Analysis of Cross-Laminated Timber Elements Subjected to Flexure

Behavior and mechanical properties of cross-laminated timber are analyzed for case of static loading. Two panels with thickness 95mm consisting from three layers were tested in laboratory. Freely supported panels with span equal to 2m, which is loaded by the uniformly distributed load was a design scheme of considered panels. The panel’s width was equal to 1m. Analytical FEM design method, which is based on the using of computational program ANSYSv14 and RFEM5.0, was checked by the experiment. The comparison of stresses acting in the edge fibers and vertical displacements shows that the considered design methodology can be used for engineering calculations. Comparing methodology of calculations and experimental results the difference between results were up to 30%. Result difference for cross and parallel laminated timber plates – load bearing capacity, horizontal displacement and deflection varies up to 10%, it can be concluded that the middle layer does not give a significant effect on the load – bearing capacity loss. The transversal layer provides a homogeneous and solid system. Finite element program for the calculation of accurate results in comparison with the calculation methodology showed RFEM5.0 program with differences up to 10% and 15%The program ANSYS up to 15%. RFEM5.0 increased accuracy of results increases built up functions for both EN1995-1-1 and GEM. Comparison of results between cross and parallel laminated timber in relative deformations, the difference is up to 6%. The cross – laminated timber middle layer does not affect load – bearing capacity. The middle layer decreases only 10 % of load – bearing capacity.

According to methodology we can offer two design methods for bending calculations of CLT: _ Method of effective cross section;

_ Effective strength and stiffness method
The study includes six stages, where the slab layer dimensions chosen by the recommended literature and information available.[2] The slab is considered as freely supported beam with span equal to 2 m.The beam is considered under load with certain step 1, 2, 3, 4, 4.5, 5, 6, 7, and 7.5 kN/m2.The load steps chosen from the studies carried out by the available resources and opportunities.

Physical experiment
The experiment is carried out to verify the accuracy of the calculation methodology in real usage conditions.The goal is to determine mismatch of analytical calculations and experiment.
For making crosslaminated timber plate is used timber with crosssections:

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.Shear stresses acting in the CLT plates are determined basing on the recommendations of [3] and deformations of CLT plates due to shear stresses action are shown in Fig. 5.
The following condition must be satisfied [3]:  -bending strength calculati Two considered methods for a laminated timber elements subjected to fl the equation 4).Let us to consider red method.Reduced cross-section method replacement of real cross-section of equivalent reeducated cross-section.Th used in the case, when fibers of each se are oriented perpendicular to the fibers d layer.Transformation of cross -sectio relation of modulus of elasticity of the lay direction: [1]

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.Shear stresses acting in the CLT plates are determined basing on the recommendations of [3] and deformations of CLT plates due to shear stresses action are shown in Fig. 5.
The following condition must be satisfied [3]:   The experiment is carried out to verify the accuracy of the calculation methodology in real usage conditions.The goal is to determine mismatch of analytical calculations and experiment.
• Wood class EN 338 -C18.Plates making process: • Preparing place; • Inlay the first external layer 25x50; • Applied polyurethane adhesive on first layer (glue usage quantity, 0.3kg/m2); • Second layer is laid 45x195 and a glue is applied (0.3kg/m2); • On the second layer is laid last layer 25x50; The experiment is carried out to verify the accuracy of the calculation methodology in real usage conditions.The goal is to determine mismatch of analytical calculations and experiment.
• Wood class EN 338 -C18.Plates making process: • Preparing place; • Inlay the first external layer 25x50; • Applied polyurethane adhesive on first layer (glue usage quantity, 0.3kg/m2); • Second layer is laid 45x195 and a glue is applied (0.3kg/m2); • On the second layer is laid last layer 25x50;    • Deflection of independent regulatory load; • Deflection of useful regulatory load; • The total deflection; • The stiffness calculation.

Verification of design methodologies Physical experiment
The experiment is carried out to verify the accuracy of the calculation methodology in real usage conditions.The goal is to determine mismatch of analytical calculations and experiment.
• Wood class EN 338 -C18.Plates making process: • Preparing place; • Inlay the first external layer 25x50; • Applied polyurethane adhesive on first layer (glue usage quantity, 0.3kg/m2); • Second layer is laid 45x195 and a glue is applied (0.3kg/m2); • On the second layer is laid last layer 25x50; • The pressure (400kg/m2) is applied.• Deflection of independent regulatory load; • Deflection of useful regulatory load; • The total deflection; • The stiffness calculation.

Verification of design methodologies Physical experiment
The experiment is carried out to verify the accuracy of the calculation methodology in real usage conditions.The goal is to determine mismatch of analytical calculations and experiment.
• Wood class EN 338 -C18.Plates making process: • Preparing place; • Inlay the first external layer 25x50; Shear stresses acting in the CLT plate must be calculated by the following equation.
The following condition must be satisfied [3]:

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.
The following condition must be satisfied [3]: Normal stresses acting in the CLT plates are determined basing on the recommendations of [3] and distribution of normal stresses in the middle and outer layers of CLT plates is shown in Fig. 6.The fibers of second layer are oriented perpendicular to the direction of fibers for outer layer.Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: where -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1]

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.
The following condition must be satisfied [3]: Normal stresses acting in the CLT plates are determined basing on the recommendations of [3] and distribution of normal stresses in the middle and outer layers of CLT plates is shown in Fig. 6.The fibers of second layer are oriented perpendicular to the direction of fibers for outer layer.Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: where -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1]

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.
The following condition must be satisfied [3]: Normal stresses acting in the CLT plates are determined basing on the recommendations of [3] and distribution of normal stresses in the middle and outer layers of CLT plates is shown in Fig. 6.The fibers of second layer are oriented perpendicular to the direction of fibers for outer layer.Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: where -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1]    Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] The following condition must be satisfied [3]: (3)

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.
The following condition must be satisfied [3]: -tangential transversal stresses, Nmm 2 ; Normal stresses acting in the CLT plates are determined basing on the recommendations of [3] and distribution of normal stresses in the middle and outer layers of CLT plates is shown in Fig. 6.The fibers of second layer are oriented perpendicular to the direction of fibers for outer layer.Bending stresses, acting at the distance z from the m plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/m Two considered methods for analysis of c laminated timber elements subjected to flexure are bas the equation 4).Let us to consider reduced cross se method.Reduced cross-section method is joined wit replacement of real cross-section of element by equivalent reeducated cross-section.This method ca used in the case, when fibers of each second layer of are oriented perpendicular to the fibers direction of the layer.Transformation of cross -section is based o relation of modulus of elasticity of the layers in longitu direction: [1]  Two considered methods for analysis of cross-laminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced crosssection method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of crosssection is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1] where:

Methodology of a analytical calculations
The plate is freely supported with span equal 2 m and loaded with distributed load.The plate is analyzed in oneway bending.If the plate would be based on the contour, it should be considered in two -way bending.The experimental procedure adapted to the available resources and opportunities to realize it.
The following condition must be satisfied [3]: -tangential transversal stresses, Nmm 2 ; Normal stresses acting in the CLT plates are determined basing on the recommendations of [3] and distribution of normal stresses in the middle and outer layers of CLT plates is shown in Fig. 6.The fibers of second layer are oriented perpendicular to the direction of fibers for outer layer.Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: where -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1] 90 (5) where 0 E -elastic module in longitudinal direction, N/mm 2 ; 90 E -elastic module in transversal direction, N/mm 2 .

Fig. 7. Cross -section area transformations
Moment of inertia of transformed cross-section should be determined by the equation: nal stresses, N/mm 2 ; ersal stresses, Nmm 2 ; alue.
CLT plates are determined s of [3] and distribution of d outer layers of CLT plates f second layer are oriented fibers for outer layer.Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: where -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1] 90 (5) where 0 E -elastic module in longitudinal direction, N/mm 2 ; 90 E -elastic module in transversal direction, N/mm 2 .

Fig. 7. Cross -section area transformations
Moment of inertia of transformed cross-section should be determined by the equation: The plate is analyzed in oneuld be based on the contour, it two -way bending.The ted to the available resources .
e CLT plates are determined ons of [3] and deformations of ses action are shown in Fig. 5.
the CLT plates are determined ons of [3] and distribution of and outer layers of CLT plates s of second layer are oriented of fibers for outer layer.Bending stresses, acting at the distance z from the middle plane are calculated by the following equation: [2] ( ) ( ) The following condition must be satisfied [3]: where -bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1] 90 (5) where 0 E -elastic module in longitudinal direction, N/mm 2 ; 90 E -elastic module in transversal direction, N/mm 2 .

Fig. 7. Cross -section area transformations
Moment of inertia of transformed cross-section should be determined by the equation: CLT plates are determined ns of [3] and deformations of es action are shown in Fig. 5.
he CLT plates are determined ons of [3] and distribution of and outer layers of CLT plates s of second layer are oriented of fibers for outer layer.-bending stresses in edge, N/mm 2 ; -bending strength calculation value, N/mm 2 .
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1]  The following condition must be satisfied [3]: where d edge ,
Two considered methods for analysis of crosslaminated timber elements subjected to flexure are based on the equation 4).Let us to consider reduced cross section method.Reduced cross-section method is joined with the replacement of real cross-section of element by the equivalent reeducated cross-section.This method can be used in the case, when fibers of each second layer of CLT are oriented perpendicular to the fibers direction of the first layer.Transformation of cross -section is based on the relation of modulus of elasticity of the layers in longitudinal direction: [1]  In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation: [5,6] where: . 2   In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation: [5,6]      ) ( ) In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation: [5,6]  ) ( ) In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation: [5,6]   In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation: [5,6]   In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation: [5,6] Effective values of composition factor k (1,2,3,4) must be determined by the well-known equations [2] depending on Effective values of composition factor k (1,2,3,4) must be determined by the well-known equations [2] depending on the CLT layer placement (Fig. 8.).The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.
Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.
The value of shear stiffness is determined by the equation: where k -reduction coefficient; G -shear modules, N/mm2; A -cross section of plate, mm2.The dependence CLT panel can be law, which is writt The results, obta and ANSYS v14 fo Effective values of composition factor k (1,2,3,4) must be determined by the wellknown equations [2] depending on the CLT layer placement (Fig. 8.).
The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.Fig. 7 Cross -section area transformations Fig. 8 Layer placement (a m-xplate and layer thickness) Fig. 9 Relative shear module proportion (To G0/Gr = 10) [3] Fig. 10 Coordinate system for software In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: Effective values of composition factor k (1,2,3,4) must be determined by the well-known equations [2] depending on the CLT layer placement (Fig. 8.).The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.
Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) ( )dx In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.
The value of shear stiffness is determined by the equation: where k -reduction coefficient; G -shear modules, N/mm2; A -cross section of plate, mm2.
ANSYSv14 and REFM 5.0.Calculations of CLT plate by the softwares ANSYSv14 and REFM 5.0 are based on mechanics of laminated materials.The coordinate system and axis designation are shown on Fig. 10.The target of the calculation is verification of the results, obtained by the reduced cross-section method and effective strength and stiffness method.The dependence between stress and strains for considered CLT panel can be described by the generalized Hooke's law, which is written for orthotropic model:   The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.
Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.
The value of shear stiffness is determined by the equation: where k -reduction coefficient; G -shear modules, N/mm2; A -cross section of plate, mm2.
the softwares ANSYSv14 and REFM 5.0 are base mechanics of laminated materials.The coordinate s and axis designation are shown on Fig. 10.The target calculation is verification of the results, obtained b reduced cross-section method and effective strength stiffness method.The dependence between stress and strains for consid CLT panel can be described by the generalized Hooke' law, which is written for orthotropic model:  The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.
Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.

FEM design methodology
CLT panel with dimensions in plan 2x1 m and thickness in 95 mm was calculated with the using of softwares ANSYSv14 and REFM 5.0.Calculations of CLT plate by the softwares ANSYSv14 and REFM 5.0 are based on mechanics of laminated materials.The coordinate system and axis designation are shown on Fig. 10.The target of the calculation is verification of the results, obtained by the reduced cross-section method and effective strength and stiffness method.The dependence between stress and strains for considered CLT panel can be described by the generalized Hooke's law, which is written for orthotropic model:    The dependence between stress and strains for considered CLT panel can be described by the generalized Hooke's law, which is written for orthotropic model: The dependence between stress and strains for considered CLT panel can be described by the generalized Hooke's law, which is written for orthotropic model:

Design methods analysis of CLT elements subjected to flexure
The main cross -laminated timber proportion should be considered in relation to the calculation methodology: 1) Physical experimental results; 2) Finite element software The cross -laminated timber proportion between

Design methods analysis of CLT elements subjected to flexure
The main cross -laminated timber proportion should be considered in relation to the calculation methodology: 1) Physical experimental results; 2) Finite element software The cross -laminated timber proportion between calculation methodology and experiments:  The dependence between stress and strains for considered CLT panel can be described by the generalized Hooke's law, which is written for orthotropic model: The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.
Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.
( ) ( ) where k -reduction coefficient; G -shear modules, N/mm2; A -cross section of plate, mm2.The dependence between stress and strains for consi CLT panel can be described by the generalized Hooke law, which is written for orthotropic model: The value of the composition factor k (1,2,3,4) depends from direction how load is apllied on structure and from layers layout.
Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.
( ) ( ) where k -reduction coefficient; G -shear modules, N/mm2; A -cross section of plate, mm2.The dependence between stress and strains for co CLT panel can be described by the generalized Hoo law, which is written for orthotropic model: Maximum vertical displacements of the CLT panels must be calculated by the following equation: [7,8,9] ( ) In case if static scheme of the CLT panel is a freely supported beam, the above mentioned equation will be simplified: where q -linear load; I ef -inertia moment; S CLT -shear stiffness.
( ) ( ) where k -reduction coefficient; G -shear modules, N/mm2; A -cross section of plate, mm2.The dependence between stress and strains fo CLT panel can be described by the generalized law, which is written for orthotropic model:

Design methods analysis of CLT elements subjected to flexure
The main cross -laminated timber proportion should be considered in relation to the calculation methodology: 1) Physical experimental results; 2) Finite element software The cross -laminated timber proportion between calculation methodology and experiments: • relative deformation of 22%; • horizontal deflection by 17%; Deflections in FEM software ANSYSv14

_
Fig.2CLT representation of the experimental

Fig. 5 .
Fig. 5. Shear deformations in CLT Shear stresses acting in the CLT plate must be calculated by the following equation.

E
-elastic module in longitudinal direction, N/mm 2 ; 90 E -elastic module in transversal direction, N/mm 2 .

Fig. 7 .
Fig. 7. Cross -section area transformations CLT plate width, mm; h CLT -CLT plate height, mm; b 1 -the middle layer width, mm;h 2middle layer height, mm.Maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels is determined by the equation:

E
-elastic module in longitudinal direction, N/mm 2 ; 90 E -elastic module in transversal direction, N/mm 2 .

E
-elastic module in longitudinal direction, N/mm 2 ; 90 E -elastic module in transversal direction, N/mm 2 .

Fig. 7 .
Fig. 7. Cross -section area transformations where b -CLT plate width, mm; h CLT -CLT plate height, mm; b 1 -the middle layer width, mm;h 2middle layer height, mm.Maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels is determined by the equation: Journal of Sustainable Architecture and Civil Engineering 2014/4/9 54 layer are oriented perpendicular to the direction of fibers for outer layer.

Fig. 6 .
Fig. 6.Normal stresses in cross -section (e 1,2,3,4 -distance from center axis, d edge, where b -CLT plate width, mm; h CLT -CLT plate height, mm; b 1 -the middle layer width, mm;h 2middle layer height, mm.Maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels is determined by the equation: -elastic module in transversal direction, N/mm 2 .(4) lculations with span equal 2 m and he plate is analyzed in onebe based on the contour, it o -way bending.The to the available resources LT plates are determined of [3] and deformations of action are shown in Fig.5.mations in CLT plate must be calculated by 0] satisfied [3]:

Fig. 6 .
Fig. 6.Normal stresses in cross -section (e 1,2,3,4 -distance from center axis, d edge, CLT plate width, mm; h CLT -CLT plate height, mm; b 1 -the middle layer width, mm;h 2middle layer height, mm.Maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels is determined by the equation: Moment of inertia of transformed cross-section should be determined by the equation: (5) calculations rted with span equal 2 m and

Fig. 6 .
Fig. 6.Normal stresses in cross -section (e 1,2,3,4 -distance from center axis, d edge, CLT plate width, mm; h CLT -CLT plate height, mm; b 1 -the middle layer width, mm;h 2middle layer height, mm.Maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels is determined by the equation: Maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels is determined by the equation: where: b -CLT plate width, mm; h CLT -CLT plate height, mm; b 1 -the middle layer width, mm; h 2 -middle layer height, mm.(6)

-
In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation:[5,6] maximum bending moment, kNm; CLT a - CLT plates height; CLT K -safety factor; 5 = i E -modulus of elasticity.The value of factor K must be found by the equation:

-
maximum bending moment, kNm; CLT a - CLT plates height; CLT K -safety factor; 5 = i E -modulus of elasticity.The value of factor K must be found by the equation:

Fig. 9 .
Fig. 9. Relative shea value of factor K must be found by the equation: ( ) (

-
maximum bending moment, kNm; CLT a - CLT plates height; CLT K -safety factor; 5 = i E -modulus of elasticity.The value of factor K must be found by the equation:

-
maximum bending moment, kNm; CLT a - CLT plates height; CLT K -safety factor; 5 = i E -modulus of elasticity.The value of factor K must be found by the equation:

Fig. 9 .
Fig. 9. Relative shear module proportion (To G 0 /G r = 1 plates height; CLT K -safety factor;5 = i E -modulus of elasticity.The value of factor K must be found by the equation:

Fig. 10 .
Fig. 10.Coordinate system for software where E 1 , E 2 , E 3 -moduli of elasticities in directions 1, 2 and 3; ij υ -Poisons ratio;G 23 , G 31 , G 12 -shear modules in 2-3, 3-1 and 1-2 planes, , -shift deformations.The results, obtained by the FEM softwares REFM 5.0 and ANSYS v14 for the CLT plate with dimensions in plan Maximum vertical displacements of the CLT panels must be calculated by the following equation:[7,8,9] (10)The value of shear stiffness is determined by the equation:In accordance with the effective strength and stiffness method, maximum value of normal stresses acting in the edge fibers of outer layers of CLT panels must be determined by the equation:[5,6] value of factor K must be found by the equation: values of composition factor k (1,2,3,4) must be determined by the well-known equations[2] depending on the CLT layer placement (Fig.8.).

Fig. 10 .
Fig. 10.Coordinate system for software calculated with the using of softwares ANSYSv14 and REFM 5.0.Calculations of CLT plate by the softwares ANSYSv14 and REFM 5.0 are based on mechanics of laminated materials.The coordinate system and axis designation are shown on Fig.10.The target of the calculation is verification of the results, obtained by the reduced cross-section method and effective strength and stiffness method.
2x1 m and thickness in 95 mm, are given in figures 11 and 12.

1
E 1 , E 2 , E 3 -moduli of elasticities in dire and 3; ij υ -Poisons ratio;G 23 , G 31 , G 12 -shear m 3, 3-1 and 1-2 planes, , -shift deform The results, obtained by the FEM softwares R and ANSYS v14 for the CLT plate with dimens , -shift deformations.(13)The main cross -laminated timber proportion should be considered in relation to the calculation methodology: Physical experimental results; 2 Finite element software.