7.5design procedure

AISC 358-22, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications

Last Updated 29 Oct 2026

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Step 1. Compute the probable maximum moment at the plastic hinge, $M_{p r}$ , in accordance with Section 2.4.3, where $Z_{e}=Z_{b}=$ plastic section modulus of the beam.

Step 2. Check beam flange tensile rupture. To preclude a net section rupture of the beam flange, the net section of the beam section shall satisfy the following:

R_{t} F_{u b} Z_{b, \text { net }} \geq R_{y} F_{y b} Z_{b}

(7.5-1)

where

$F_{y b} \quad$ = specified minimum yield stress of beam, ksi (MPa)
$F_{u b} \quad$ = specified minimum tensile strength of beam, ksi (MPa)
$\begin{aligned} R_{t} & =\text { ratio of expected tensile strength to specified minimum tensile strength }\end{aligned}$
$R_{y}$ = ratio of expected yield stress to specified minimum yield stress
$\begin{aligned} Z_{b} & =\text { plastic section modulus of the beam, in. }^{3}\left(\mathrm{~mm}^{3}\right)\end{aligned}$
$Z_{b, \text { net }}=$ plastic section modulus of net section of the beam at location of the plastic hinge, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

User Note: $Z_{b, \text { net }}$ of the beam may be computed by accounting for only the holes in the tension flange, or more simply, $Z_{b, \text { net }}$ of the beam may be computed by accounting for the holes in both flanges. Note that if the former approach is employed, the plastic neutral axis will not be at the mid-depth of the beam. If the latter approach is employed, the calculations are simpler, and the requirement of Equation 7.5-1 may be met with a maximum bolt-hole diameter that is determined by

d_{\text {hole }} \leq\left[\frac{Z_{b}}{2 t_{f}\left(d-t_{f}\right)}\right]\left(1-\frac{R_{y} F_{y}}{R_{t} F_{u}}\right)-\frac{1}{16} \text { in. }

(7.5-2)

d_{\text {hole }} \leq\left|\frac{Z_{b}}{2 t_{f}\left(d-t_{f}\right)}\right|\left(1-\frac{R_{y} F_{y}}{R_{t} F_{u}}\right)-2 \mathrm{~mm}

(7.5-2M)

where

$d \quad$ = depth of beam, in. (mm)

$d_{\text {hole }}=$ nominal hole diameter for bolts between flange plate and beam flange as specified in AISC Specification Table J3.3 or Table J3.3M, in. (mm)

$t_{f} \quad$ = thickness of the beam flange, in. (mm)

After the maximum bolt hole diameter is determined, the maximum bolt diameter can be determined from AISC Specification Table J3.3 or Table J3.3M.

Step 3. Assume a flange plate thickness, $t_{p}$ . Estimate the width of the flange plate, $b_{f p}$ , considering bolt gage, bolt edge distance requirements, and the beam flange width. Determine the controlling nominal shear strength per bolt considering bolt shear and bolt bearing:

$r_{n}=\min\left\{\begin{array}{l}1.0F_{nv}A_{b}\\ 2.4F_{ub}d_{b}t_{f}\\ 2.4F_{up}d_{b}t_{p}\end{array}\right.$ (7.5-3)

where

$A_{b}=$ nominal unthreaded body area of bolt, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$
$F_{n v}=$ nominal shear stress of bolt from the AISC Specification, ksi (MPa)

$F_{u b}=$ specified minimum tensile strength of beam material, ksi (MPa)

$F_{u p}=$ specified minimum tensile strength of plate material, ksi (MPa)

$d_{b}=$ nominal diameter of bolt, in. (mm)

$t_{f} \quad$ = thickness of beam flange, in. (mm)

$t_{p} \quad$ = thickness of flange plate, in. (mm)

Step 4. Select a trial number of bolts.

User Note: The following equation may be used to estimate $n$ , the trial number of bolts rounded to the next higher even number increment:

n \geq \frac{1.25M_{p r}}{\phi_{n}r_{n}(d+t_{p})}\qquad(7.5\text{-}4)

where $d =$ depth of beam, in. (mm)

Step 5. Determine the distance of the plastic hinge from the face of the column, $S_{h}$ .

S_{h}=S_{1}+s\left(\frac{n}{2}-1\right)

(7.5-5)

where

$S_{1}=$ distance from face of column to nearest row of bolts, in. (mm)
$n$ = number of bolts
$s \quad=$ spacing of bolt rows, in. (mm)

The bolt spacing between rows, $s$ , and the edge distance shall be sufficiently large to ensure that $l_{c}$ , as defined in the AISC Specification, is greater than or equal to $2 d_{b}$ .

Step 6. Compute the shear force at the plastic hinge, $V_{h}$ , in accordance with Section 2.4.4.

Step 7. Calculate the probable maximum moment at the face of the column, $M_{f}$ , in accordance with Section 2.4.5.

Step 8. Compute $F_{p r}$ , the force in the flange plate due to $M_{f}$ .

F_{p r}=\frac{M_{f}}{\left(d+t_{p}\right)}

(7.5-6)

Step 9. Confirm that the number of bolts, $n$ , selected in Step 4 is adequate:

n \geq \frac{F_{p r}}{\phi_{n} r_{n}}

(7.5-7)

Step 10. Check that the thickness of the flange plate assumed in Step 3 is adequate:

\frac{F_{p r}}{d F_{y} b_{f p}} \quad(7.5-8)

where

$\begin{aligned} F_{y} & =\text { specified minimum yield stress of flange plate, ksi (MPa) } \\ b_{f p} & =\text { width of flange plate, in. (mm) }\end{aligned}$

Step 11. Check the flange plate for the limit state of tensile rupture:

F_{p r} \leq \phi_{n} R_{n}

(7.5-9)

where $R_{n}$ is defined in the tensile rupture provisions of AISC Specification Section J4.1.

Step 12. Check the beam flange and the flange plate for the limit state of block shear rupture:

F_{p r} \leq \phi_{n} R_{n}

(7.5-10)

where $R_{n}$ is as defined in the block shear rupture provision in AISC Specification Section J4.3.

Step 13. Check the flange plate for the limit state of buckling.

F_{p r} \leq \phi_{n} R_{n}

(7.5-11)

where $R_{n}$ is defined in AISC Specification Section J4.4.

User Note: When checking compression buckling of the flange plate, the effective length, $K L$ , may be taken as $0.65 S_{1}$ .

User Note: Some iteration from Steps 3 through 13 may be required to determine an acceptable flange plate size.

Step 14. Check the design shear strength of beam in accordance with the AISC Specification.

The required shear strength of the beam shall be determined in accordance with Section 2.5.

Step 15. Design the beam web-to-column connection.

The beam web-to-column connection shall be a single-plate shear connection meeting the requirements of the AISC Specification.

The required shear strength of the single-plate connection shall be taken equal to the required shear strength of the beam, and shall be assumed to be located at the face of the column.

Step 16. Check the continuity plate requirements in accordance with Section 2.6.

Step 17. Check the panel zone in accordance with Section 2.7.

When computing the required panel zone shear strength, the depth of the panel zone shall be taken as the depth of the beam plus the thickness of one flange plate.

Step 18. Check the column-beam moment ratio in accordance with Section 2.8.

End of chapter · NextChapter 8 Welded unreinforced flange-welded web (WUF-W) moment connection

7.5design procedure

AISC 358-22, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications

Last Updated 29 Oct 2026

Hover any section to copy its link or text, ask Copilot about it, or bookmark it.

Step 1. Compute the probable maximum moment at the plastic hinge, $M_{p r}$ , in accordance with Section 2.4.3, where $Z_{e}=Z_{b}=$ plastic section modulus of the beam.

Step 2. Check beam flange tensile rupture. To preclude a net section rupture of the beam flange, the net section of the beam section shall satisfy the following:

R_{t} F_{u b} Z_{b, \text { net }} \geq R_{y} F_{y b} Z_{b}

(7.5-1)

where

$F_{y b} \quad$ = specified minimum yield stress of beam, ksi (MPa)
$F_{u b} \quad$ = specified minimum tensile strength of beam, ksi (MPa)
$\begin{aligned} R_{t} & =\text { ratio of expected tensile strength to specified minimum tensile strength }\end{aligned}$
$R_{y}$ = ratio of expected yield stress to specified minimum yield stress
$\begin{aligned} Z_{b} & =\text { plastic section modulus of the beam, in. }^{3}\left(\mathrm{~mm}^{3}\right)\end{aligned}$
$Z_{b, \text { net }}=$ plastic section modulus of net section of the beam at location of the plastic hinge, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

d_{\text {hole }} \leq\left[\frac{Z_{b}}{2 t_{f}\left(d-t_{f}\right)}\right]\left(1-\frac{R_{y} F_{y}}{R_{t} F_{u}}\right)-\frac{1}{16} \text { in. }

(7.5-2)

d_{\text {hole }} \leq\left|\frac{Z_{b}}{2 t_{f}\left(d-t_{f}\right)}\right|\left(1-\frac{R_{y} F_{y}}{R_{t} F_{u}}\right)-2 \mathrm{~mm}

(7.5-2M)

where

$d \quad$ = depth of beam, in. (mm)

$d_{\text {hole }}=$ nominal hole diameter for bolts between flange plate and beam flange as specified in AISC Specification Table J3.3 or Table J3.3M, in. (mm)

$t_{f} \quad$ = thickness of the beam flange, in. (mm)

After the maximum bolt hole diameter is determined, the maximum bolt diameter can be determined from AISC Specification Table J3.3 or Table J3.3M.

$r_{n}=\min\left\{\begin{array}{l}1.0F_{nv}A_{b}\\ 2.4F_{ub}d_{b}t_{f}\\ 2.4F_{up}d_{b}t_{p}\end{array}\right.$ (7.5-3)

where

$A_{b}=$ nominal unthreaded body area of bolt, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$
$F_{n v}=$ nominal shear stress of bolt from the AISC Specification, ksi (MPa)

$F_{u b}=$ specified minimum tensile strength of beam material, ksi (MPa)

$F_{u p}=$ specified minimum tensile strength of plate material, ksi (MPa)

$d_{b}=$ nominal diameter of bolt, in. (mm)

$t_{f} \quad$ = thickness of beam flange, in. (mm)

$t_{p} \quad$ = thickness of flange plate, in. (mm)

Step 4. Select a trial number of bolts.

User Note: The following equation may be used to estimate $n$ , the trial number of bolts rounded to the next higher even number increment:

n \geq \frac{1.25M_{p r}}{\phi_{n}r_{n}(d+t_{p})}\qquad(7.5\text{-}4)

where $d =$ depth of beam, in. (mm)

Step 5. Determine the distance of the plastic hinge from the face of the column, $S_{h}$ .

S_{h}=S_{1}+s\left(\frac{n}{2}-1\right)

(7.5-5)

where

$S_{1}=$ distance from face of column to nearest row of bolts, in. (mm)
$n$ = number of bolts
$s \quad=$ spacing of bolt rows, in. (mm)

The bolt spacing between rows, $s$ , and the edge distance shall be sufficiently large to ensure that $l_{c}$ , as defined in the AISC Specification, is greater than or equal to $2 d_{b}$ .

Step 6. Compute the shear force at the plastic hinge, $V_{h}$ , in accordance with Section 2.4.4.

Step 7. Calculate the probable maximum moment at the face of the column, $M_{f}$ , in accordance with Section 2.4.5.

Step 8. Compute $F_{p r}$ , the force in the flange plate due to $M_{f}$ .

F_{p r}=\frac{M_{f}}{\left(d+t_{p}\right)}

(7.5-6)

Step 9. Confirm that the number of bolts, $n$ , selected in Step 4 is adequate:

n \geq \frac{F_{p r}}{\phi_{n} r_{n}}

(7.5-7)

Step 10. Check that the thickness of the flange plate assumed in Step 3 is adequate:

\frac{F_{p r}}{d F_{y} b_{f p}} \quad(7.5-8)

where

$\begin{aligned} F_{y} & =\text { specified minimum yield stress of flange plate, ksi (MPa) } \\ b_{f p} & =\text { width of flange plate, in. (mm) }\end{aligned}$

Step 11. Check the flange plate for the limit state of tensile rupture:

F_{p r} \leq \phi_{n} R_{n}

(7.5-9)

where $R_{n}$ is defined in the tensile rupture provisions of AISC Specification Section J4.1.

Step 12. Check the beam flange and the flange plate for the limit state of block shear rupture:

F_{p r} \leq \phi_{n} R_{n}

(7.5-10)

where $R_{n}$ is as defined in the block shear rupture provision in AISC Specification Section J4.3.

Step 13. Check the flange plate for the limit state of buckling.

F_{p r} \leq \phi_{n} R_{n}

(7.5-11)

where $R_{n}$ is defined in AISC Specification Section J4.4.

User Note: When checking compression buckling of the flange plate, the effective length, $K L$ , may be taken as $0.65 S_{1}$ .

User Note: Some iteration from Steps 3 through 13 may be required to determine an acceptable flange plate size.

Step 14. Check the design shear strength of beam in accordance with the AISC Specification.

The required shear strength of the beam shall be determined in accordance with Section 2.5.

Step 15. Design the beam web-to-column connection.

The beam web-to-column connection shall be a single-plate shear connection meeting the requirements of the AISC Specification.

The required shear strength of the single-plate connection shall be taken equal to the required shear strength of the beam, and shall be assumed to be located at the face of the column.

Step 16. Check the continuity plate requirements in accordance with Section 2.6.

Step 17. Check the panel zone in accordance with Section 2.7.

When computing the required panel zone shear strength, the depth of the panel zone shall be taken as the depth of the beam plus the thickness of one flange plate.

Step 18. Check the column-beam moment ratio in accordance with Section 2.8.

End of chapter · NextChapter 8 Welded unreinforced flange-welded web (WUF-W) moment connection