The main horizontal seismic force H_{X} is applied at each diaphragm of a building due to the seismic action along the axis X of the building. Thisforce is applied at the diaphragm's centre of mass C_{M} and generates the moment M_{CT}_{Χ} of magnitude H_{X} · e_{oY} about the centre of stiffness C_{T}. The same situation exists for the Y axis where the corresponding moment M_{CTY} has a magnitude equal to H_{Y} · e_{oX}. The sign of seismic forces changes continuously resulting in combinations having either positive or negative values of them. The magnitude of bending moments depends however on the size of the structural eccentricities e_{oX}, e_{oY}. The position of the centre of stiffness and thus of the structural eccentricities is examined in §5.4 and in the Appendices C and D.
Figure 6.51: Typical floor plan. C_{M} is the centre of mass. C_{T} is the centre of stiffness. Figure 6.51: Typical floor plan. C_{M} is the centre of mass. C_{T} is the centre of stiffness.

Figure 6.52: Detail of the C_{M}, C_{T} region. e_{oX}, e_{oY} are the structural eccentricities. Figure 6.52: Detail of the C_{M}, C_{T} region. e_{oX}, e_{oY} are the structural eccentricities.
 The axes Χ, Y are conventional because in reality, during an earthquake, there will always exist components of the seismic action along both X and Y directions either because the seismic waves arrive at an angle other than 0º or 90º or because the geometry of the structure is such that a seismic excitation along X generates one along Y and viceversa. The two most unfavourable directions for each diaphragm, are those of the principal system. In multistorey buildings each diaphragm affects the others and in this respect the EC8 deals with this issue, together with other uncertainties, prescribing the simultaneous application of the seismic action along X or Y or Z, combined with the 30% of the seismic action along the other two directions. Regardless of the C_{M}, C_{T }locations thecombination A of gravity loads g and q multiplied by the safety factors of actions always exists . For any specific location of C_{M}, C _{T}, 8 additional combinations of the seismic forces exist, due to the most probable masses 1.00g+0.30q (^{2}) during the earthquake: Loading combination table for a specific location of the centre of mass Combination A: "1.35g+1.50q (^{1})" for the whole structure, without seismic action  Combinations B, C, D, E, F, G, H, I: 1.00g + 0.30q (^{2}) with extra seismic actions (^{3}) E_{X}, E_{Y} 1.00g + 0.30q ± 1.00E_{X} ± 0.30E _{Υ} 1.00g + 0.30q ± 0.30E _{Χ} ± 1.00E_{Y} The combinations are illustrated in the following figures: 
Figure 6.53 B: +1.00E_{x} + 0.30E_{y} Figure 6.53 B: +1.00E_{x} + 0.30E_{y}

Figure 6.54 C: +1.00E_{x}  0.30E_{y} Figure 6.54 C: +1.00E_{x}  0.30E_{y}

Figure 6.55 D: +0.30E_{x} + 1.00E_{y} Figure 6.55 D: +0.30E_{x} + 1.00E_{y}

Figure 6.56 D: +0.30E_{x} + 1.00E_{y} Figure 6.56 D: +0.30E_{x} + 1.00E_{y}

Figure 6.57 F: 1.00E_{x}  0.30E_{y} Figure 6.57 F: 1.00E_{x}  0.30E_{y}

Figure 6.58 G: 1.00E_{x} + 0.30E_{y} Figure 6.58 G: 1.00E_{x} + 0.30E_{y}

Figure 6.59 H: 0.30E_{x} – 1.00E_{y} Figure 6.59 H: 0.30E_{x} – 1.00E_{y}

Figure 6.510 I: +0.30E_{x} – 1.00E_{y} Figure 6.510 I: +0.30E_{x} – 1.00E_{y}
 (^{1}) The general case is "γ_{g} · g + γ_{q} · q", while the probably required unfavourable loadings and the probable special checks are set according to chapter 2. (^{2}) The general case is 1.00g + ψ_{2} · q. The values of ψ_{2} are cited in §2.2.4. (^{3}) For simplicity reasons and since the effect of the vertical component of the seismic action is either insignificant or of local importance only, the Z direction is omitted. (^{4}) The symbol "+1.00E_{X}" implies «100% of action effects due to application of the seismic action along direction X», while the symbol "0.30E_{Y}" implies «30% of the action effects due to application of the seismic action along direction Y". The symbol "+" implies «to be combined with». According to §5.4 seismic moment on a diaphragm causes rotation resulting in increased displacements of the perimeter columns and in the development of biaxial bending in columns. The centre of mass of a storey is defined by the architectural design and is minimally affected by the mass of the structural elements. The fluctuation of the centre of stiffness can be significant because it depends on the crosssections of the structural elements and mainly of the columns. The architectural limitations cause some difficulties which may be overcome by the cooperation of the structural engineer and the architect. Thus, the structural engineer's art consists in designing a structure in such way that the storey's centres of mass and stiffness are as close as possible, i.e. in minimizing the structural eccentricities e_{oX}, e_{oY}. The attainment of such a goal has also a profound positive effect on nonearthquake resistant structures due the reduction of the undesirable structural rotations and the consequent structural displacements. The most efficient design achieves the coincidence of centres of mass and stiffness, an easy task in buildings symmetrical in plan with respect to the two orthogonal axes. Of course, the centre of mass of the diaphragm may be shifted during the earthquake, due to eccentric loading. Uncertainties also arise in the location of the centre of stiffness due to several reasons, such as the different potential mechanisms of elastoplastic failure at various floor regions e.g. due to masonry walls or unintended construction flaws including heavily reinforced beams with respect to columns, etc. In order to limit the uncertainties, EC8 imposes the use of accidental eccentricities, e_{cc}_{Χ} and e_{ccY} equal to 5% to 10% of the L_{X} and L_{Y} diaphragm dimensions, respectively. These eccentricities should be considered for all possible combinations. Table of the most adverse relative locations of centres of mass and stiffness
Figure 6.511: The possible locations of C_{Τ} as to C_{Μ} (or equivalent of C_{M} as to C_{T}) Figure 6.511: The possible locations of C_{Τ} as to C_{Μ} (or equivalent of C_{M} as to C_{T})

Figure 6.512: Example of the adverse combination 1G,M_{CT} =1.00H_{X}e_{Y}+0.30H_{Y}e_{X} Figure 6.512: Example of the adverse combination 1G,M_{CT} =1.00H_{X}e_{Y}+0.30H_{Y}e_{X}
 In a coordinate system parallel to X0Y with C_{T} as origin, the coordinates of the four points are equal to: 1 (e_{oX}+e_{ccX}, e_{oY}+e_{ccY}), 2(e_{oX}+e_{ccX}, e_{oY}e_{ccY}),3(e_{oX}e_{ccX}, e_{oY}+e_{ccY}), 4(e_{oX}e_{ccX}, e_{oY}e _{ccY}) In the specific example, it is: 1(2.3, 2.1), 2(2.3, 0.7), 3(0.3, 2.1), 4(0.3, 0.7) For each of the four points there are eight combinations, i.e. totally required: the Α combination and the 4 · 8=32 combinations à total amount of 33 combinations. The bending moment and shear force envelopes derive from these 33 combinations. The most unfavourable stress resultants of columns and beams cannot be predicted since it derives from the superposition of gravity and seismic loadings each multiplied by different weighting coefficients. Moreover the most unfavourable biaxial bending of a nonsquare column cannot be predicted. An efficient way to determine the most unfavourable bending of e.g. column crosssection of a storey, is to perform the dimensioning of the 33 cases under biaxial bending and select that corresponding to the maximum total area of reinforcement A_{s,tot} (of course for a specific arrangement of bars). This technique is used by the related software. Therefore for every type of structure, even if coincidence of the centres of mass and stiffness occurs due to double symmetry, biaxial bending will still be developed due to the accidental eccentricity which induces a significant seismic moment at each diaphragm. A significant torsional stiffness should therefore be provided to diaphragms (according to §5.4 torsional stiffness is K_{θ}=M/θ_{Z}) i.e. a significant resistance in moment M resulting in a relatively small diaphragm rotation θ_{Z} about Z axis. To limit large deformations due to rotation and to prevent columns from being subjected to high biaxial bending, the arrangement of adequately high stiffnesses along the diaphragm perimeter is required for minimizing the diaphragmatic rotation. For instance high stiffness is provided by a shear wall or a strong frame.
