Design of Reinforced Concrete Shear wall

Design code: ACI 318-05

• Design of shear reinforcement
• Shear strength of concrete
• Shear reinforcement
• Effective depth
• Maximum shear strength permitted
• Location of Critical Section
• Minimum shear reinforcement
• Bar placement
• Design of Flexural reinforcement

Design of shear reinforcement

1. The shear strength, fV_n  must equal or be greater than the factored shear, V_u

        fV_n ³ V_u                                           ACI eq (11-1)

where f = 0.75 is strength reduction factor, and 

        V_n = V_c + V_s                                             ACI eq (11-2)

where V_c is shear strength of concrete, and V_s is strength of shear reinforcement.

Shear strength of concrete

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

a. V_c = 2 Öf_c' h d

Or the lesser of

b. V_c = 3.3 Öf_c' h d + N_u d/ (4 l_w)            ACI eq (11-29)

c. V_c = { 0.6 Öf_c' + l_w ( 1.25 Öf_c' + 0.2 [N_u/(l_w* h)]) /( M_u/V_u - l_w/2)} h d        ACI eq (11-30)

        (It does not apply when M_u/V_u - l_w/2 < 0)

where f_c' is compressive strength of concrete, 

h is thickness of the wall, 

d is effective depth,

l_w is overall length of wall.

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

M_u is moment parallel to the direction of the wall.

Shear reinforcement

When V_u > f V_c, 

shear strength provided by horizontal shear reinforcement shall be calculated aS

V_s = A_v f_y d /s                                        ACI eq. (11-31)

where A_v is area of reinforcement, f_y is yield strength of reinforcement, d is effective depth, and s is spacing of reinforcement.

Maximum shear strength permitted

fV_n = 10 Öf_c'                                     ACI section 11.10.3

Effective depth

1. d = 0.8 l_w

_{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. l_w /2

whichever is smaller.

Minimum shear reinforcement

When f V_c > V_u ³ 0.5 f V_c

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

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

 r_l = 0.0025 + 0.5 (2.5 - h_w/ l_w )( r_t - 0.0025)  ³ 0.0025                      ACI eq. (11-32)

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

When V_u < 0.5 f V_c

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 f_y  > 6000 psi

b. 0.0025 for deformed bars #5 or larger.

Bar placement

1. Maximum spacing of  horizontal reinforcement

    a. l_w /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: 

fM_n ³ M_u   

2. Load bearing shear wall

Design as a column subject to axial load and bending

fP_n ³ P_u   

fM_n ³ M_u   

Location of flexural reinforcement:

Flexural reinforcement shall be placed at each end of walls

Design examples