Effective Width in Rectangular HSS Connections
HSS Connection Design
Effective Width in Rectangular HSS Connections
Finding Be and Bep for use in branch and weld checks with rectangular HSS · AISC 360-22 Section K1.2a
When a force is applied normal to the flat face of a rectangular HSS, it does not spread evenly across the connected element. The HSS face is stiffer near the rounded corners, where the sidewalls clamp it, and more flexible at the center. Load follows stiffness, so it concentrates toward the edges of the branch or plate.
Because the edges carry more load, forces do not distribute evenly across the full width of the connected element. Design equations capture this by using an effective width: the reduced width treated as fully active. There are two, Be for local yielding and Bep for shear yielding (punching, where the branch tends to punch through the chord face). This guide shows how to find them for the connection types where they apply.
WHAT THIS GUIDE COVERS
Finding Be and Bep for use in checks for branch local yielding and shear yielding (punching) (the member), and effective weld length (the weld). The capacity calculations themselves can be found in the examples and tables referenced on the back.
WHAT THIS GUIDE COVERS
The connecting face behaves like a fixed-end beam, stiff at the corners and flexible at the center, so it draws load toward the edges.
THE STRESS PEAKS AT THE EDGES
Because the edges carry the most stress, the design equations concentrate the load over the effective width Be, split between the two edges, and ignore the lightly loaded center.
AISC 360-22
LOCAL YIELDING · EQ. K1-1
SHEAR YIELDING (PUNCHING) · EQ. K1-2
Both Be and Bep are capped at the actual width Bb: if the formula gives a value ≥ Bb, the full width is effective and there is no reduction. A thinner chord (small t), wider chord (large B), or stronger/thicker branch all shrink the effective width. Other connection types use related forms, shown per type on the back. In the HSS-to-HSS truss equations, Bep appears as the dimensionless ratio βeop = Bep/B.
CHECKING THE BRANCH MEMBERS
Local yielding & punching shear
Be sets the effective width for local yielding of the branch or plate; Bep sets it for punching shear, where the branch tends to punch through the chord face. Both check the strength of the connection.
CHECKING THE WELD
Local yielding & punching shear
Be also sets the effective length of the transverse weld (e.g. le = 2Be for a plate, per Table K5.1). Bep is a member check only and is not used here.
VARIABLES USED CONSISTENTLY THROUGHOUT THIS GUIDE
CHORD (MAIN MEMBER)
B connecting face width
H chord depth
t chord wall design thickness
Fy chord yield strength
BRANCH OR PLATE
Bb branch/plate width
Hb branch height (HSS branch)
tb branch wall thickness (= tp for a plate)
Fyb branch/plate yield strength
RESULT & GEOMETRY
Be effective width, local yielding
Bep effective width, shear yielding
βeop = Bep/B, ratio form used in truss equations
le effective weld length
θ angle between branch and chord
HSS Connection Type
Finding Be and Bep
For the connection types where these checks apply, the table below shows how each behaves and the equations that define Be (local yielding) and Bep (punching shear).
Connections shown in elevation, branch(es) welded to the chord face. Graphics: AISC Design Guide 24, 2nd Ed.
CONNECTION
ELEVATION
CONNECTION BEHAVIOR
EFFECTIVE WIDTH EQUATIONS
Transverse plate
Plate across the chord face
AISC DG24, Table 8-2, p. 225
The full plate width reduces to Be for the check of local yielding of the branch plate, and to Bep for the check of shear yielding (punching).
Be: AISC 360-22 Eq. K1-1, with tb = tp and Bb = plate width.
Bep: AISC 360-22 Eq. K1-2.
T-, Y- & cross
HSS branch, axial load
AISC DG24, Table 9-2, p. 255
The two branch walls across the face reduce to Be for
local yielding and to Bep for punching shear. The two walls
parallel to the chord sit over the stiff zone and stay fully
effective.
Be: AISC 360-22 Eq. K1-1, with tb = branch wall thickness.
Bep: AISC 360-22 Eq. K1-2, utilized in the punching-shear check as the ratio βeop = Bep/B.
Gapped K
Two branches, a gap
between them
AISC DG24, Table 9-2, p. 256
Opposing branch forces stiffen the inner region, so only
each branch’s outer (heel) wall reduces to Be for local
yielding (Bep applies for punching shear). The other three
walls stay fully effective.
Be: AISC 360-22 Eq. K1-1, applied to the outer wall of each branch.
Bep: AISC 360-22 Eq. K1-2, utilized in the punching-shear check as the ratio βeop = Bep/B.
Overlapped K
One branch laps over the other
AISC DG24, Table 9-2, p. 256
The outer wall of each branch reduces, with effective widths that depend on the relative stiffness of all three members and the percent overlap. At high overlap, more
of the overlapping branch becomes effective.
Be: the overlap-case equations in AISC 360-22 Table K3.2 (Eq. K3-10 to K3-12), selected by percent overlap.
Bep: not applicable. Neither AISC 360-22 nor DG24 requires a punching-shear check for overlapped K-connections; the overlapping branches transfer load directly to each other rather than solely through the chord face.
Moment (T-connection)
In-plane & out-of-plane bending
AISC DG24, Table 10-2, pp. 308–309
Same as T/Y/cross: the branch walls across the face
reduce to Be (local yielding) and Bep (punching shear); the
walls parallel to the chord carry the force couple due to
bending but stay fully effective.
Be: AISC 360-22 Eq. K1-1, applied to the transverse walls.
Bep: AISC 360-22 Eq. K1-2.
Two limits to remember: The effective width equations are empirical, valid only inside the connection’s limits of applicability (chord/branch yield ≤ 52 ksi, width ratios, slenderness, gap/overlap geometry); outside them, rational analysis is required. See STI’s HSS Limits of Applicability article. Also, the member effective width reduction applies to square & rectangular HSS only; round HSS do not use Be (though its welds have their own effective length rules).
MORE ON Be AND Bep
COMPANION TOOL · THE WELD SIDE
HSS Effective Weld Length Calculator
Turns Be into effective weld length and weld group properties (Table K5.1) for plate-to-HSS and HSS-to-HSS connections.
EVERY LIMIT STATE EQUATION
STI HSS Limit State Tables
The free tables of every HSS connection limit state equation (360-22), for each connection type. Pairs with the Limits of Applicability article cited in the note above.
BACKGROUND ON THE MECHANISM
Local Yielding Due to Uneven Load
Distribution
The STI article by Mike Manor covering the mechanism, the derivation, and the branch local yielding check this guide condenses.
DESIGN EXAMPLES THAT USE THIS CHECK
Transverse flange plate (moment). WF-to-HSS moment connection, AISC 360-22, including the plate local yielding check.
Overlapped K-connection. AISC 360-22 example covering branch local yielding due to uneven load distribution and the hidden-toe-weld question.