3107F.2.7.1 Joint Shear Capacity

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:

1. Determine the nominal shear stress in the joint region corresponding to the pile plastic moment capacity.

   (7-23)

   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 31F-7-9

   D_p = Diameter of pile

   

2. Determine the nominal principal tension p_t, stress in the joint region:

   (7-24)

   where:

   (7-25)

   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 31F-7-10. The moment capacity of the connection at which joint failure initiates can be established from Equations (7-27) and (7-28).

   

   For p_t = 5.0 f ' c , determine the corresponding joint shear stress, v_j:

   (7-26)

3. The moment capacity of the connection can be approximated as:

   (7-27)

   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 31F-7-11.

   

   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 31F-7-12):

   (7-28)

   A_s = Area of slab stirrups on one side of joint

   h_d = See Figure 31F-7-9 (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:

   (7-29)

   

4. Using the same initial stiffness as in Section 3107F.2.5.4, the moment-curvature 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:

   (7-30)

   M_n is defined in Figure 31F-7-4.

   The plastic curvature, ϕ_p, corresponding to a joint rotation of 0.04 can be calculated as:

   (7-31)

   Where L_p, is given by Equation (7-5).

   The adjusted ultimate curvature, ϕ'_u, can now be calculated as:

   (7-32)

   Note that M_c,r = 0 unless deck stirrups are present as discussed above. Examples of adjusted moment curvature relationships are shown in Figure 31F-7-13.