In all the codes in one way or the other the following parameters are involved. • elastic seismic coefficient (base shear); • design force reduction; • lateral force distribution; • overturning moments.
Comparison of codes
In all the codes in one way or the other the following
parameters are involved.
• elastic
seismic coefficient (base shear);
• design
force reduction;
• lateral
force distribution;
• overturning
moments.
1 Base shear
NEHRP provisions, the source document of the IBC, gives the
period formula identical to the Rayleigh method in which static
deflection due to a set of lateral forces F_{i} is u_{i}
assumed as shape function. The period formula given by the NBCC has the same
base except that the lateral forces used to determine the static deflections
are equal to the lumped weight at the floors. For a linear elastic system we
have seen that elastic seismic coefficient C_{e} is related to
pseudo-acceleration spectrum for an SDOF system
By taking R = Q′ = q′
= 1 C_{e} in the building code corresponds to A/g
and these two values given by Eq. 19.65 and 19.66 are not identical.
2 Design force
reduction
Most codes specify that the
design base shear to be smaller than the elastic base shear (determined from
using elastic seismic coefficient C_{e}). For most of the codes
discussed the reduction factors are R, Q′ and q′
where R = Q′ = q′ = 4
factors independent of T_{1} in IBC and NBCC and depends
on period in MFDC and EC. The actual strength of the building exceeds
design strength, especially for short period systems. The over-strength of a
building is usually not recognized explicitly in building codes.
3 Lateral force
distribution
According to structural dynamics force at any floor level i
If φ_{jn} is
proportional to h_{j} then NBCC agrees with structural dynamics
formula. Linear mode shape is a reasonable shape for a building in between ρ = 0 and ∞ (ρ = beam to column stiffness). In IBC the height-wise
distribution of lateral force based on the assumption that lateral displacement
is proportional to the heights when T_{1} ≤ 0.5 s and to h ^{2}_{j}
when T_{1} ≥ 2.5 s
and to an intermediate power of the height for intermediate values of T_{1}.
This is intended to recognize the changing fundamental mode and increasing
higher mode contributions to response with increasing T_{1}. The
Indian code uses
but stipulates dynamic analysis for regular buildings h
> 40 m in Zones IV and V and h > 90 m in Zones II and III. In such
cases
and storey shears for all modes must be done using SRSS and
CQC rules.
4 Overturning
moments
Certain building codes such as
NBC, IBC, and MFDC allow reduction of overturning moment relative to the values
computed by lateral force F_{j} by statics because the response
contribution of higher modes are more significant for storey shear than the
overturning moments. The reduction factor in IBC at the base of the building
varies between 1 (no reduction) and 0.8, depending on the number of stories.
The EC-8 permits no reduction of overturning moments relative to the values
computed from lateral forces by statics.
In the following, we will calculate
shear in various buildings based on IS1893 2002, Part 1. The method used in the
other codes will be similar except for some variations. The reader can adapt
the following problems according to their country’s seismic code or
international building code.