Stress Concentration Factors for Simple Tubular T/Y Joints

Axial load - chord ends fixed

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 $\gamma \tau^{1.1} \left( 1.11 - 3 \left(\beta - 0.52\right)^2\right)\left(\sin \theta\right)^{1.6}$ F1
Chord crown $\gamma^{0.2} \tau \left( 2.65 - 5 \left(\beta - 0.65\right)^2\right) + \tau \beta \left(0.25 \alpha - 3 \right) \sin \theta$ None
Brace saddle $1.3 + \gamma \tau^{0.52}\alpha^{0.1}\left(0.187 - 1.25 \beta^{1.1}\left(\beta - 0.96\right)\right)\left(\sin \theta\right)^{2.7 - 0.01 \alpha}$ F1
Brace crown $3 + \gamma^{1.2} \left( 0.12 \exp\left(-4 \beta \right) + 0.011 \beta^2 - 0.045\right) + \beta \tau \left( 0.1 \alpha - 1.2 \right)$ None

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

$F1 = 1 - \left( 0.83 \beta - 0.56 \beta^2 - 0.02 \right) \gamma^{0.23} \exp \left( -0.21 \gamma^{-1.16} \alpha^{2.5}\right)$