Stress Concentration Factors for Simple Tubular X Joints

Axial load - balanced, chord ends fixed

X image
$$ \beta = \frac{d}{D} $$
$$ \alpha = \frac{2L}{D} $$
$$ \gamma = \frac{D}{2T} $$
$$ \tau = \frac{t}{T} $$
Location Equation Short chord correction
Chord saddle $3.87 \gamma \tau \beta \left(1.10-\beta^{1.8}\right)\left(\sin\left(\theta\right)^{1.7}\right)$ F1
Chord crown $\gamma^{0.2}\tau\left(2.65+5\left(\beta-0.065\right)^2\right)-3\tau\beta\sin\left(\theta\right)$ None
Brace saddle $1+1.9\gamma\tau^{0.5}\beta^{0.9}\left(1.09-\beta^{1.7}\right)\left(\sin\left(\theta\right)\right)^{2.5}$ F1
Brace crown $3 + \gamma^{1.2} \left( 0.12 \exp\left(-4 \beta \right) + 0.011 \beta^2 - 0.045\right)$ None

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

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