# D1.B.3.3 Calculation Steps

1. 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 = bf / 2tf
• Width to thickness ratio of web reinforcement, F2 = br / tr
• Limiting width to thickness ratio, B1 = 65 / √Fy
• F1 and F2 must not exceed B1.
2. Check for web buckling

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

• Width to thickness ratio of web, W1 = (d – 2tf) / tw
• W1 must not exceed 520/√Fy
3. 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 ao / ho as given below,

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

ao / ho must not exceed 3.0,

If W1 is > 420/√Fy but ≤ 520/√Fy then

ao / ho must not exceed 2.2,

2. ho / d must not exceed 0.7
3. The opening parameter, po = (ao / ho) + (6 ho / d) must not exceed 5.6
4. 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 st ≥ 0.15d, sb ≥ 0.15d

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

a0 / sb≤ 12, a0 / st ≤ 12

5. 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:

 Fytwd/√3 ≤ 4

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

6. Calculation for Maximum Moment Capacity, Mm

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

For unperforated section

Mp = FyZ

ΔAs = hotw - 2Ar

Unreinforced Opening:

$M m = M p [ 1 − Δ A s ( h o 4 + e ) Z ]$

Reinforced Opening:

1. If tw e < Ar

$M m = M p [ 1 − t w ( h o 2 4 + h o e − e 2 ) − A r h o Z ] ≤ M p$
2. If tw e ≥ Ar

$M m = M p [ 1 − Δ A s ( h o 4 + e − A r 2 t w ) Z ] ≤ M p$
7. Calculation for Maximum Shear Capacity, Vm

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

Vpb and Vpt = Plastic shear capacity of the web of the tee

Vpb = Fy tw sb / √3

Vpt = Fy tw st / √3

The values of aspect ratios νb and νt and factors μb and μt(which appear in the equations shown below) are different for reinforced and unreinforced openings.

Unreinforced Opening:

• For the bottom tee, νb = ao / sb and μb= 0
• For the top tee, νt = ao / st and μt = 0

Reinforced Opening:

• st1 and sb1 are used to calculate for n reinforced opening.

st1 = st - Ar / (2bf)

sb1 = sb - Ar / (2bf)

• Pr = Force in reinforcement along edge of opening = Fy Ar ≤ Fytwao / (2√3)
• drt and drb = Distance from outside edge of flange to centroid of reinforcement.

drt = st - ½ tr

drb = sb - ½ tr

For the bottom tee, νb = ao / sb1 and μb = 2Pr drb / (Vpb sb)

For the top tee, νt = ao / st1 and μt = 2Pr drt / (Vpt st)

General Equations:

Using equations given below for αvb and αvt

• αvb = Ratio of nominal shear capacity of bottom tee, Vmb to plastic shear capacity of the web of the tee = (√6 + μb) / (νb + √3) ≤ 1
• αvt = Ratio of nominal shear capacity of top tee, Vmt to plastic shear capacity of the web of the tee = (√6 + μt) / (νt + √3) ≤ 1

Vmb = Vpbavb

Vmt = Vptavt

Vm = Maximum nominal shear capacity at a web opening = Vmb + Vmt

8. Check against Maximum Shear Capacity Vm

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

• Vp = Plastic shear capacity of unperforated web = Fy tw d /√3
• If W1 ≤ 420/√Fy , Vm must not exceed 2/3 Vp
• If W1 > 420/√Fy but ≤ 520/√Fy , Vm must not exceed 0.45 Vp
9. Check against Moment Shear Interaction

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

R1 = Vu / Vm ≤ 1.0

R2 = Mu / Mm ≤ 1.0

R13 + R23 ≤ R3, R ≤ 1.0

10. Corner Radii (for reinforced opening only)

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

• Minimum radii = the greater of 2tw or 5/8 inch
11. 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,

 Rwr = 2Pr

Where:

• Rwr = Required strength of the weld

The reinforcement should be extended beyond the opening by a distance

L1 = ao / 4 or L1 = Ar√3 / (2tw)

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

Rwr = Fy Ar

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

• Af = area of flange = bf⋅tf
1. Ar ≤ Af / 3
2. ao / ho ≤ 2.5
3. V1 = st / tw or V2 = sb / tw

V1 and V2 ≤ 140 / √Fy

4. Mu / (Vu d) ≤ 20

12. Calculation for spacing of openings

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

Rectangular Opening:

S ≥ ho

S ≥ ao (Vu / Vp) / [1 - (Vu / Vp)]

Circular Opening:

S ≥ 1.5 Do

S ≥ Do (Vu / Vp) / [1 - (Vu / Vp)]

13. 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.