Formulas: General Analysis Requirements

Formula 1

For sway columns with nominally simply supported base conditions, the errors in the second-order internal moment and in the second-order displacements from a $P-\Delta$-only analysis are generally smaller than $3 \%$ and $5 \%$, respectively, when $\alpha P_{r} / P_{e L} \leq 0.05$,

Formula 2

$P_{e L}=\pi^{2} E I / L^{2}$ if the analysis uses nominal stiffness, kips (N)

Formula 3

uses nominal stiffness, or $1.5\left(0.8 \tau_{b} E I / L\right)$ if the analysis uses a flexural stiffness reduction of $0.8 \tau_{b}$, the errors in the second-order internal moments and displacements from a $P-\Delta$-only analysis are generally smaller than $3 \%$ and $5 \%$, respectively, when $\alpha P_{r} / P_{e L} \leq 0.12$.

Formula 4

Notional loads, $N_{i}$, would also be defined using 1.0 times ASD load combinations, in other words, $\alpha=1.0 . \tau_{b}$ would be redefined as $\tau_{b}=1.0$ when $P_{r} / P_{n s} \leq 0.3$ and $\tau_{b}=4\left(P_{r} / 0.6 P_{n s}\right)\left(1-P_{r} / 0.6 P_{n s}\right)$ when $P_{r} / P_{n s}>0.3$.

Formula 5

Formula 6

Formula 7

Found in

• CALCULATION OF REQUIRED STRENGTHS