Stress Concentration Factors for Simple Tubular T/Y Joints

Axial load - General fixity conditions

T image
$$ \beta = \frac{d}{D} $$
$$ \alpha = \frac{2L}{D} $$
$$ \gamma = \frac{D}{2T} $$
$$ \tau = \frac{t}{T} $$
Location Equation Short chord correction
Chord saddle $\gamma \tau^{1.1} \left( 1.11 - 3 \left(\beta - 0.52\right)^2\right)\left(\sin \theta\right)^{1.6} + C_1\left(0.8\alpha-6\right)\tau\beta^2\left(1-\beta^2\right)^{0.5}\left(\sin\left(2 \theta\right)\right)^2$ F2
Chord crown $\gamma^{0.2}\tau\left(2.65+5\left(\beta-0.65\right)^2\right)+\tau\beta\left(C_2\alpha - 3\right)\sin \theta$ None
Brace saddle $1.3 + \gamma \tau^{0.52}\alpha^{0.1}\left(0.187 - 1.25 \beta^{1.1}\left(\beta - 0.96\right)\right)\left(\sin \theta\right)^{2.7 - 0.01 \alpha}$ F2
Brace crown $3 + \gamma^{1.2} \left( 0.12 \exp\left(-4 \beta \right) + 0.011 \beta^2 - 0.045\right) + \beta \tau \left( C_3 \alpha - 1.2 \right)$ None

Short chord correction factor $\left(\alpha \lt 12 \right)$

$F2 = 1 - \left( 1.43 \beta - 0.97 \beta^2 - 0.03 \right) \gamma^{0.04} \exp \left( -0.71 \gamma^{-1.38} \alpha^{2.5}\right)$

Chord-end fixity parameter

$C_1 = 2(C-0.5)$

$C_2 = C/2$

$C_3 = C/5$

$0.5 \le C \le 1.0$, Typically $C=0.7$