*l _{eff}=l_{n}+α_{left}+α_{right} where α=min(t/2,h/2)*

· At the end support of the first slab, the width is considered to be a=t_{1}/2=125 mm which is acceptable as in favor of the safety.

· The width of beam-column supports, is taken into account more efficiently, when the analysis uses rigid bodies (see next paragraph).

*Continuous beam: l _{o} distance between consecutive points of zero moments*

*Continuous frame beam: l _{o} distance between consecutive points of zero moments*

Earthquake resistant structures require strong columns and fixed column-beam connections. This requirement demands the creation of a frame set of beams, forming a continuous structure with respect to geometry, but autonomous with respect to the adjacent beams. This fact leads to the conclusion that, in general, the supports of a beam are* *rarely pinned*.* Therefore, *l*_{o}*=0.70***×***l* can be chosen for all the earthquake resistant beams.

*b*_{eff}*=b*_{w}*+b*_{eff,1}*+b*_{eff,2}*≤b*_{lim} where *b*_{eff,1}*=0.20***×***b*_{1}*+0.10***×***l*_{o}*≤0.20***×***l*_{o}* *and* **b*_{eff,2}*=0.20***×***b _{2}+0.10*

· Τhe effective widths at supports have practical meaning mainly for the dimensioning of inverted concrete beams under bending.

· When an adjacent slab is cantilever, of a span l_{n}, the corresponding b_{1} or b_{2} is equal to l_{n}.

*The actual structure and the space model (screen shot captured by HoloBIM)*

The space frame model comprises nodes (e.g. node 1, 5, 9 etc.) and members (e.g. member 1, 2, 5 etc.). Nodes are symbolic geometric points where members end.

In general, each node has 6 displacements (6 degrees of freedom), three translations *δx, δy, δz* and three rotations *φx, φy, φz*. The objective of the analysis is the calculation of the 6 displacements for all nodes.

*Plan and 3D of column-beam nodes: Master node (5) and slave node (6)*

Provided the 6 displacements of the master node are *δ*x, *δ*y, *δ*z, *φ*x, *φ*y, *φ*z, the corresponding *δ*x,s, *δ*y,s, *δ*z,s, *φ*x,s, *φ*y,s, *φ*z,s of the slave node are:

*φ* x,s = *φ* x , *φ* y,s = *φ* y , *φ* z,s = *φ* z , *δ* x,s = *δ* x -*s*y × *φ* z (given *sz=0*), *δ* y,s = *δ* y +*s*x × *φ* z (given *sz=0*),

*δ* z,s = *δ* z -*s*x × *φ* y +*s*y × *φ* x_{}

*Diaphragmatic behaviour of floor and the displacements of a random point i of the diaphragm due to φz*_{}

The 3 displacements *δ*z, *φ*x, *φ*y of each node belonging to the diaphragm are independent of each other, while the rest *δ*x, *δ*y, *φ*z are depended on the 3 displacements of point CT called Center of Elastic Torsion of the diaphragm. Displacements *δ*xi, *δ*yi, *φ*zi at the point i of the horizontal diaphragm are expressed as: