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Abstract: Approximate methods provide the basis for selecting preliminary member sizes for rigorous analysis to determine whether design criteria are met. Hence simplified analyses are often used for preliminary design and for gaining valuable insight into system performance. The zero moment point method for single bay multi-storey frame and portal, cantilever, factor and stiffness centre methods for multi-storey and multi-bay frames are discussed and a comparison is made.

**Response
of structures to earthquakes: approximate analysis techniques for lateral loads**

**Abstract: **Approximate
methods provide the basis for selecting preliminary** **member sizes for
rigorous analysis to determine whether design criteria are met. Hence simplified
analyses are often used for preliminary design and for gaining valuable insight
into system performance. The zero moment point method for single bay
multi-storey frame and portal, cantilever, factor and stiffness centre methods
for multi-storey and multi-bay frames are discussed and a comparison is made.

**Key words: **zero moment point, portal,
cantilever, contra-flexure, stiffness** **centre.

**Introduction **

Even in today’s high-speed
computer-oriented world with all its sophisticated analysis capability, there
is still a need for approximate analysis of structures. First it provides a
basis for selecting preliminary member sizes because the design of a structure,
no matter how simple or complex, begins with a tentative selection of members.
With the preliminary sizes, an analysis is made to determine if design criteria
are met. If not, an analysis of the modified structure is made to improve its
agreement with the requirements and the process is continued until a design is
obtained within the limits of acceptability.

When it comes to earthquakes,
earthquake-resistant structural design often requires the ability to analyse
complex frames for lateral loads arising from systematic loading.
Sophisticated, very accurate analysis may not be necessary since large
uncertainties are involved in seismic loading. Hence simplified analyses are
often used for preliminary gaining and for getting valuable insight into system
performance. Preliminary designs are very useful in locating weak solutions.

In order to model a structure subjected to earthquake loading
several assumptions and approximations are made. Hence the results arising from
these will not reflect the true behaviour. It is customary to assume a
structure has a shear frame for the purposes of determining natural
frequencies, periods and mode shapes. For such an idealization the beam slab
system is assumed to be infinitely rigid in comparison with columns. Even
though it is deviating from reality, this reduces the dynamic degrees of
freedom quite significantly.

Frames with uniform distribution
of mass and stiffness are called regular frames and they may be idealized as a
single multi-storeyed frame for the purpose of analysis in elevation.
Structures which are unsymmetrical in plan produce torsion in plan and
introduce more shears on perimeter and corner columns. When a diaphragm is
discontinuous, it will significantly affect the distribution of forces between
the vertical lateral load resisting (VLLR) elements. Usually codal guidelines
are given for ensuring good seismic performance in the absence of detailed
analysis tools.

**Simplified analysis for
lateral loads **

The following assumptions are made:

• Horizontal
loads are concentrated at floor levels.

• The
effect of shear on deformation is neglected. This is valid for frames but not
for walls.

• The
effect of axial force in deformation is neglected. This is true as long as
total length is not small with respect to the height.

The methods of analysis are:

• For
multi-storey, single bay frame

• *Zero
moment point method *

• *Continuum
*method
(only for buildings with large degree of uniformity)* *

• For
multi-storey, multi-bay frames

• portal
method,

• cantilever
method,

• factor
method,

• stiffness
centre method.

These will be discussed in more detail in the following
sections.

Tags : Civil - Structural dynamics of earthquake engineering

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