetrate the cement matrix. This is characterized by local crushing and microcracking.

Region 2-The plateau of Region 2 is only observed in confined concrete (refer to Table 1). It is characterized by continued crushing of the concrete surrounding the lugs, shearing of the concrete between the lugs, and the appearance of transverse cracking in the member.

Region 3-The decreasing branch results from the reduction in bond due to the formation of longitudinal splitting cracks. More precisely, the loss of frictional bond stress and (very) local confinement to the concrete crushed by the lugs, as the splitting cracks allow the concrete to separate from the reinforcing bar as explained as follows.

Region 4-Residual bond capacity, with bond stress τ^sub f^ , results from the presence of transverse reinforcement, which maintains concrete integrity and provides mechanical interaction with the longitudinal steel. This mechanical interaction may be quite significant in the case of corner bars.

Bond stress distribution

The bond stress-slip relationship is not uniform along the length of a lap splice. Bond stress degradation is a function of the deterioration of the concrete locally and separation of this concrete from the reinforcing bar. The concrete may separate from the bar as a result of concrete dilation and eventual spalling of the cover or as a result of the decrease in the steel sectional area resulting from yielding of the steel (Viwathanatepa et al. 1979). The distribution of bond stress along an embedment length for a monotonic pull-out test may be simplified as being essentially triangular (Viwathanatepa et al. 1979) resulting in the generalization that the average bond stress along the length of a splice is one half the peak bond stress.

Lap splice capacity

Due to varying bond stress along the length of a splice, it is more convenient to consider an average bond stress over the entire splice length. Orangun et al. (1977) propose the following relationship for the average bond stress capacity of a lap splice u'^sub cal^ as the sum of the capacity of the unconfined lap splice ucal and a contribution associated with the presence of transverse reinforcement utr

... (1)

As an empirical expression, Eq. (1) is presented in its original form where required units for each parameter are as follows:

A^sub tr^ = area of transverse reinforcement normal to splitting plane;

c = smallest concrete clear cover;

d^sub b^ = diameter of spliced reinforcement;

f'^sub c^ = compressive strength of concrete;

f^sub yt^ = yield strength of transverse reinforcement;

l^sub s^ = length of lap splice; and

s = spacing of transverse reinforcement;

Orangun et al. (1977) propose the following limits to the parameters of the bond stress equation c/d^sub b^ ≤ 2.5, beyond which a pullout mode of failure dominates the lap splice response; and ..., empirically observed to be the limit of effectiveness of transverse reinforcement.