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:
M_n = 0.5F*_y t (H_b + 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. 

R_n = F_ywt_w(5k + l_b)           For l_end > H                                                      [AISC 360-22 Section J10.2]
               l_b = H_b
               t_w = t_des of HSS chord = t
               k = t                Consider a conservative 1:1 slope for dispersion in lieu of k = 1.5t.
               F*_y = F_y            for HSS T-Connections
                    = 0.8F_y          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.                                                                            

M_n = F_yZ_eff                                                                                            [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 Z_eff)

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:
M_n = F*_y(B – t) (H_b + 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. 

R_n = F_ywt_w (5k + l_b)       For l_end > H                                                                                 [AISC 360-22 Section J10.2]
               t_w = t_des of HSS chord = t
               k = t                Consider a conservative 1:1 slope for dispersion in lieu of k = 1.5t.
               l_{b =} H_b / sinθ    For θ = 90, l_b = H_b
               F*_y = F_y                  for HSS T-connections
                    = 0.8F_y          for HSS Cross-Connections

Substituting to determine available strength:
R_n = F*_y t [5t + H_b] = F*_y t (H_b + 5t) for l_end > H
R_n = F*_y t [5t + H_b] = F*_y t (H_b + 2. 5t) for l_end < 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. 

M_n = F_yZ_eff                                                                                            [AISC 360-22 Eqn F7-1]

The steps to determine Z_eff 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 (Z_b)

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