3107F.2.7 Pile/Deck Connection Strength
The joint shear capacity shall be computed in accordance with ACI 318 [7.7]. For existing MOTs, the method [7.1, 7.2] given below may be used:

Determine the nominal shear stress in the joint region corresponding to the pile plastic moment capacity.
(723)
where:
v_{j} = Nominal shear stress
M_{p} = Over strength moment demand of the plastic hinge (the maximum possible moment in the pile) as determined from the procedure of Section 3107F.2.5.7.
l_{dv} = Vertical development length, see Figure 31F79
D_{p} = Diameter of pile

Determine the nominal principal tension p_{t}, stress in the joint region:
(724)
where:
(725)
is the average compressive stress at the joint center caused by the pile axial compressive force N and h_{d} is the deck depth. Note, if the pile is subjected to axial tension under seismic load, the value of N, and fa will be negative.
If p_{t} < 5.0 √ f '_{c}, psi, joint failure will occur at a lower moment than the column plastic moment capacity M_{p}. In this case, the maximum moment that can be developed at the pile/deck interface will be limited by the joint principal tension stress capacity, which will continue to degrade as the joint rotation increases, as shown in Figure 31F710. The moment capacity of the connection at which joint failure initiates can be established from Equations (727) and (728).
For p_{t} = 5.0 f ' c , determine the corresponding joint shear stress, v_{j}:
(726)

The moment capacity of the connection can be approximated as:
(727)
This will result in a reduced strength and effective stiffness for the pile in a pushover analysis. The maximum displacement capacity of the pile should be based on a drift angle of 0.04 radians.
If no mechanisms are available to provide residual strength, the moment capacity will decrease to zero as the joint shear strain increases to 0.04 radians, as shown in Figure 31F711.
If deck stirrups are present within h_{d}/2 of the face of the pile, the moment capacity, M_{c,r}, at the maximum plastic rotation of 0.04 radians may be increased from zero to the following (see Figure 31F712):
(728)
A_{s} = Area of slab stirrups on one side of joint
h_{d} = See Figure 31F79 (deck thickness)
d_{c} = Depth from edge of concrete to center of main reinforcement
In addition, the bottom deck steel (A_{s}, deckbottom) area within h_{d}/2 of the face of the pile shall satisfy:
(729)

Using the same initial stiffness as in Section 3107F.2.5.4, the momentcurvature relationship established for the pile top can now be adjusted to account for the joint degradation.
The adjusted yield curvature, ϕ'_{y}, can be found from:
(730)
M_{n} is defined in Figure 31F74.
The plastic curvature, ϕ_{p}, corresponding to a joint rotation of 0.04 can be calculated as:
(731)
Where L_{p}, is given by Equation (75).
The adjusted ultimate curvature, ϕ'_{u}, can now be calculated as:
(732)
Note that M_{c,r} = 0 unless deck stirrups are present as discussed above. Examples of adjusted moment curvature relationships are shown in Figure 31F713.
The minimum development length, l_{dc}, is:
(733)
where:
d_{b} = dowel bar diameter
f_{ye} = expected yield strength of dowel
f'_{c} = compressive strength of concrete
In assessing existing details, actual or estimated values for f_{ye} and f'_{c} rather than nominal strength should be used in accordance with Section 3107F.2.1.1.
When the development length is less than that calculated by the Equation (733), the moment capacity shall be calculated using a proportionately reduced yield strength, f_{ye,r}, for the vertical pile reinforcement:
(734)
where:
l_{d} = actual development length
f_{ye} = expected yield strength of dowel