PSI - Issue 17

Ivan Baláž et al. / Procedia Structural Integrity 17 (2019) 734 – 741 Ivan Baláž, Yvona Koleková, Lýdia Moroczová / Structural Integrity Procedia 00 (2019) 000 – 000

7

740

Approximate value of relative critical force and critical force are according to a) Hetényi (1971) and b) authors:

0.2 2  − +   k

k

F

F

0

cr 

a)

,

,

b)

F cr 

kEI

(29)

cr



2

Formula (29a) is represented in figure 5 by bold dotted straight line. It gives F cr on unsafe side. Formula (29b) is represented by parallel line above it. Coordinates of the intersection points (figure 5):

3 4

3 4 p

k    

2 2  p

,

,

F

(30)

p 1, 2, 3... =

n

. cr p =

2

p  = 

Fig. 5. F cr / F E for 3 different boundary conditions

6. Conclusion

Stability analysis of the compression member on elastic springs is presented. The members under investigation have seven various numbers of the fields n = 2, 3, 4, 7 and ∞ (figures 1 , 2, 3 and 4). The members have uniform bending rigidity EI , uniform normal force N and ( n – 1) elastic springs with equal spring stiffness C w . The results are presented in the form of eight diagrams. The curves of diagrams were replaced by the straight lines to be able derived approximate formulae (equations 4 – 19) for calculation of the critical force. It is shown that approximate formulae give the values of the critical forces F cr.a which differ from diagram values F cr less than 3.3 %, being slightly on the safe side (table 1). The values of the critical forces F cr obtained from the solution of the stability