Formulas: Slender Element Members Excluding Round HSS

Equation C-E7-1

where

• $E=\operatorname{modulus}$ of elasticity, ksi (MPa)
• $b=$ width of stiffened compression element, in. (mm)
• $f$ = critical stress when slender element is not considered, ksi (MPa)
• $t=$ thickness of element, in. (mm)

Equation C-E7-2

This may be compared with the generalized effective width, Equation E7-3:

where

$F_{e l}$ is the local elastic buckling stress, and $c_{1}$ is the empirical correction factor typically associated with imperfection sensitivity. The two expressions are essentially equivalent if one recognizes that

Equation C-E7-3

where

$\mathrm{v}=\mathrm{Poisson}^{\prime} \mathrm{~s}$ ratio

= 0.3

Formula 4

and utilizes $k=4.0$ for the stiffened element, $c_{1}=0.18$ for the imperfection sensitivity factor, and sets $f=F_{n}$.

Formula 5

At the limiting width-to-thickness ratio, $\lambda=\lambda_{r}, b=b_{e}$, and $F_{e l}=F_{e l-r}$; therefore, at this limit, local elastic buckling implies

Formula 6

Equation C-E7-4

Equation C-E7-6

which may be used to back-calculate the plate buckling coefficient, $k$, assumed in Table B4.1a:

Equation C-E7-7

This relationship provides a prediction of the elastic local buckling stress consistent with the $k$ implicit in Table B4.1a, after substitution:

Equation C-E7-8

Equation C-E7-9

Equation C-E7-10

Equation C-E7-11

Equation C-E7-12

where

$c_{3}$ is the constant associated with slenderness limits given in Table B4.1a (Geschwindner and Troemner, 2016). Combining the constants in Equation C-E7-12 with $c_{4}=c_{2} c_{3}$ and $c_{5}=c_{1} c_{2} c_{3}$ yields

Formula 15

Combining the constants in Equation C-E7-12 with $c_{4}=c_{2} c_{3}$ and $c_{5}=c_{1} c_{2} c_{3}$ yields

Formula 16

Equation C-E7-13

Found in

• MEMBERS WITH SLENDER ELEMENTS