PSI - Issue 72

Denys Mykhailovskyi et al. / Procedia Structural Integrity 72 (2025) 315–322

321

Fig. 7 shows stress-deformed state of the cantilever-hanging part of the curved beam cover construction (stadium bleachers). In this case, the entire cross section is tensile, and a predominant moment appears. The cross section in that case will be compressed. Stretching can only occur in suspended or cantilevered enclosures. Such constructures are very rarely.

Fig. 7. Stress-deformed state of the cantilever-hanging part of the curved beam cover construction (stadium bleachers)

Table 1 shows the equilibrium equations for all compressed-bent and stretched-bent stress-strain states. They consider the deformation diagrams of the material under tension and compression. The tension and compression diagrams of wood are different. And the use of materials for reinforcement also has its own characteristics. The stretched and compressed zone can be reinforced with metal reinforcement. But in the tension zone, reinforcement with fiber composite is possible.

Table. 1 Equilibrium equations for all cases of compressed-bent and stretched-bent stress-deformed states

Case of state

Domination force or moment

Stress in the cross-section tensile and compression

System of equilibrium equations

compressed-bent stress deformed states

predominant moment

    wc M M M M M N N N N N   , ,1 s c       , ,1 , ,1 1 , ,1 , ,1 , ,1 1 wt wc t сs s c wt     s c M M M M N N N N       , ,2 , ,2 2 с w     w t M M M M N N N N        , ,3, s t h , ,3 3 , ,3 , ,3, s t l 3 w t  0  , ,2 , ,2 , ,2 2 , ,2 c сs s c wc сs с , ,2, s t h  w t M M M M M N N N N N          , ,4 , ,4 , ,4 4 c сs wc s t  0 , ,1 , ,1 t сs 0   0 , ,3, s t h    

0



compressed-bent stress deformed states

predominant compressive force

only compression

stretched-bent stress deformed states

predominant tensile force

only tensile

0

stretched-bent stress deformed states

predominant moment

tensile and compression

0



, ,4

0



4

, ,4

, ,4

, ,4

, ,4

wc

w t

s c

t сs

It is not difficult to determine the stress-strain state of a bending element. However, it is necessary to take into account the deformation scheme of the bending element for modeling and calculating the work of compressed-bent elements. In this case, it is important to take into account the curvature of the element, the occurrence of deflection and the displacement of the neutral line in the cross section during loading.