Level 0.0 m
Figure 4.8 Structural layout taken for regularity checks
The floor slabs in the tower are rectangular, without branches, and have an aspect ratio in the tower (see 4 below) of 56 m/20 m = 2.8, which is relatively compact. Given the uniform distribution of mass and lateral load resisting elements (i.e. the frames and shear walls) in the long direction, a continuous concrete solid slab or topping slab over precast elements of at least 70 mm would not be expected to give rise to uneven load distributions, unless there ere substantial openings in the slabs.
4 The ratio of longer side to shorter sides in plan does not exceed 4. The ratio in the tower is 2.8 (see above).
5 The torsional radius, r , in the X (short) direction must exceed 3.33 times e , the eccentricity bettveen centres of stiffness and mass in the X direction. Similarly, r must exceed 3.33 times e .
The EC 8 Manual (ISE/AFPS 2009) gives conservative but simplified rules for satisfying this condition for some standard cases, but does not cover that of a uniform space frame with isolated shear walls, as here. The well distributed layout of shear walls and frames suggests that the structure should possess adequate torsional stiffness. 3 computer analysis was carried out to perform a detailed check, as follows.
Top deflection at top of building in X (short) direction under 1000 kN load applied at stiffness centre in X direction: 7.35 mm
Top deflection at top of building in Y (long) direction under 1000 k load applied at stiffness centre in Y direction: 7.14 mm
Top rotation at top of building about Z (vertical) axis under 1000 kNm moment about Z axis: 8.18 E-6 radians
Note: The building is taken as perfectly symmetrical, and so the geometric centre, the centre of stiffness and the centre of ass all coincide. For cases where the stiffness and mass centre do not coincide with the geometric centre, see the example calculation in Appendix A of the EC8 Manual (ISE/ AFPS 2009).
stiffness Y stiffness =
orsional stiffness r =
1000/(7.35E-3) = 1000/(7.14E-3) = 1000/(8.18E-6) = (122E6/140E3) * = 0.3*29.5 = (61.7E6/137E3)* = 0.3*30 =
Therefore, the separation bettveen centres of mass and stiffness needs to be less than about 9 m.
rx and ry must exceed the radius of gyration, l, otherwise the building is classified as 'torsionally flexible', and the q values in concrete buildings are greatly reduced.
The radius of gyration, assuming a uniform mass distribution, is calculated as follows. It can be seen that the requirement for regularity is satisfied.
ls =[(562 + 202)/12] * = 17.2 m < rx (=29.5 m) and < ry (=30 m) - OK.
The EC 8 Manual (ISE/AFPS 2009) notes that an alternative demonstration that this condition is satisfied is to show that the first predominantly torsional mode has a lower period than either of the first predominantly translational modes in the two principal directions. A 3D computer analysis, which assumed that the mass and stiffness centres coincided, gave the following values, confirming that this applies to the present structure. The period of the first torsional ode is ell belo that of the first to translational odes, reflecting the large excess of rx and ry over ls calculated previously.
Period of first Y translational mode 0.90 s Period of first translational ode 0.88 s Period of first torsional mode 0.62 s ence all the conditions for regularity in plan are satisfied.
4.9.3 Regularity in elevation
The following conditions must be met:
1 All the vertical load resisting elements must continue uninterrupted from foundation level to the top of the building or (where setbacks are present - see 4 below) to the top of the setback.
2 Mass and stiffness must either remain constant with height or reduce only gradually, without abrupt changes. Quantification is not provided in EC8; the EC8 Manual (ISE/AFPS 2009) recommends that buildings here the ass or stiffness of any storey is less than 70 per cent of that of the storey above or less than 80 per cent of the average of the three storeys above should be classified as irregular in elevation.
The ground floor has a storey height of 4.3 m, compared with 3.5 m for the upper storeys, which tends to reduce stiffness by a factor of approximately (3.5/4.3)2 = 66 per cent, which is a bit less than the 70 per cent or 80 per cent proposed above. However, there are more columns in the ground floor
- an additional 50 per cent - which offsets this, as does the base fixity of the ground floor columns and shear walls. Overall, this suggests that the stiffness ratio is within limits.
A 3D computer analysis shows that under earthquake loading, the ground floor storey drift is significantly less than that of the first floor, confirming that the stiffness check is satisfied. here is a stiffness change here the columns reduce in section at the fifth floor, but this is a reduction in stiffness so the regularity condition is et.
The assumption that there is similar use of the floors in the tower at all levels above ground level leads to the conclusion that the ass at one level is always less that of the level below.
Hence the 'soft storey' check is satisfied.
3 In buildings with moment-resisting frames, the lateral resistance of each storey (i.e. the seismic shear initiating failure within that storey, for the code-specified distribution of seismic loads) should not vary 'disproportionately' between storeys. Generally, no quantified limits are stated by EC8, although special rules are given where the variation in lateral resistance is due to masonry infill within the frames. The ISE Manual on EC8 (ISE/AFPS 2009) recommends that buildings where the strength of any storey is less than 80 per cent of that of the storey above should be classified as irregular in elevation.
It is unlikely that any viable design ould violate this condition. It cannot, of course, be checked without knowledge of the reinforcement in the beams, columns and walls.
4 Buildings with setbacks (i.e. where the plan area suddenly reduces bettveen successive storeys) are generally irregular, but may be classified as regular if less than limits defined in the code. The limits broadly speaking are a total reduction in idth fro top to botto on any face not exceeding 30 per cent, ith not ore than 10 per cent at any level compared to the level below. However, an overall reduction in width of up to half is permissible within the lowest 15 per cent of the height of the building.
The reduction in building width between the ground and first floors, as the tower rises above the podium, constitutes a setback. Since the ground floor height, at 4.3 m, is less than 15 per cent of the total height of 28.8 m (28.8 times 0.15= 4.32 m), and the reduction in width is from 40 m to 20 m (= 50 per cent reduction), the setback remains (just) within 'regular' limits. ence all the conditions for regularity in elevation are satisfied.
Booth E. and Key D. (2006) Earthquake design practice for buildings. Thomas Telford, London.
Chen W-F. and Scawthorn C. (2003) (editors) Earthquake engineering handbook.
Press, oca aton F . Hamburger R. and Nazir N. (2003) Seismic design of steel structures. In: Chen and Scawthorn (editors), Earthquake engineering handbook. CRC Press, Boca Raton FA.
ISE/AFPS (2009) Manual for the seismic design of steel and concrete buildings to
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