The crossed formation of the board layers allows for the insertion of the cross laminated timber element for bracing purposes.
The resulting direction of shear force from a horizontal header load produces shear stresses in the individual board layers. The horizontal and vertical layers must be considered seperate from each other. The direction of shear force in element planes from a header load Fd amounts to:
Hence the following shear stresses result in the
• vertical layers (x-direction):
• horizontal layers (y-direction):
With a joint free construction with narrow side bonding the following applies for the shear stresses:
The proofs are:
If no narrow side bonding of the board layer is provided then additional torsion moments and therefore torsion shear stresses at the cross points occur.
The torsion moment of a cross point amounts to:
Under the assumption of a linear distribution the effective maximum torsion shear stress in the bonded joints of a cross point of two board laminates is calculated thus:
n = number of board layers
For the characteristic torsion shear strength ftor,k the value 2.50 N/mm2 is given in the general building control permits. The proof of the torsion shear stress in the limit state of the load bearing capacity is as follows:
For bracing wall panels the shearing strain in xy plane and the panel shear strength Dxy connected with it are of significance. For bonded cross laminated timber according to appendix D of DIN 1052:2008 they can be determined as follows:
If the individual boards are bonded together on the narrow side then the full element thickness may be applied:
The horizontal displacement uy,d at the wall header amounts to:
For bracing wall panels DIN 1052:2008 requires a limiting of the horizontal deformation uy,d at the wall header of uy,d≤h/100. From the point of view of the load bearing capacity this may indeed be sufficient, however, for reasons of the serviceability limiting the displacement uy,k to h/500 is recommended.