Consideration for the shear deformation and/or the flexible composite follows according to the method of the shear analogy and is included in paragraph D3 of DIN 1052:2008. The low rolling shear module of the cross layers has the effect that with compact element dimensionings or stress through individual loads leads to the relatively large shear deformation of the cross layers quasi to a flexible composite of the layers running in a parallel direction to the main girders. Through the consideration of the flexible composite the centre of gravity strain distribution σ_{c/t,0,d} in the individual layers is reduced while the proportion of the bending stress σ_{m,d} increases.
__ __ Fixed shear ______ Flexible bond
Thus resulting in greater, for the dimensioning, standard edge stress σ_{R,d.} With the observed elements the individual slabs of the cross layers are not glued together on the narrow sides. In this case the E-module of the cross layer is set equal to zero. Therefore resulting in no longitudinal stress in the cross layers.
With glued CLT the stress determination according to the fixed composite theory pursuant to appendix D2 of DIN 1052:2008 supplies sufficiently accurate results in so far as a simple supported beam under equal load with a ratio of width L to element thickness d of L/d>20 is present. Thereof varying systems are assessed taking into account the shear deformation.
For the preliminary estimates according to the fixed composite theory it is sufficient to apply load distribution only to the longitudinal layers parallel to the stress direction.
If the longitudinal layers consist of lamination of equal strength classes then the moment of inertia for the sections of self contingent as well as the parallel axis contingent of the longitudinal layers are compounded together. For a metre wide panel strip the following applies:
_{ }
_{ }
The stress on the bending edge σ_{R,d} of the outer skin hence amounts to:
Under the assumption of a constant direction of shear force an assessment is possible for the shear dimensioning of standard rolling shear stress from the prevailing lateral force V_{z,d} as well as the centre of gravity clearance to the outer skin:
The combined longitudinal and shear stress proofs in the limit state of the load bearing capacity are included in paragraph 10.7 of DIN 1052:2008. The following proofs in each individual layer are required:
- Longitudinal stress with combined panel and plate stresses.
- with: n = number of boards lying next to each other in the outer skins.
Thus the proof is:
- • Shear stress
τ_{d}: Shear stress from shear force
τ_{drill,d}: Shear stress from twisting moment
- • Stress perpendicular to the fibre direction and rolling shear
σ _{c / t,90,d}: Pressure/ tensile stress perpendicular to the fibre direction from bending and normal force
τ _{R,d}: Rolling shear stress
The dimensioning values of the tensile and/or pressure stresses and bending strength are dependant on the strength class of the lamination used and can be determined by the characteristic strength values according to appendix F of DIN 1052:2008. For the characteristic value of the rolling shear strength the values given in the permits of the respective products apply. These vary between 0.75 N/mm^{2} and 1.25 N/mm^{2} for white wood. For pine wood marginally higher values are generally given.
In the limit state of the serviceability the deformation proof, according to paragraph 9.2 of DIN 1052:2008 is to be administered. With deformation calculations the shear deformation contingent should be considered in every case. In order to avoid discomfort caused by vibration of floors in housing and residence premises an additional vibration proof is to be provided according to paragraph 9.3 of DIN 1052:2008. The bending of precast floor sections under constant and quasi constant influences (w_{perm} = g_{k} + ψ_{2,1}∙ q_{k}) ) is to be restricted to the limit value of 6.0 mm. This corresponds to a self frequency of the floor of approx. 7.2 Hz. With continuous beams the proof is to be conducted in the field with the largest width, whereby the elastic end restraints in the neighbouring fields may be considered. If the simplified vibration proof is not maintained then special analysis of the vibration characteristics is to be conducted. The following dimensioning diagram for a simple supported beam under equal load in xx forms the basis of the deformation limit of 6.0 mm under constant and quasi constant influences (w_{perm} = g_{k} + ψ_{2,1}∙ q_{k)} As a rule this proof is standard for the dimensioning.
Deflections limit of 6.0mm at the simple support beam
Span L [m]