# Tubular Joint Calculation

12.4.9.1.1 Punching Shear

Vp = Tf sin#

where f is the nominal axial, in-plane bending, or out-of-plane bending stressing the brace.

 FIGURE 12.19 Geometric parameters for a tubular joint. t, brace thickness; g, gap between brace; T, chord thickness; d, brace diameter; D, chord diameter; в, brace angle measured from the chord.

The allowable punching shear stress in the chord wall is lower than the AISC shear allowable value or

Vpa = QqQf (fyc/0-6g)

Qf = 1.0 – XyA2

where

X = 0.30 for brace axial stress = 0.045 for brace in-plane bending stress = 0.021 for brace out-of-plane bending stress

Qf = 1.0 when all extreme fiber stresses in the chord are tensile.

The value of Qq will be obtained from Table 12.9.

Qe = 0.3/((1 – 0.833в)) For p> 0.6

Qe = 1.0 For в < 0.6

Qg = 1.8 – 0.1(g/T) For у < 20

Qg = 118- 4(g/D) For у > 20

In any case, Qg should be higher than or equal to 1.0.

Joint classification of K, T and Y, or cross should apply to individual braces according to their load pattern for each load case. To be considered a K joint, the punching load in a brace should be essentially balanced by loads on

TABLE 12.9

Values of Qq

 Axial Compression Axial Tension In-Plane Bending Out-of-Plane Bending K (gap) T and Y Cross without diaphragms Cross with diaphragm (1.10 + 0.2/e)Qg (1.10 + 0.2/в) (1.10 + 0.20/в) (0.75 + 0.20/e)Qe (1.10 + 0.20/в) (3.27 + 0.67/в) (1.37 + 0.67/e)Qe

other braces in the same plane on the same side of the joint. In T and Y joints, the punching load is reached as a beam shear in the chord. In cross joints, the punching load is carried through the chord to the braces on the opposite side.

12.4.9.1.2 Allowable Joint Capacity

The allowable joint capacity will be calculated as follows:

Pa = QuQfFycT 2/1.7 sin<9
Ma = QuQfFyCT 2/1.7 sinfl(0.8d)

Pa and Ma are the allowable capacity for the brace axial load and the bending moment, respectively. Values of Qu are shown in Table 12.10.