STI Limit State Table Derivations

The derivations shown below are intended to demonstrate the equivalence of limit state equations between the current AISC 360-22 Specification and 16th Ed. Manual Part 9 with the prescriptive tables that were previously shown in AISC 360-10 Specification Chapter K.

The following limit state derivations are included:

• 1) Limit State = Local Yielding of HSS Chord Sidewalls
• STI Limit State Table = Moment Table
• Connection = Rectangular HSS-to-Rectangular HSS under In-Plane Moment
• 2) Limit State = Local Yielding of Branches Due to Uneven Load Distribution
• STI Limit State Table = Moment Table
• Connection = Rectangular HSS-to-Rectangular HSS under In-Plane Moment
• 3) Limit State = Local Yielding of HSS Chord Sidewalls
• STI Limit State Table = Moment Table
• Connection = Rectangular HSS-to-Rectangular HSS under Out-of-Plane Moment
• 4) Limit State = Local Yielding of Branches Due to Uneven Load Distribution
• STI Limit State Table = Moment Table
• Connection = Rectangular HSS-to-Rectangular HSS under Out-of-Plane Moment

1) Limit State: Local Yielding of HSS Chord Sidewalls | In-Plane Moment for Rectangular HSS (Refer to Moment Limit State Table M2)

Refer to AISC 360-10 Eqn K3-7:
Mn = 0.5F*y t (Hb + 5t)2                                                                       [AISC 360-10 Eqn K3-7]

Refer to AISC 360-22 Specification Section J10.2 to derive available strength to match AISC 360-10 Eqn K3-7, based on local yielding of rectangular HSS Sidewalls under in-plane moment.

Rn = Fywtw(5k + lb)           For lend > H                                                      [AISC 360-22 Section J10.2]
lb = Hb
tw = tdes of HSS chord = t
k = t                Consider a conservative 1:1 slope for dispersion in lieu of k = 1.5t.
F*y = Fy            for HSS T-Connections
= 0.8Fy          for HSS Cross-Connections
2 Sidewalls
Φ = 1.00, Ω = 1.50

Per Cidect Design Guide 3, pp. 62, moment derived from 2 stress blocks can be represented as:

2) Limit State: Local Yielding of Branches Due to Uneven Load Distribution | In-Plane Moment Conn for Rectangular HSS (Refer to Moment Limit State Table M2)

Refer to AISC 360-22 Specification Section F7 to derive available strength to match AISC 360-10 Eqn K3-8, based on local yielding of rectangular HSS branches due to uneven load distribution under in-plane moment.

Mn = FyZeff                                                                                            [AISC 360-22 Eqn F7-1]

(The approximation ignores the HSS thickness in the last term only which results in a conservative value that underestimates Zeff)

Since the branch member is primarily an axial member rather than a flexural member, the following resistance/safety factors are applied for this limit state:

Φ = 0.95, Ω = 1.58

3) Limit State: Local Yielding of HSS Chord Sidewalls | Out-of-Plane Moment for Rectangular HSS (Refer to Moment Limit State Table M2)

Refer to AISC 360-10 Eqn K3-10:
Mn = F*y(B – t) (Hb + 5t)                                                                      [AISC 360-10 Eqn K3-10]

Refer to AISC 360-22 Specification Section J10.2 to derive available strength to match AISC 360-10 Eqn K3-10, based on local yielding of rectangular HSS Sidewalls under out-of-plane moment.

Rn = Fywtw (5k + lb)       For lend > H                                                                                 [AISC 360-22 Section J10.2]
tw = tdes of HSS chord = t
k = t                Consider a conservative 1:1 slope for dispersion in lieu of k = 1.5t.
lb = Hb / sinθ    For θ = 90, lb = Hb
F*y = Fy                  for HSS T-connections
= 0.8Fy          for HSS Cross-Connections

Substituting to determine available strength:
Rn = F*y t [5t + Hb] = F*y t (Hb + 5t) for lend > H
Rn = F*y t [5t + Hb] = F*y t (Hb + 2. 5t) for lend < H

Φ = 1.00, Ω = 1.50

4) Limit State: Local Yielding of Branches Due to Uneven Load Distribution | Out-of-Plane Moment Conn for Rectangular HSS (Refer to Moment Limit State Table M2)

Refer to AISC 360-22 Specification Section F7 to derive available strength to match AISC 360-10 Eqn K3-11, based on local yielding of rectangular HSS branches due to uneven load distribution under out-of-plane moment.

Mn = FyZeff                                                                                            [AISC 360-22 Eqn F7-1]

The steps to determine Zeff are as follows:

1. Find effective width of the two HSS branch walls transverse to the HSS chord
2. Subtract plastic modulus of non-effective wall area from total HSS plastic modulus (Zb)

Since the branch member is primarily an axial member rather than a flexural member, the following resistance/safety factors are applied for this limit state:

Φ = .95, Ω = 1.58