Broch

STRUCTURAL DESIGN
General
Building practice approximation
method
for calculation of
cutting forces and
deformations.
Version 1 / 2011
M1 BSP crossplan
Components made of M1 BSP crossplan are designed and executed according to the following
standards:
• Design according to DIN 1052:2008 allowing for German technical approval
(Z-9.1-638)
or
• Design according to EN 1995 (Eurocode 5) allowing for Appendices 2 to 4 of European
technical approval ETA-09 / 0036
The structural analysis for M1 BSP crossplan must be conducted in each individual case and
the standards and regulations applicable at the site of use must be complied with.
Analysis of the stress distribution and internal forces and moments must be conducted according
to the composite theory allowing for shear deformations.
An approximation method is required in practical use. Here, the calculation is carried out as
for a beam under bending moment with fl exible joining means (Austrian standard B 4100 / 2;
DIN 1052; EN 1995-1-1, Appendix B), but the shear deformation of the transverse layers is
taken into consideration instead of the fl exibility of the joining means.
Using this approach, it is possible to achieve a good approximation for the stress and deformation
calculations.
At the same time, for the actual design the moments of inertia are multiplied by a reduction
factor - which takes into account the net moments of inertia and the rolling shear deformation
of the transverse layers.
Using the eff ective moments of inertia (Ieff ) obtained as a result, it is possible to calculate
the cutting forces and deformations as for beams under bending moment with a rigid bond.
M Q
Lamellas stressed in the direction of the fibres
� High stiffness
Cross-section
Q
Tension
Lamellas stressed transverse to the direction of the fibres
� No stiffness E = 0
M
σ = 0
Normal stress due to bending
Pressure
σ = 0
Shear stress
Rolling shear transversally
Rolling shear transversally
Note:
The solution only applies exactly for single span beams with sinusoidal uniform load. It should
also be noted that the eff ective moments of inertia Ieff depend on the width between supports
of the panels. The shorter the width between supports, the greater the proportion of
shear deformation and thus also the percentage reduction of the moments of inertia (compare
table of cross-sectional values). Beyond this, a more accurate calculation method is
necessary particularly in the case of point loads and very short beam lengths.
In the case of continuous beams, the width between supports of the fi eld concerned should
be used for the width between supports for selection of the eff ective moment of inertia 4 / 5
Ieff , in the case of cantilever beams double the protruding length should be used (cf. EN
1995-1-1, Appendix B). However, calculation of the cutting force and deformation must be
performed using the actual widths between supports or protruding lengths.
This approximation method is also the basis of the design charts.
Mayr-Melnhof Kaufmann 9