• The horizontal dimension is l_w≥min(4.0 m, 2h_w/3),

• The walls collectively support at least 20% of the total gravity load from above in the seismic design situation.

• The fundamental period of the structure is ≤0.5 sec

Figure 6.1.5.1

Figure 6.1.5.1

1. With respect to the lateral stiffness and mass distribution, the building structure shall be approximately symmetrical in plan with respect to two orthogonal axes.

Each floor shall be delimited by a polygonal convex line. If in plan set-backs exist, regularity in plan may still be considered as being satisfied, provided that these setbacks do not affect the floor in-plan stiffness. For each set-back, the area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5 % of the floor area.

Example:

Consider e_ox=0.94 m≤0.30r_x=0.30 · 3.91=1.17 m, but e_oy=1.34 m>0.30r_y=0.30 · 3.08=0.92 m which does not satisfy the necessary condition, thus the building comprising that specific floor is not considered as being regular in plan .

Regularity in elevation [EC8 §4.2.3.3]

For a building to be categorised as being regular in elevation, it shall satisfy all the following conditions:

i. All lateral load resisting systems, such as cores, structural walls, or frames, shall run without interruption from their foundations to the top of the building or, if setbacks at different heights are present, to the top of the relevant zone of the building. Cases of regular and non-regular in elevation buildings are presented in the following figures.

ii.Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually, without abrupt changes, from the base to the top of a particular building.The storey stiffness is defined as the ratio of the applied seismic force το the relative lateral stiffness (or equivalently, the displacement of the centre of stiffness).

The storey stiffness may be approximated by the sum all columns stiffnesses, i.e. Σ(E· I/h³).

In the absence of particular data provided by the EC8, the limit values for the stiffness and mass fluctuation may be taken as being equal to:

Mass increase ΔM_i=(M_i+1-M_i)≤0.35M_i,

Mass reduction ΔM_i=(M_i-M_i+1)≤0.50M_i,

while for each main horizontal direction x, y

Relative stiffness increase

Δ K_i=(K_i+1-K_i)≤0.35K_i , Relative stiffness reduction

Δ K_i=(K_i-K_i+1)≤0.50K_i ,

Notes

iii. In framed buildings the ratio of the actual strength of columns and beams to the strength required by the analysis should not vary disproportionately from the corresponding overstrength factor between adjacent storeys. For each floor and each direction the column resistance moments ΣM_c,Rd in both directions (+x, -x) και (+y, -y) and the two corresponding beam resistant moments ΣM_b,Rd are added.

iv. When setbacks are present, the following additional conditions apply for each direction:

- For gradual setbacks preserving axial symmetry, the setback at any floor shall be not greater than 20 % of the previous plan dimension in the direction of the setback.

It shall be

- If the setbacks do not preserve symmetry, in each face the sum of the setbacks at all storeys shall be not greater than 30 % of the plan dimension at the ground floor above the foundation or above the top of a rigid basement, and the individual setbacks shall be not greater than 10 % of the previous plan dimension.

It shall be

and

- For a single setback within the lower 15 % of the total height of the main structural system, the setback shall be not greater than 50 % of the previous plan dimension. In this case the structure of the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at least 75% of the horizontal shear forces that would develop in that zone in a similar building without the base enlargement.

It shall be

Ductility classes [EC8 §5.2.1]

Earthquake resistant buildings are classified in three ductility classes.

(α) DCL from the initials of Ductility Category Low

(β) DCM from the initials of Ductility Category Medium

(γ) DCH from the initials of Ductility Category High

DCL

Buildings belonging to Ductility Category Low are designed for low energy dissipation capacity and low ductility, following the provisions of EC2 that concern the dimensioning without of course accounting for the reduction of seismic forces, i.e. the behaviour factor q shallbe taken equal to 1.0. The only construction requirement concerns the use of B or C steel class [EC2, 3.2.2(3)A ].

This category is recommended for the classification of buildings in low seismicity regions.

DCM

Buildings belonging to Ductility Category Medium are designed for medium energy dissipation capacity and medium ductility, and conform to the particular design and construction rules of EC8.

DCH

Buildings belonging to Ductility Category High are designed for high energy dissipation capacity and high ductility and conform to the strictest relevant design and construction rules.

Buildings classified as frame system and brittle masonry are not allowed to belong to this class.

Notes

Basic value of the behaviour factor q_o [EC8 §5.2.2.2]

Table 6.1.5.5-1: Basic value of the behaviour factor q_o

The values of factor a_u/a₁ may be obtained either from push over analysis or from the following table:

Table 6.1.5.5-2: Values of the multiplication factor a_u/a₁

Notes on the above tables

Summarizing the above results in the following table:

Table 6.1.5.5-3: Basic value of the behaviour factor q_o

Examples for wall-equivalent dual system (4) with more than two walls:

Regular in elevation - regular in plan :

for DCM q_o=3.0 · 1.1=3.30, for DCH q_o=4.5 ·1.1=4.95

Regular in elevation - non- regular in plan :

for DCM q_o=3.0 · 1.05= 3.15, for DCH q_o=4.5 ·1.05= 4.725

Non-regular in elevation - regular in plan :

for DCM q_o=0.8 · 3.0 · 1.1=2.64, for DCH q_o=0.8 · 4.5 ·1.1=3.96

Non-regular in elevation - non- regular in plan :

for DCM q_o=0.8 · 3.0 · 1.05=2.52, for DCH q_o=0.8 · 4.5 ·1.05=3.78

Failure mode factor k_w [EC8 §5.2.2.2]

The behaviour factor is given by the expression q=k_wq_o≥1.5, where q _ο is the basic value of the behaviour factor, presented in the previous paragraph and k_w is the failure mode factor.

k_w=1.0for frame systems (1), or frame-equivalent dual systems (3), while for the remaining wall systems (2), (4), (5),K_w=(1+a_o)/3, where a_o is the aspect ratio of the walls equal to a_o=Σh_w,i/Σl_w,i. In any casek_w should satisfy the relation 0.50≤k_w≤1.0.

The failure mode factor k_w is ≤1.0 provided that a_o≤2.0, meaning walls of averagelength l_w>h_w/2, i.e. in a one-storey building of height h_w=3.0 m for walls of lengthl_w>3.0/2=1.50 m, in a two-storey building ofh_w=2·3.0=6.0 m for walls of l_w>6.0/2=3.0 m and, respectively, in a similar four-storey building for walls of l_w>6.0 m and for aten-storey building for walls of l_w>15 m. For common multistorey buildings without large lightly reinforced walls, applies k_w=1.0.

Conclusion

A few brief results, based on the previous paragraphs, are presented here: