Formulas: Design for Strength Using Allowable Strength Design (ASD)

Formula 1

Using the live plus dead load combinations with $L=3 D$ yields the following relationships.

Equation C-B3-3

Formula 3

Equation C-B3-4

Formula 5

Equation C-B3-5

Formula 7

An alternative way to present the relationship between LRFD and ASD is to consider the ratio of the LRFD demand-to-capacity ratio $\left(D C R_{L R F D}=R_{u} / \phi R_{n}\right)$ to the ASD demand-to-capacity ratio $\left[D C R_{A S D}=R_{a} /\left(R_{n} / \Omega\right)\right]$ (Salmon et al.

Formula 8

Equation C-B3-6

Formula 10

With the parameters $R_{u}=1.2 D+1.6 L, R_{a}=D+L$, and $\Omega=1.5 / \phi$, Equation C-B3-6 will provide ratios of DCRs ranging from 0.830 to 1.067 .

Formula 11

Formula 12

Values of $L / D<3$ have a ratio below unity (indicating ASD is conservative compared to LRFD) and values of $L / D>3$ have a ratio above unity (indicating ASD is unconservative compared to LRFD).

Formula 13

Formula 14

For example, for members in which the ratio of the wind load effect to the dead load effect is high ( $W / D>3$ ), a situation that may be assumed for the design of several elements in a lateral force-resisting system such as diagonal braces and often the columns that support them, the ratio of the DCRs ranged from 0.90 to as high as 1.36 depending on the significance of second-order effects, which were vari

Formula 15

With the exception of $L / D<0.2$, all of the ratios of DCRs exceeded unity, with values exceeding 1.20 for the majority of the range of $B_{2}$ and $L / D$ considered.

Found in

• DESIGN BASIS