(New)Boundary Elements of Special Structural Walls

Notation

A_s = area of nonprestressed longitudinal tension reinforcement, in²
A_g = gross area of concrete section, in²
A_ch = cross-sectional area of a member measured to the outside edges of transverse reinforcement, in.²
A_cv = gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered in the case of walls, and gross area of concrete section in the case of diaphrams. Gross area is total area of defined section minus area of any openings, in.²
A_v = area of shear reinforcement within spacing s, in.²
b = width of compression face of member, in.
c = distance from extreme compression fiber to neutral axis, in.
f_c^' = specified compressive strength of concrete, psi
√f_c‘ = square root of specified compressive strength of concrete, psi
f_y = specified yield strength for nonprestressed reinforcement, psi
f_yt = specified yield strength of transverse reinforcement, psi
h = overall thickness, height, or depth of member, in.
h_u = laterally unsupported height at extreme compression fiber of wall or wall pier, in. equivalent to l_u for compression members
h_w = height of entire wall from base to top, or clear height of wall segment or wall pier considered, in.
h_wcs = height of entire structural wall above the critical section for flexural and axial loads, in.
h_x =maximum center-to-center spacing of longitudinal bars laterally supported by corners of crossties or hoop legs around the perimeter of a column or wall boundary element, in.
l_n = length of clear span measured face-to-face of supports, in.
l_u = unsupported length of column or wall, in.
l_w = length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.
M_u = factored moment at section, in.-lb
V_e = design shear force for load combinations including earthquake effects, lb
V_u = factored shear force at section, lb
ρ_s = ratio of volume of spiral reinforcement to total volume of core confined by the spiral, measured out-to-out of spirals
δ_c = wall displacement capacity at top of wall, in.
δ_u = design displacement, in.

According to ACI 18.10.6.2; wall or wall piers with h_wcs/l_w ≥ 2.0 that are designed to have a single critical section for flexure and axial loads and are effectively continuous from the base of structure to top of wall should satisfy two conditions given below;

1. Compression zones should be reinforced with special boundary elemants where ACI Eq. (18.10.6.2a) is satisfied. c means the largest neutral axis depth calculated for the factored axial force and nominal moment strength consistent with the direction of the design displacement δ_u.
   Minimum δ_u/h_wcs ratio is 0.005

   

2. If special bounday elements are reqired by Condition 1, then (a) and either (b) or (c) should be satisfied. (a), (b) and (c) are given below.

   1. Transverse reinforcement of special boundary element should extend vertical below and above the critical section at least the maximum value of l_w and M_u/4V_u.

   2. b ≥ (0.025*l*c_w)^0.5

   3. δ_c /h_wcs ≥ 1.5δ_u /h_wcs and the maximum δ_c /h_wcs ratio is 0.015.

      

According to ACI 18.10.6.3; structural walls not designed in accordance with ACI 18.10.6.2 should have special boundary elements at boundaries and edges around openings of structural walls where the maximum extreme fiber compressive stress exeeds 0.2f_c^'. The special boundary element can be discontinued where the compressive stress is less than 0.15f_c^'. Compressive stress is calculated by using factored loads including earthquake effects.

According to ACI 18.10.6.4; if special boundary elements are reqired by ACI 18.10.6.2 or 18.10.6.3, conditions given below should be satisfied;

1. The boundary element shall extend horizontally from the extreme compression fiber a distance at least the greater of c – 0.1l_w and c/2.

2. Minimum width of the flexural compression zone, b, over the horizontal distance calculated by condition 1 , including flange if present, should be h_u /16.

3. For walls or wall piers with h_w/l_w ≥ 2.0 that are designed to have a single critical section for flexure and axial loads, and with c/l_w ≥ 3/8 , minimum width of the flexural compression zone b over the length calculated in condition 1 should be 12 in.

4. In flanged sections, the boundary element should include the effective width in compression and should extend at least 12 in. into the web.

5. The boundary element transverse reinforcement should be satisfied column transverse reinforcement requirements ACI 18.7.5.2 and ACI 18.7.5.3. Instead of "one fourth of the minimum column length" in ACI 18.7.5.3, “one-third of the least dimension of the boundary element” should be used.

6. Maximum transverse reinforcement spacing h_x between laterally supported longitudinal bars around the perimeter of the boundary element is the lesser of 14 in. and two-thirds of the boundary element thickness. Lateral support should be provided by a seismic hook of a crosstie or corner of a hoop. The maximum length of a hoop leg is two times the boundary element thickness, and adjacent hoops shall overlap at least the lesser of 6 in. and two-thirds the boundary element thickness.

7. The amound of transverse reinforcement should be in accordance with ACI Table 18.10.6.4(g);
   

8. Concrete within the thickness of the floor system at the special boundary element location should have specified compressive strength at least 0.7f_c^'. (f_c^' is concrete compressive strength of the wall).

9. For a distance above and below the critical section, web vertical reinforcement should have lateral support provided by the corner of a hoop or by a crosstie with seismic hooks at each end. Maximum transverse reinforcement spacing is 12 in. and diameter shoud satisfied ACI 25.7.2.2.

10. If the critical section occurs at the wall base, transverse reinforcement of the boundary element at the wall base shoul extend into the support at least l_d in accordance with ACI 18.10.2.3, of the largest longitudinal reinforcement in the special boundary element. Where the special boundary element terminates on a footing, mat, or pile cap, special boundary element transverse reinforcement should extend at least 12 in. into the footing, mat, or pile cap, unless a greater extension is required by ACI 18.13.2.4.

11. Horizontal reinforcement in the wall web should extend to within 6 in. of the end of the wall. Reinforcement should be anchored to develop fy within the confined core of the boundary element using standard hooks or heads. Where
    the confined boundary element has sufficient length to develop the horizontal web reinforcement, and A_sf_y/s of the horizontal web reinforcement does not exceed A_sf_yt/s of the boundary element transverse reinforcement parallel to the horizontal web reinforcement, it shall be permitted to terminate the horizontal web reinforcement without a standard hook or head.

According to ACI 18.10.6.5; if special boundary elements are not reqired by ACI 18.10.6.2 or 18.10.6.3, conditions given below should be satisfied;

1. Except where V_u in the plane of the wall is less than λ√f_c‘A_cv, horizontal reinforcement terminating at the edges of structural walls without boundary elements shall have a standard hook engaging the edge reinforcement or the edge reinforcement should be enclosed in U-stirrups having the same size and spacing as, and spliced to, the horizontal reinforcement.

2. If the maximum longitudinal reinforcement ratio is greater than 400/f_y , boundary transverse reinforcement should satisfy ACI 18.7.5.2 (except 18.7.5.2(e)) over the distance calculated in accorance with ACI 18.10.6.4(a) (condition 1). The vertical transverse reinforcement spacing at the wall boundary should be in accordance with ACI Table 18.10.6.5(b).