Check for local buckling of compression flange and reinforcement (if any)

(AISC Design Guide 2 for Web Openings: section 3.7.a.1)

• Width to thickness ratio of compression flange, F₁ = b_f / 2t_f
• Width to thickness ratio of web reinforcement, F₂ = b_r / t_r
• Limiting width to thickness ratio, B₁ = 65 / √F_y
• F₁ and F₂ must not exceed B₁.

Check for web buckling

(AISC Design Guide 2 for Web Openings: section 3.7.a.2)

• Width to thickness ratio of web, W₁ = (d – 2t_f) / t_w
• W₁ must not exceed 520/√F_y

Check for opening dimensions to prevent web buckling

(AISC Design Guide 2 for Web Openings: section 3.7.a.2 & section 3.7.b.1)

1. Limit on a_o / h_o as given below,

   If W₁ is ≤ 420/√F_y then web qualifies as stocky,

   a_o / h_o must not exceed 3.0,

   If W₁ is > 420/√F_y but ≤ 520/√F_y then

   a_o / h_o must not exceed 2.2,

2. h_o / d must not exceed 0.7
3. The opening parameter, p_o = (a_o / h_o) + (6 h_o / d) must not exceed 5.6

Check for tee dimensions

(AISC Design Guide 2 for Web Openings: section 3.7.b.1)

1. The maximum depth of the web opening is governed by the following rules:

   Depth s_t ≥ 0.15d, s_b ≥ 0.15d

2. Aspect ratios of the tees (v = a₀ / s) should not be greater than 12

   a₀ / s_b≤ 12, a₀ / s_t ≤ 12

Check for buckling of tee-shaped compression zone

(AISC Design Guide 2 for Web Openings: section 3.7.a.3)

The tee, which is in compression, is investigated as an axially loaded column. For unreinforced members this is not done when the aspect ratio of the tee is less than or equal to four:

For reinforced openings, this check is only done for large openings in regions of high moment.

Calculation for Maximum Moment Capacity, M_m

(AISC Design Guide 2 for Web Openings: section 3.5.a)

For unperforated section

M_p = F_yZ

ΔA_s = h_ot_w - 2A_r

Unreinforced Opening:

Reinforced Opening:

1. If t_w e < A_r

   $M_m=M_p[1-\frac{t_w(\frac{{h_o}^2}{4}+h_{o}e-e^2)-A_r{h}_o}{Z}]\le M_p$

2. If t_w e ≥ A_r

   $M_m=M_p[1-\frac{\Delta A_s(\frac{h_o}{4}+e-\frac{A_r}{2t_w})}{Z}]\le M_p$

Calculation for Maximum Shear Capacity, V_m

(AISC Design Guide 2 for Web Openings: section 3.6.a)

V_pb and V_pt = Plastic shear capacity of the web of the tee

V_pb = F_y t_w s_b / √3

V_pt = F_y t_w s_t / √3

The values of aspect ratios ν_b and ν_t and factors μ_b and μ_t(which appear in the equations shown below) are different for reinforced and unreinforced openings.

Unreinforced Opening:

• For the bottom tee, ν_b = a_o / s_b and μ_b= 0
• For the top tee, ν_t = a_o / s_t and μ_t = 0

Reinforced Opening:

• s_t1 and s_b1 are used to calculate for n reinforced opening.

s_t1 = s_t - A_r / (2b_f)

s_b1 = s_b - A_r / (2b_f)

• P_r = Force in reinforcement along edge of opening = F_y A_r ≤ F_yt_wa_o / (2√3)
• d_rt and d_rb = Distance from outside edge of flange to centroid of reinforcement.

d_rt = s_t - ½ t_r

d_rb = s_b - ½ t_r

For the bottom tee, ν_b = a_o / s_b1 and μ_b = 2P_r d_rb / (V_pb s_b)

For the top tee, ν_t = a_o / s_t1 and μ_t = 2P_r d_rt / (V_pt s_t)

General Equations:

Using equations given below for α_vb and α_vt

• α_vb = Ratio of nominal shear capacity of bottom tee, V_mb to plastic shear capacity of the web of the tee = (√6 + μ_b) / (ν_b + √3) ≤ 1
• α_vt = Ratio of nominal shear capacity of top tee, V_mt to plastic shear capacity of the web of the tee = (√6 + μ_t) / (ν_t + √3) ≤ 1

V_mb = V_pba_vb

V_mt = V_pta_vt

V_m = Maximum nominal shear capacity at a web opening = V_mb + V_mt

Check against Maximum Shear Capacity V_m

(AISC Design Guide 2 for Web Openings: section 3.7.a.2)

• V_p = Plastic shear capacity of unperforated web = F_y t_w d /√3
• If W₁ ≤ 420/√F_y , V_m must not exceed 2/3 V_p
• If W₁ > 420/√F_y but ≤ 520/√F_y , V_m must not exceed 0.45 V_p

Check against Moment Shear Interaction

AISC Design Guide 2 for Web Openings: section 3.2 & section 3.4)

R1 = V_u / V_m ≤ 1.0

R2 = M_u / M_m ≤ 1.0

R1³ + R2³ ≤ R³, R ≤ 1.0

Corner Radii (for reinforced opening only)

(AISC Design Guide 2 for Web Openings: section 3.7.b.2)

• Minimum radii = the greater of 2t_w or 5/8 inch

Calculation of length of fillet weld (for reinforced opening only)

(AISC Design Guide 2 for Web Openings: section 3.7.b.5)

For reinforcing bars on both sides / on one side of the web:

Fillet welds should be used on both sides of the reinforcement on extensions past the opening. The required strength of the weld within the length of the opening is,

Where:

• R_wr = Required strength of the weld

The reinforcement should be extended beyond the opening by a distance

L₁ = a_o / 4 or L₁ = A_r√3 / (2t_w)

whichever is greater, on each side of the opening. Within each extension, the required strength of the weld is

R_wr = F_y A_r

Additional requirements for reinforcing bars on one side of the web:

• A_f = area of flange = b_f⋅t_f

1. A_r ≤ A_f / 3
2. a_o / h_o ≤ 2.5

3. V1 = s_t / t_w or V2 = s_b / t_w

   V1 and V2 ≤ 140 / √F_y

4. M_u / (V_u d) ≤ 20

Calculation for spacing of openings

(AISC Design Guide 2 for Web Openings: section 3.7.b.6)

Rectangular Opening:

S ≥ h_o

S ≥ a_o (V_u / V_p) / [1 - (V_u / V_p)]

Circular Opening:

S ≥ 1.5 D_o

S ≥ D_o (V_u / V_p) / [1 - (V_u / V_p)]

Check for deflection

The deflection check is performed using the approximate procedure described in section 6.2 of the AISC Design Guide 2 for Web Openings.