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# Design of Reinforced Concrete Shear wall

## Design of shear reinforcement

1. The shear strength, fVn  must equal or be greater than the factored shear, Vu

fVn ³ Vu                                           ACI eq (11-1)

where f = 0.75 is strength reduction factor, and

Vn = Vc + Vs                                             ACI eq (11-2)

where Vc is shear strength of concrete, and Vs is strength of shear reinforcement.

### Shear strength of concrete

2. Shear strength of concrete shear wall shall be calculated as

a. Vc = 2 Öfc' h d

Or the lesser of

b. Vc = 3.3 Öfc' h d + Nu d/ (4 lw)            ACI eq (11-29)

c. Vc = { 0.6 Öfc' + lw ( 1.25 Öfc' + 0.2 [Nu/(lw* h)]) /( Mu/Vu - lw/2)} h d        ACI eq (11-30)

(It does not apply when Mu/Vu - lw/2 < 0)

where fc' is compressive strength of concrete,

h is thickness of the wall,

d is effective depth,

lw is overall length of wall.

Nu is axial force, positive for compression, negative for tension,

Mu is moment parallel to the direction of the wall.

### When Vu>f Vc,

shear strength provided by horizontal shear reinforcement shall be calculated aS

Vs = Av fy d /s                                        ACI eq. (11-31)

where Av is area of reinforcement, fy is yield strength of reinforcement, d is effective depth, and s is spacing of reinforcement.

### Maximum shear strength permitted

fVn = 10 Öfc'                                     ACI section 11.10.3

### Effective depth

1. d = 0.8 lw

2. Calculate based on strain compatibility analysis (same as in a beam section).

### Location of Critical Section

1. One-half of the wall height.

2. lw /2

whichever is smaller.

### Minimum shear reinforcement

#### Whenf Vc > Vu³0.5f Vc

1.  Minimum horizontal shear reinforcement ratio to gross section area, rt = 0.0025.

2. Minimum vertical shear reinforcement ratio to gross section area,

rl = 0.0025 + 0.5 (2.5 - hw/ lw )( rt - 0.0025)  ³ 0.0025                      ACI eq. (11-32)

and need not be greater than  calculated based on ACI eq. 11-31.

#### When Vu< 0.5f Vc

1. Minimum vertical wall reinforcement: (Section 14.3.2)

a. 0.0012 for deformed bars smaller than #5 and fy > 6000 psi

b. 0.0015 for deformed bars #5 or larger

2. Minimum horizontal wall reinforcement: (Section 14.3.3)

a. 0.0020 for deformed bars smaller than #5 and fy  > 6000 psi

b. 0.0025 for deformed bars #5 or larger.

### Bar placement

#### 1. Maximum spacing of  horizontal reinforcement

a. lw /5.  b. 3 h   c. 18 inches.

2. Bar shall be placed uniformly across the length and height of walls

## Design of Flexural reinforcement

### 1. Non-load bearing shear wall

Design as a cantilever beam:

fMn ³ Mu

### 2. Load bearing shear wall

Design as a column subject to axial load and bending

fPn ³ Pu

fMn ³ Mu

### Location of flexural reinforcement:

Flexural reinforcement shall be placed at each end of walls