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Steel Designers' Manual - 6th Edition (2003)
368 Applicable dynamics
Table 12.4 Typical modal damping values by structure type
Structure type Structure damping (% critical)
Unclad welded steel structures 0.3%
(e.g. steel stacks)
Unclad bolted steel structures 0.5%
Composite footbridges 1%
Floor (fitted out), composite and 1.5%–3%
non-composite (may be higher when many
partitions on floor)
Clad buildings (lateral sway) 1%
Damping is usually expressed as a fraction or percentage of critical (x), but the
logarithmic decrement (d ) is also used. The relationship between the two expressions
is x = d/2p.
Table 12.4 gives typical values of modal damping that are suggested for use in calculations
when amplitudes are low (e.g. for occupant comfort). Somewhat higher
values are appropriate at large amplitudes where local yielding may develop, e.g. in
seismic analysis.
12.5 Finite element analysis
Many simple dynamic problems can be solved quickly and adequately by the
methods outlined in previous sections. However, there are situations where more
detailed numerical analysis may be required and finite element analysis is a versatile
technique widely available for this purpose. Numerical analysis is often necessary
for problems such as:
(1) determination of natural frequencies of complex structures
(2) calculation of responses due to general time-varying loads or ground motions
(3) non-linear dynamic analysis to determine seismic performance.
12.5.1 Basis of the method
As explained in Chapter 9 the finite element method describes the state of a structure
by means of deflections at a finite number of node points. Nodes are connected
by elements which represent the stiffness of the structural components.
In static problems the equilibrium of every degree of freedom at the nodes of the
idealization is described by the stiffness equation:
F = KY
where F is the vector of applied forces, Y is the vector of displacements for every
degree of freedom, and K is the stiffness matrix. Solution of unknown displacements
for a known force vector involves inversion of the stiffness matrix.