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Width of boundary element

Figure 4.44. Shear wall example; schematic reinforcement.

Width of boundary element

Figure 4.44. Shear wall example; schematic reinforcement.

The vertical extension of the boundary element must not be less than lw = 366 in. or ^ controls

4Vu 1400 Confinement of 16 X 75 in. Boundary Elements.

Confinement Perpendicular to the Wall. Maximum allowable spacing of hoops and crossties, assuming #5 bars, smax = 0.25 X minimum member dimensions = 0.25 X 16 = 4 in. (Controls) = 6 X diameter of longitudinal bar = 6 X 1.41 = 8.5 in.

(14 - bx \ „ (14 - 10> jr/,„. = = 4 + (J = 4 + (-3-j =533 in.

The required cross-sectional area of confining reinforcement Ash, in the 16 X 75 in. boundary elements, using s = 4 in., is given by

Jy where hc = cross-sectional dimension of boundary element measured center-to-center of confining reinforcement.

In our case, hc = 16 - (3 + 3) + 1.41 + 0.625 = 12 in.

No. 5 hoops with two legs provide Ash = 2 X 0.31 = 0.62 in.2 > 0.36 in.2

Confinement Parallel to the Wall.

With two hoops consisting of two legs each, and five crossties,

Ash provided = 9 x 0.31 = 2.79 in.2 > 2.13 in.2 OK

In most designs, special boundary elements may not be required by calculations for the entire height of walls. However, to prevent buckling of boundary longitudinal elements even in cases where they are not needed by design, Section 21.7.6.5 requires transverse ties not exceeding a vertical spacing of 8 in., if the vertical reinforcement ratio is greater than 400/fy. The transverse reinforcement shall consist of either single or overlapping hooks. As in ductile columns, crossties are permitted. For calculating the ratio 400/f,, only the reinforcement within the wall boundary element is included.

Using the most common value of fy = 60,000 psi, the ratio 400/f, = 400/60,000 = 0.0067. If the ratio of vertical reinforcement is greater than this value, then hoops supplemented with crossties are required. What if the ratio of vertical bars placed in between the boundary zones is greater than 0.0067? Do they also need to be tied? Yes, but only if the vertical reinforcement ratio is greater than 0.01, or where the vertical reinforcement is required as a compression reinforcement. See Section 14.3.6. A schematic placement of reinforcement is shown in Fig. 4.45. A construction photograph of a shear wall in zone 4 is shown in Fig. 4.45 a.

4.2.9.10. Special Reinforced Concrete Coupled Shear Walls

Given. A 40-ft-long by 16-inch-thick shear wall with openings as shown in Fig. 4.46. The shear wall forms part of a lateral load-resisting system of a 10-story concrete building located in a high seismic zone. A computer analysis has been performed for the building using code-prescribed lateral forces and gravity loads. The analysis typically has provided moment and shear forces for each coupling beam, and moments, shear forces, and axial forces for each wall segment commonly referred to as wall pier. In modeling the shear walls, effective section properties, rather than gross properties, are used as required by most current codes.

The first step in design is the determination of ultimate design values, generally the Pu, Mu, and Vu using code-specified load combinations. Typically, the design of an element such as a wall pier or a coupling beam is verified for a number of design load combinations. This is because several lateral load analyses are performed to account for changes in load directions, minimum eccentricities in each direction, uplift and downward effects of seismic loads, etc. Computation of design values using different load combinations that includes several lateral load analyses is indeed a major task invariably necessitating use of computers. Without dwelling on this further, we will proceed with the design of coupling beam CB1 and wall pier W1 by presupposing the following ultimate design values.

CB1 Vu = 300 kips

Mu = 12,000 kip-ft, left end Mu = 8000 kip-ft, right end

Wall pier W1 Pu = 1500 kips Vu = 210 kips Mu = 45,000 kip-ft.

Provide confinement reinf. max spacing of 8", if vert. reinf. ratio of boundary reinf. > 400/y

No lap splices permitted in the region of anticipated plastic hinge. Mechanical splices OK. Outside of plastic hinge regions, stagger splices to avoid weak sections. See1999 Blue Book Commentary, Section C 402.7 for lap splice recommendations.

Figure 4.45. Wall elevation showing schematic placement of reinforcement.

Figure 4.45a. Photograph of a shear wall in seismic zone 4 showing wall-pier and boundary-element reinforcement. (Photo courtesy of Mr. Walter Steimle, John A. Martin and Assoc., Los Angeles, CA.)

Coupling beam CB2

Wall pier W2

Coupling beam CB2

Wall pier W2

Wall pier W1

Wall pier W2 Wall pier W3

Wall pier W1

Wall pier W2 Wall pier W3

8'-0"

6'-0"

12'-0"

6'-0"

8'-0"

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