PSI - Issue 64

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

994

4

2

    

         

2 2 2    1 32 1   −

   

   

   

   

8 

1

8 

e A 

e A 

1

1

1 − +

1

+

+

+

  

2

2

2

W

W

c 

N

pl

pl

c

c

(6)

cr

=

2

N

y

where W pl is the plastic section modulus, M y is the yield moment (= W el ∙ f y ), M p is the full-pastic moment (= W pl ∙ f y ).

Fig. 3. Axial force N and bending moment M trail at midpoint of the member.

2.2. Flexural buckling strength with added reinforcement One way to increase the buckling strength of an eccentrically loaded member is to add a component that enhances its bending stiffness around the buckling axis. This is often done in practical situations using snug tightened bolts at the joint, as shown in Fig. 4. The use of snug-tightened bolts instead of slip-critical bolts means that the reinforcement component only increases the bending stiffness by itself. The strength formula used to assess the reinforcement is based on the following assumptions. • The bending stiffness around the buckling axis will be determined by adding up individual values • The additional reinforcement component is not intended to support any axial force • The bending moment resulting from the second-order effect will be distributed in proportion to the individual bending stiffness value If the extra reinforcement component is the same size as the main member (referred to as the primary member), the formula for strength corresponding to full-plastic strength can be expressed as follows: As shown in Fig. 3, the axial force N and bending moment M , which are located at midpoint of the primary member, can be depicted by a single-pointed line. The point where the lines intersect corresponds to the strength formula (indicated by the legend in red). The formula is derived from the assumption of flexural buckling and remains valid only where this assumption can be applied.