PSI - Issue 64

Atsushi Sato et al. / Procedia Structural Integrity 64 (2024) 991–998 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

993

3

N



(

)

sec

(2)

M N u e N e = + =  

2

c

N

2

z l =

0

N 0 is the Eular buckling strength, and the member length, l , defines it. Moreover, the normalized slenderness ratio is defined by Eq. (4).

2

2 y EI



N

(3)

=

0

l

N N

y

(4)

 =

c

0

where e is the amount of eccentricity that is the perpendicular distance between the loading point to C.G. of the buckling axis, N is the subjected axial force, EI y is the bending stiffness around the minor axis (i.e., buckling axis), l is member length, N y is axial yield strength (= A ∙ f y ), A is gross area, and f y is yield unit stress.

a)

b)

Fig. 2. Loading conditions: (a) Eccentric axial load in the member; (b) Equivalent coupling forces.

In Fig. 3, the axial force N and bending moment M are shown at the midpoint of the member (indicated by the dotted line). The figure is based on an example using an angle-L150×150×10, with a slenderness ratio (  c ) of 2.0 and an eccentricity ( e ) of 14.14mm. Two straight lines on the figure represent different criteria: Eq. (5a) corresponds to the point where the outermost fibre reaches the yield unit stress ( f y ), while Eq. (5b) corresponds to the full-plastic strength of the cross-section. The intersection of these lines defines the strength formula, indicated by the legend in blue.

y y N M N M p N M N M y

1.0

(5a,)

+ =

1.0

(5b)

+ =

The strength formula corresponding to the full-plastic strength can be expressed as follows: