D1.B.3.3 Calculation Steps

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, F_{1} = b_{f} / 2t_{f}
 Width to thickness ratio of web reinforcement, F_{2} = b_{r} / t_{r}
 Limiting width to thickness ratio, B_{1} = 65 / √F_{y}
 F_{1} and F_{2} must not exceed B_{1}.

Check for web buckling
(AISC Design Guide 2 for Web Openings: section 3.7.a.2)
 Width to thickness ratio of web, W_{1} = (d – 2t_{f}) / t_{w}
 W_{1} 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)

Limit on a_{o} / h_{o} as given below,
If W_{1} is ≤ 420/√F_{y} then web qualifies as stocky,
a_{o} / h_{o} must not exceed 3.0,
If W_{1} is > 420/√F_{y} but ≤ 520/√F_{y} then
a_{o} / h_{o} must not exceed 2.2,
 h_{o} / d must not exceed 0.7
 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)

The maximum depth of the web opening is governed by the following rules:
Depth s_{t} ≥ 0.15d, s_{b} ≥ 0.15d

Aspect ratios of the tees (v = a_{0} / s) should not be greater than 12
a_{0} / s_{b}≤ 12, a_{0} / s_{t} ≤ 12


Check for buckling of teeshaped 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:
F_{y}t_{w}d/√3 ≤ 4 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_{y}Z
ΔA_{s} = h_{o}t_{w}  2A_{r}
Unreinforced Opening:
${M}_{m}={M}_{p}[1\frac{\Delta {A}_{s}(\frac{{h}_{o}}{4}+e)}{Z}]$Reinforced Opening:

If t_{w} e < A_{r}
${M}_{m}={M}_{p}[1\frac{{t}_{w}(\frac{{{h}_{o}}^{2}}{4}+{h}_{o}e{e}^{2}){A}_{r}{h}_{o}}{Z}]\le {M}_{p}$ 
If t_{w} e ≥ A_{r}
${M}_{m}={M}_{p}[1\frac{\Delta {A}_{s}(\frac{{h}_{o}}{4}+e\frac{{A}_{r}}{2{t}_{w}})}{Z}]\le {M}_{p}$


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_{y}t_{w}a_{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_{pb}a_{vb}
V_{mt} = V_{pt}a_{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 W_{1} ≤ 420/√F_{y} , V_{m} must not exceed 2/3 V_{p}
 If W_{1} > 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
R1^{3} + R2^{3} ≤ R^{3}, 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,
R_{wr} = 2P_{r} Where:
 R_{wr} = Required strength of the weld
The reinforcement should be extended beyond the opening by a distance
L_{1} = a_{o} / 4 or L_{1} = 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}
 A_{r} ≤ A_{f} / 3
 a_{o} / h_{o} ≤ 2.5

V1 = s_{t} / t_{w} or V2 = s_{b} / t_{w}
V1 and V2 ≤ 140 / √F_{y}

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.