How To Make Seismic Load On Roofs Design and Calculation?

Seismic Loads Calculations
The engineering approach to seismic design differs from that for other load types. For live, wind or snow loads, the intent of a structural design is to preclude structural damage. However, to achieve an economical seismic design, codes and standards permit local yielding of a structure during a major earthquake.

Local yielding absorbs energy but results in permanent deformations of structures. Thus seismic design incorporates not only application of anticipated seismic forces but also use of structural details that ensure adequate ductility to absorb the seismic forces without compromising the stability of structures.

Provisions for this are included in the AISC specifications for structural steel for buildings. The forces transmitted by an earthquake to a structure result from vibratory excitation of the ground. The vibration has both vertical and horizontal components.

However, it is customary for building design to neglect the vertical component because most structures have reserve strength in the vertical direction due to gravity-load design requirements. Seismic requirements in building codes and standards attempt to translate the complicated dynamic phenomenon of earthquake force into a simplified equivalent static force to be applied to a structure for design purposes.

For example, ASCE 7-95 stipulates that the total lateral force, or base shear, V (kips) acting in the direction of each of the principal axes of the main structural system should be computed from
V = CsW(9.139)

where Cs seismic response coefficient
W total dead load and applicable portions of other loads

The seismic coefficient, Cs, is determined by the following equation:
Cs = 1.2Cv /RT^2/3(9.140)

where Cv seismic coefficient for acceleration dependent (short period) structures
R response modification factor
T fundamental period, s

Alternatively, Cs need not be greater than
Cs = 2.5Ca/R(9.141)

where Ca seismic coefficient for velocity dependent (intermediate and long period) structures.

A rigorous evaluation of the fundamental elastic period, T, requires consideration of the intensity of loading and the response of the structure to the loading. To expedite design computations, T may be determined by the following:
Ta = CThn^3/4(9.142)

where CT 0.035 for steel frames
CT 0.030 for reinforced concrete frames
CT 0.030 steel eccentrically braced frames
CT 0.020 all other buildings
hn height above the basic to the highest level of the building, ft

For vertical distribution of seismic forces, the lateral force, V, should be distributed over the height of the structure as concentrated loads at each floor level or story. The lateral seismic force, Fx, at any floor level is determined by the following equation:
Fx = CuxV(9.143)

where the vertical distribution factor is given by
where wx and wi height from the base to level x or i
k 1 for building having period of 0.5 s or less 2 for building having period of 2.5 s or more  use linear interpolation for building periods between 0.5 and 2.5 s

For horizontal shear distribution, the seismic design story shear in any story, Vx, is determined by the following:


where Fi the portion of the seismic base shear induced at level i. The seismic design story shear is to be distributed to the various elements of the force resisting system in a story based on the relative lateral stiffness of the vertical resisting elements and the diaphragm. Provision also should be made in design of structural framing for horizontal torsion, overturning effects, and the building drift.

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