Civil Engineering Reference
In-Depth Information
loads in large structures is inversely proportional to the size of the structure (Nowak and Collins, 2000 ).
Therefore, the plan aspect ratio should be not greater than 2-3. Alternatively, the structure may be
subdivided into independently responding parts by using seismic joints. Movement gaps are relatively
easy to construct for bridge structures but are often highly unreliable in buildings. Separation joints
should be large enough to accommodate lateral displacements between adjacent buildings and to avoid
pounding, as discussed in Section A.1.2. Out-of-phase movements dictate the size of the gap between
adjacent structures. As a rule of thumb, the separation(s) can be assumed as 1/100 of the maximum
height (
H
) of the adjacent structures, in metres. Separation joints can help to mitigate unfavourable
seismic effects on multi-mass structures. It should, however, be noted that they can have disastrous
effects because of gas entrapment during post- earthquake fi res. Debris from severely damaged or
partially collapsed upper storeys can also fall in separation joints. These should be sealed, where
possible, to prevent such occurrences.
Irregularities in plan arise when vertical elements of the lateral force-resisting system are not parallel
to or symmetric with major orthogonal axes. Shapes with sharp corners are unsuitable for seismic
resistance because of the high probability of torsional forces under earthquake motions. Wedge- shape
plans have large eccentricity between centre of mass and centre of rigidity. In addition, different relative
stiffnesses between narrower and wider perimeter sides exacerbate torsional effects.
Discontinuities in horizontal and vertical lateral resistant systems are an additional source of irregu-
larity in plan. Out-of-plane offsets of vertical elements, for example, may impose signifi cant demands
on structural components of earthquake-resistant structures. Extensive damage may be caused by these
offsets; they should not be employed in seismic areas.
A.1.2 Elevation Regularity
Structural systems can be characterized by several types of irregularities in elevation depending on their
geometrical confi guration and mechanical properties along the height. For example, asymmetrical geom-
etry with respect to the vertical axis can cause vertical irregularities in buildings. Structures with setbacks,
i.e. with re-entrant corners along the height are irregular. Setbacks often introduce stiffness and strength
discontinuities in lateral force-resisting systems. High inelastic demands are concentrated in zones of
vertical offsets. Damage is likely to occur in these ' notch regions ' during earthquakes. Unfavourable
effects due to setbacks depend on the relative proportions and absolute size of the system. Pyramid and
inverted pendulum confi gurations are extreme examples of vertical setbacks (Figure A.7), but they do not
have corners. The pyramid is the optimal geometric shape for earthquake resistance. The bulk of the mass
is located near the ground and its plan density is extremely high. By contrast, the inverted pendulum (or
inverted setback) has low resistance to overturning and unfavourable location of the mass at the top of
the structure. In both cases, the absence of re-entrance prevents concentration of inelastic demand at
corners along the height. Inverted pendulum structures also have low redundancy and overstrength, and
concentrate their inelastic behaviour at their bases. They exhibit substantially lower energy dissipation
capacity compared to pyramidal shapes, as well as to several other lateral resisting systems.
The aspect ratio of the building in elevation affects the overturning moment exerted on the founda-
tions. Very slender structures suffer from higher mode contributions, which can cause damage at
intermediate storeys. In addition, structures with higher mode effects exhibit a complex dynamic
response that necessitates the use of more elaborate seismic force calculation methods. Therefore,
buildings and structures employing low aspect ratios (
H
/
B
) are considered regular.
Post-earthquake observations have shown that a considerable percentage of damaged structures suffer
from non - orthogonal and non -coaxial member axes. Axes with offsets are found either in plan or eleva-
tion in several RC multi-storey buildings. All beams and columns should therefore have the same axes
with no offset between adjacent members. Examples of members with offsets are shown in Figure A.8 .
Large variations in size between connected members undermine the uniformity of load paths
