The fundamental natural frequency of the joist mode and
the girder mode can be determined from equation 3.3 on page 11 of the design
guide:
For the combined mode, the fundamental natural frequency
can be determined from equation 3.4 on page 11 of the design guide:
Δj and
Δg
are the local deflection of the joist and the girder determined from a
secondary operation after the analysis. The stiffness analysis will yield the
global deflection values for the girder beams. A line joining the start and the
end nodes of the girder beam in its deflected position is created as a base
line. Relative to this base line, the deflection values are zero for the start
and end nodes. The local deflection values of the intermediate points of the
girder beam are evaluated from the global deflection values relative to this
base line.
It is this local deflection that is used in calculating
the fundamental natural frequency as shown in the earlier equations. Further,
the local deflection is also used in calculating the equivalent uniform loading
on the joist and the girder, wj and wg, as shown in the equation on page 21 of
the AISC Design Guide:
In addition to the terms
fj,
Δj,
wj
shown above , the following additional terms —Ds,
Dj,
Bj,
and Wj — which
are explained below, are also reported for the joist mode.
For the girder mode, the terms reported include
fg ,
Δj,
wg
which were explained earlier, and,
Dg ,
Bg,
and Wg which are
described below.
For the combined mode of vibration the parameters
reported are fn,
W,
β, Peak
Acceleration and Acceleration Limit.
fn is calculated from equation 2 shown above.
W is the equivalent
panel weight in the combined mode and is calculated from the equation shown on
page 21 of the AISC Design Guide:
The peak acceleration due to walking excitation is then determined from the equation 4.1
on page 17 and on page 21 of the AISC Design Guide:
The acceleration limit is determined from Table 4.1 on
page 18 of the Design Guide.