Formulas: first-order analysis method

Formula 1

(b) The initial out-of-plumbness in the structure is assumed as $\Delta_{o} / L=1 / 500$ , but the initial out-of-plumbness does not need to be considered in the calculation of $\Delta$ .

\Delta_{o} / L=1 / 500

Formula 2

If this approach is employed, it can be shown that, for $B_{2} \leq 1.5$ and $\tau_{b}=1.0$ , the required additional lateral load to be applied with other lateral loads in a first-order analysis of the structure, using the nominal (unreduced) stiffness, is

B_{2} \leq 1.5

Equation C-A-7-12

N_{i}=\left(\frac{B_{2}}{1-0.2 B_{2}}\right) \frac{\Delta}{L} Y_{i} \geq\left(\frac{B_{2}}{1-0.2 B_{2}}\right) 0.0002 Y_{i}

where

these variables are as defined in Chapter C, Appendix 7, and Appendix 8. Note that if $B_{2}$ based on the unreduced stiffness is set equal to the 1.5 limit prescribed in Chapter C, then

Equation C-A-7-13

N_{i}=2.1\left(\frac{\Delta}{L}\right) Y_{i} \geq 0.00042 Y_{i}

Formula 5

The minimum value of $N_{i}$ of $0.0042 Y_{i}$ assumes a minimum first-order drift ratio, due to any effects, of $\Delta / L=1 / 500$ .

\Delta / L=1 / 500

Found in

FIRST-ORDER ANALYSIS METHOD