Table K3.2

Available Strengths of Rectangular HSS-to-HSS Truss Connections

Connection Type Connection Available Axial Strength

Gapped K-Connections

Figure description:

Technical diagram of a Gapped K-Connection involving rectangular hollow structural sections (HSS:

• Main Member (Chord: Specified by height ($H$, width ($B$, and wall thickness ($t$.
• Branch Members: Two diagonal members with height ($H_b$, width ($B_b$, and wall thickness ($t_b$, applied axial load ($P$, and connection angle ($\theta$.
• Connection Geometry:
  • $g$: Gap distance between the two branch members on the chord face.
  • $e$: Eccentricity, indicating the vertical offset between the branch axes intersection and the chord centerline.

Overlapped K-Connections

Figure description:

Key Information: Overlapped K-Connection

• Connection Type: Overlapped K-connection joining two diagonal branch members (labeled i and j to a main horizontal chord.
• Chord Dimensions:
  • $B$: Chord width
  • $H$: Chord height
  • $t$: Chord wall thickness
• Branch Dimensions (Members i & j:
  • $B_b$: Branch width
  • $H_b$: Branch height/depth
  • $t_b$: Branch wall thickness
• Geometric & Structural Parameters:
  • $\theta$: Angle between the branch and the chord.
  • $e$ (Eccentricity: Vertical distance between the chord's longitudinal axis and the intersection point of the branches' axes.
  • $P$: Axial force applied to branch members.
• Configuration Detail: Branch i overlaps branch j at the junction on the chord surface.

Note that the force arrows shown for overlapped K-connections may be reversed; i and j control member identification.

Limit state: chord wall plastification, for all $\beta$ $P_{n}\sin \theta =F_{y}t^{2}\left( 9.8\beta _{eff}\gamma ^{0.5}\right) Q_{f}$ (K3-7) $\phi =0.90$ (LRFD) $\Omega =1.67$ (ASD) Limit state: shear yielding (punching), when $B_{b}<B-2t$ This limit state need not be checked for square branches. $P_{n}\sin \theta =0.6F_{y}tB\left( 2\eta +\beta +\beta _{eop}\right)$ (K3-8) $\phi =0.95$ (LRFD) $\Omega =1.58$ (ASD) Limit state: shear of chord side walls in the gap region Determine $P_{n}\sin \theta$ in accordance with Section G4. This limit state need not be checked for square chords. Limit state: local yielding of branch/branches due to uneven load distribution This limit state need not be checked for square branches or where $B/t\geq 15$. $P_{n}=F_{yb}t_{b}\left( 2H_{b}+B_{b}+B_{e}-4t_{b}\right)$ (K3-9) $\phi =0.95$ (LRFD) $\Omega =1.58$ (ASD)

Limit state: local yielding of branch/branches due to uneven load distribution $\phi=0.95(\text{LRFD})$ $\Omega=1.58(\text{ASD})$ When $25\%\le O_v<50\%$ $P_{n,i}=F_{ybi}t_{bi}\left[\frac{O_v}{50}(2H_{bi}-4t_{bi})+B_{eoi}+B_{eov}\right]$ (K3-10) When $50\%\le O_v<80\%$ $P_{n,i}=F_{ybi}t_{bi}\left(2H_{bi}-4t_{bi}+B_{eoi}+B_{eov}\right)$ (K3-11) When $80\%\le O_v\le100\%$ $P_{n,i}=F_{ybi}t_{bi}\left(2H_{bi}-4t_{bi}+B_{bi}+B_{eov}\right)$ (K3-12) $B_{eoi}=\frac{10}{B/t}\left(\frac{F_y t}{F_{ybi}t_{bi}}\right)B_{bi}\le B_{bi}$ (K3-13) $B_{eov}=\frac{10}{B_{bj}/t_{bj}}\left(\frac{F_{ybj}t_{bj}}{F_{ybi}t_{bi}}\right)B_{bi}\le B_{bi}$ (K3-14) Subscript $i$ refers to the overlapping branch. Subscript $j$ refers to the overlapped branch. $P_{n,j}=P_{n,i}\left(\frac{F_{ybj}A_{bj}}{F_{ybi}A_{bi}}\right)$ (K3-15)

Functions

$\beta_{eff}=\left[\left(B_{b}+H_{b}\right)_{compression\ branch}+\left(B_{b}+H_{b}\right)_{tension\ branch}\right]/4B$ (K3-16) $\beta_{eop}=\frac{B_{ep}}{B}$ (K3-17)