PSI - Issue 59

Andrii Pavluk et al. / Procedia Structural Integrity 59 (2024) 566–574 Andrii Pavluk et al./ Structural Integrity Procedia 00 (2019) 000 – 000

568

3





, , m y d

, , m z d



1,

k



m

f

f

, , m y d

,z, m d

(1)





, , m y d

, , m z d

1,

k





f

f

m

, , m y d

, z, m d

(2)

Formulas (1) and (2) make it possible to calculate the strength of obliquely bent beams only in the elastic stage of behaviour. Research on wooden beams subjected to oblique bending (Sobczak-Piastka et.al (2023)) has shown that a fold is formed under loading of 0.8M max in the compressed zone during pure bending. The formation of this fold leads to a change in the stress distribution in the compressed zone, with maximum compressive stresses occurring slightly below the outermost wood layers. Formulas (1) and (2) do not account for this. Therefore, this work aims to develop a calculation method for the load-carrying capacity of wooden beams under oblique bending conditions, considering their actual behaviour. 2. Methods of theoretical research The methodology for calculating rectangular cross-section wooden beams using the deformation model is based on the following assumptions (Fig. 1): - normal cross- section along the longitudinal axis of the beam is used for calculations within the beam’s span. - stresses in the normal section are calculated using two functions (3) and (4) (Gomon et al. (2022)). - elements in which the influence of transverse force on deflections is not significant are considered. - average values of temporary support for wooden elements are adopted as calculated values. - compressive zone deformations are taken with a negative sign, while tensile zone deformations are taken with a positive sign. The criterion for determining the loss of load-carrying capacity of the cross-section is based on: - destruction of the stretched zone of the wood due to reaching the most stretched layer’s limit of deformations; - an extreme criterion involving the imbalance between internal and external forces. Stresses in the normal cross-section of the beam are calculated using functions (Gomon et al. (2022)):

1

1

2

2 2

( )

( )

f u

k u k u E z k    

z

   

,





1

d

c d

c d

с

с,

1 ,

2 ,

2

(3)

1

(4)

( )

,

f u

E u E z 

   



2

, t d

, t d t

The coefficients of the polynomials were calculated using the following formulas:

2

f



(5)

, , , c o d

k



u

1

, c fin d ,

(6)

f

, , c o d

,

k



2

2

u

, c fin d ,