Formulas: Stiffness for Calculation of Required Strengths

Formula 1

The reduced stiffness, $E I^{*}=0.8 \tau_{b}(E I)_{e f f}$, where $(E I)_{e f f}$ is as calculated in Section I2, and $E A^{*}=0.8\left(E_{s} A_{s}+E_{s} A_{s r}+E_{c} A_{c}\right)$, mirrors that used for bare steel.

Formula 2

Formula 3

This approximates the margin of safety implied in the design provisions for slender composite columns by the effective length procedure, where from Equation I2-3, $\phi P_{n}=0.75\left(0.877 P_{e}\right)=0.66 P_{e}$.

Formula 4

For the case of a structure containing both composite members and highly loaded ( $\alpha P_{r}>0.5 P_{n s}$ ) bare steel members, a conservative approach to avoid a variable stiffness in the analysis would be to apply the additional notional load so that $\tau_{b}=1.0$ can be used for the bare steel members and maintain $\tau_{b}=0.8$ for the composite members.

Formula 5

It is recommended that when using the effective length method with composite compression members that either (a) the nominal stiffness be taken as the effective stiffness, $E I=\left(E I\right)_{e f f}$, and the interaction strength of Section H1.1 be used, or (b) the nominal stiffness be taken as 0.8 times the effective stiffness, $E I=0.8\left(E I\right)_{e f f}$, and the interaction strength be determined using one of the methods described in Commentary Section I5.

Formula 6

the effective length method with composite compression members that either (a) the nominal stiffness be taken as the effective stiffness, $E I=\left(E I\right)_{e f f}$, and the interaction strength of Section H1.1 be used, or (b) the nominal stiffness be taken as 0.8 times the effective stiffness, $E I=0.8\left(E I\right)_{e f f}$, and the interaction strength be determined using one of the methods described in Commentary Section I5.

Found in

• GENERAL PROVISIONS