Coupling Beam Design (v12)

Notation

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_cw = area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear, in².
A_g = gross area of concrete section, in²
A_sh = total cross-sectional area of transverse reinforcement, including crossties, within spacing s and perpendicular to dimension b_c, in.²
b_c = cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area A_sh, in.
b_w = width of compression face of member, in.
c₁ = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, in.
c₂ = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c₁, 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_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.
l_n = length of clear span measured face-to-face of supports, in.
l_w = length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.
s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.
s_o = center-to-center spacing of transverse reinforcement within the length l_o, in.
V_n = nominal shear strength, lb
α = angle definin the orientation of reinforcement

According to ACI 18.10.7.1; coupling beams with with (l_n/h) ≥ 4 should satisfy the requirements of Beams of Special Moment Frames (ACI 18.6). In addition, the wall boundary is designed as a column. If it can be shown by analysis that the beam has sufficient lateral stability, the following two provisions specified in ACI 18.6.2.1 need not to be satisfied;

• Minimum width b_w should be lesser of 0.3h and 10 in.

• Projection of the beam width beyond the width of the supporting column on each side should be less than than the smallest value of c₂ and 0.75c₁.

According to ACI 18.10.7.2, coupling beams with with (l_n/h) < 4 and with V_u ≥ 4λ√f_c^‘A_cw should be reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan.

According to ACI 18.10.7.3, coupling beams not governed bu ACI 18.10.7.1 or 18.10.7.2 can be reinforced either with two intersecting groups of diagonally placed bars symmetrical about the midspan or with the wall boundary is designed as a column.

According to ACI 18.10.7.3, Coupling beams reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan should satisfy the conditions given below;

• V_n is be calculated by ACI Eq. (18.10.7.4);

  

  α is the angle between the diagonal bars and the longitudinal axis of the coupling beam.

• Each group of diagonal bars shall consist of a minimum of four bars provided in two or more layers.

According to ACI 18.10.7.3, Coupling beams reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan should satisfy either of the two conditions given below;

1. Each diagonal bars group should be enclosed bu rectilinear transverse reinforcement having out-to-out dimensions of at least b_w/2 in the b_w direction and b_w/5 along the other sides. The transverse reinforcement should satisfy ACI 18.7.5.2, and minimum transverse reinforcement area A_sh is given below;

   

   The transverse reinforcement spacing should be satisfy ACI Eq. (18.7.5.3) and not exceeding 6d_b of the smallest diagonal bars, and the maximum spacing of crossties or legs of hoops is 14 inches.

   

   The transverse reinforcement should continue through the intersection of the diagonal bars. At the intersection, it is permitted to modify the arrangement of the transverse reinforcement provided the spacing and volume ratio requirements are satisfied. Additional longitudinal and transverse reinforcement should be distributed around the beam perimeter with total area in each direction of at least 0.002b_ws and spacing not exceeding 12 in.

2. The transverse reinforcement should satisfy ACI 18.7.5.2 for the entire beam cross-section and minimum transverse reinforcement area A_sh is given below;

   

   Maximum longitudinal spacing of transverse reinforcement is the lesser of 6 in. and 6d_b of the smallest diagonal bars. Maximum Spacing of crossties or legs of hoops both vertically and horizontally in the plane of the beam cross section should be 8 in. Each crosstie and each hoop leg shall engage a longitudinal bar of equal or greater diameter.