A single #4 loop around four diagonal bars with two legs gives Ash = 0.40 in.2 Hence, #4 ties at 4-inch spacing are OK for the bursting steel requirements.

Note in our example, the core dimensions of diagonal reinforcement are the same in both directions. In a general case, with differing cross-section dimensions, Ash is calculated for each direction.

Wall pier-

Wall pier boundary element

Use crossties ^ to confine development length ld

Wall pier boundary element

Wall pier horizontal and vertical reinf.

Wall pier

Figure 4.49. Coupling beam with diagonal reinforcement. Each diagonal reinforcement must consist of at least four bars with closely spaced ties. Use wider closed ties or crossties at central intersection. Use crossties to confine development length €d.

By Section (d), diagonal bars are required to be developed for tension into the wall piers. This is shown in Fig. 4.49 where the diagonal bars extend a distance of ld beyond the face of the wall pier. Instead of loops, crossties are used along the development length and at the intersection of diagonal bars at the center of diagonal beam.

In addition to the reinforcement calculated thus far, supplemental horizontal and vertical reinforcements are required by Sections 11.8.4 and 11.8.5. The intent of additional reinforcement is to contain the concrete outside the diagonal cores, in case the concrete is damaged by earthquake loading. Since the diagonal reinforcement is designed to resist the entire shear and flexure in the coupling beam, additional transverse and longitudinal reinforcement acts primarily as a basketing reinforcement to contain concrete that may spall. It is not necessary to develop the horizontal bars into the wall piers.

The minimum reinforcement, Av, perpendicular to the longitudinal axis of the coupling beam (meaning vertical reinforcement) shall not be less than Av > O.OO25 bws (Section 11.8.4). The area of horizontal (longitudinal) reinforcement, Avh, shall not be less than O.OO15 bws2, and s2 shall not exceed d/5 or 12 in. (Section 11.8.5).

For the example beam, assuming #4 @ eight loops as vertical reinforcement,

= a2 x 2 x 12 = o.6O in.2 > O.OO25bws = O.OO25 x 16 x 8 = O.32 in.2 OK

Assuming six #4 horizontal bars at each face,

Avh > O.OO25 bw x h = O.OO25 x 16 x 50 = 2 in.2 < 6 x 2 x O.2 = 2.4 in.2 OK A schematic section of the coupling beam is shown in Fig 4.5O. Shear Design. For the example pier W1, Vu = 300 kips. The parameter ac, the coefficient defining the relative contribution of concrete shear strength to the total

6- #4 bars, — coupling beam horizontal reinforcement, each face

#4 @ 8"Q coupling beam vertical reinforcement

Wall pier vertical reinforcement

Wall pier horizontal reinforcement

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