Formulas: Adjustments to Stiffness

Formula 1

Reduced stiffness $\left(E I^{*}=0.8 \tau_{b} E I\right.$ and $\left.E A^{*}=0.8 \tau_{b} E A\right)$ is used in the direct analysis method for two reasons.

Formula 2

Formula 3

This is roughly equivalent to the margin of safety implied in the design provisions for slender columns by the effective length procedure where, from Equation E3-3, $\phi P_{n}=0.90\left(0.877 P_{e}\right)=0.79 P_{e}$.

Formula 4

The $\tau_{b}$ factor is similar to the inelastic stiffness reduction factor implied in the column curve to account for loss of stiffness under high compression loads $\left(\alpha P_{r}>0.5 P_{n s}\right)$, and the 0.8 factor accounts for additional softening under combined axial compression and bending.

Formula 5

It is for this reason that the beam-column interaction for in-plane flexural buckling is checked using an axial strength, $P_{n L}$, calculated from the column curve using the actual unbraced member length, $L_{c}=L$, in other words, with $K=1.0$.

Formula 6

The stiffness reduction may be taken conservatively as $E A^{*}=0.8 E A$ and $E I^{*}=0.8 E I$ for all cases.

Formula 7

Found in

• CALCULATION OF REQUIRED STRENGTHS