Design Procedures: Standards and Codes

5.2.2.1 NZS1170.5

The New Zealand Structural Design Actions Standard NZS1170.5:2004 (Standards New Zealand, 2004a) provides restrictions on the use of some analysis methods. The ESA method may be employed when at least one of the following criteria is satisfied:

The height between the base and the top of the structure is less than 10m; The largest translational period calculated is less than 0.4s;

The structure is not classified as irregular by the Standard and the largest translational period is less than 2.0s.

For structures which do not met the criteria for the ESA method, a two dimensional (2D) modal response spectrum method may be employed if the structure is not classified as torsionally sensitive, as per (Standards New Zealand, 2004a). If the structure is classified as torsionally sensitive either a three dimensional modal response spectrum or a time history analysis should be employed. Generally, time history analyses are made for major structures to check that structures, designed on the basis of the modal response spectrum approach, are adequate.

The New Zealand Structural Design Actions Standard provides requirements on how floor diaphragms should be analysed. These require buildings over 15m in height, which are classified as irregular, to be analysed with either the three dimensional modal response spectrum method or by three dimensional THA and also consideration is given to the of flexibility diaphragms for diaphragms which are assessed to be flexible.

5.2.2.2 FEMA450

The American Seismic Design Standard FEMA450 (National Earthquake Hazards Reduction Program (U.S.) et al., 2004) is similar to other design codes in that it imposes restrictions on the use of some design methods for more complicated types of structures. The use of all analytical methods including: the ESA, modal response spectrum procedure, elastic and inelastic time history analysis methods, are permitted for both regular and irregular structures which have a low associated seismic hazard level. Further, a structure which is of light framed construction, limited irregularities and has a fundamental period which is less than 3.5 times Ts, where Ts is the period where the constant velocity section of the response spectrum starts, may also be designed with all of these analyses methods. All other structures are not permitted to be designed using the ESA method and other, more complex, approaches are required.

In the USA, the design method for diaphragms depends on the seismic design category and the structural characteristics of the building (seismic force resisting system, fundamental period of vibration and the configuration of the structure). The seismic design category is based on the importance of the structure and the seismicity of the region. Seismic design category A is the least hazardous and seismic design category F is the most hazardous.

For seismic design category A, the lateral force applied to the diaphragms shall be calculated from Equation 5 1.

x

x w

F =0.01 _{Equation 501}

Where Fx is the design lateral force and wx is the portion of total seismic weight, located at

level x.

For seismic category B, a minimum force that should be used, applied to the diaphragm, is equal to 20% of the short period design spectral response acceleration, SDS, multiplied by the weight of the floor, together with the weight of other attached elements plus the portion of base shear force at the level which is to be resisted by the seismic force resisting system.

For seismic design category C, the structural analysis methods, which are allowed to be used to determine the design forces, are the same as those in seismic category B with some additional restrictions.

For seismic design category D, E and F, diaphragms shall be designed to resist the forces obtained from proportioning the values from the ESA method to the relative weight of the floor diaphragm, as indicated by Equation 5 2.

px n x i i n x i i px w w F F

∑

∑

= = = Equation 502

Where wi is the weight associated with level i, Fi is the lateral force at level i, n represents the

number of levels and wpx is the weight associated with the diaphragm of interest.

In the situation where vertical or plan irregularity may exist, the design forces are increased by an adjustment factor which gives an additional 25% for connections of diaphragms to

vertical resisting system elements. Criteria for when diaphragm flexibility should be considered in a design are also provided.

5.2.2.3 Eurocode 8

In Eurocode 8 (British Standards Institution., 2005) the design criterion for floor diaphragms is similar to that provided in the New Zealand Structural Design Actions Standard. The ESA method may be used for structures where higher modes do not significantly affect the structural response and the structure meets the regularity requirements. Modal response spectrum analyses are to be carried out when the ESA method does not satisfy the criteria outlined above. Structures which do not meet these criteria were required to be designed using modal response spectrum 3 dimensional analysis.

Structural regularity is considered in Eurocode 8 (2004) by considering the: symmetry, stiffness and mass distribution of the building, set backs in the floor, stiffness and the slenderness of the floor diaphragm. If the structure is found to be irregular, a reduction factor of 0.8 is applied to the behaviour factor (the behaviour factor is an approximation of the ratio of the seismic force that is expected to occur in the structure if the structure was to remain elastic and the seismic force that can be used in design) and limits are imposed on the method of analysis that can be used. This factor results in increasing the strength of the structure by 25% and it is similar to the adjustment factor that is used in FEMA450.

5.2.3 Bull (2003)

Bull (2003) suggested that a type of pseudo equivalent static analysis (pESA) method could be used to find floor diaphragm forces. This approach was suggested as an alternative method to the “Parts and Component” and the ESA methods. The “Parts and Components” approach vastly over predicts the forces and the ESA method under predicts the forces at the lower levels of the structure. Bull (2003) described the pESA method as one that is based on the application of a set of static forces, which is static method which is similar to the ESA method, but it accounts for over strength of the structure due to the inelastic response of the lateral force resisting system.

The pESA method was visualised as an equivalent type of method where equilibrium was maintained in the system allowing the force paths to be tracked through the floor diaphragm to different parts of the lateral force resisting system. The method was also envisaged to account for both the affects of transfer and inertial forces.

5.2.4 Rodriguez et al. (2000)

Rodriguez et al. (2000) carried out an analytical investigation on earthquake induced horizontal floor accelerations that developed in regular buidings with rigid diaprhagms. A new method, referred to as the first mode reduced method, which estimates the accelerations which develop in floor diaphagms was proposed from their work.

The first mode reduced method determines the absolute floor accelerations by the use of Equation 5 3. It is based on findings from a parametric analysis that was carried out on a twelve storey cantilever wall building that was designed with a structural ductility of 5. The parametric study was carried out using non linear time history analysis. The findings from this parametric study were:

− The maximum floor amplification occurs when the building responds elastically;

− The floor amplification tends to diminish as the ductility demand increases. The absolute floor acceleration, Aqn, is given by Equation 5 3.

q q q q n q q n R T Sa A =ΓΦ ( ,

ξ

) Equation 503

Where Гq is the participation factor for mode q, Φ q

n is the mode shape for mode q at level n,

Sa is the spectral acceleration, Tq is the period of free vibration associated with mode q, ξq is

the damping ratio for mode q and Rq is the reduction factor to account for the ductility of the

system.

A simplification of this method was made as a parametric study found that higher modes are not significantly affected by the ductility of the system. This allowed Rq, for modes greater

than 1, to equal 1. Additional assumptions were made to allow it to be used with a generic design spectrum. These included:

− Assume all modes of free vibration have the same damping ratios, which allows the spectral acceleration terms to be obtained from the same design spectra;

− All natural periods of free vibration corresponding to the high translational modes are associated with the maximum spectral ordinate.

The simplified equation, based on these assumptions, is shown in Equation 5 4 and how this correlates to the horizontal design force for a floor is given in Equation 5 5.

[

]

2 2 1 1 1

₍

_,1)

_0.7ln(

₎

ho h pm

C

T

n

C

R

n

C



+











=

Equation 504 p pi p p ph S R ZC W F = Equation 505

Where n1, is a first mode contribution coefficient, R1, a ductility factor ( /2 or 1, the greater),

Ch(T,1), is the horizontal seismic coefficient, Cho, is the peak ground acceleration divided by

the acceleration of the gravity defined in the basic hazard acceleration design spectra, Sp is

the structural performance factor, Rp is the risk factor for the part, Z is the seismic zone factor,

Cpi is the basic design coefficient at the intermediate level between the base and the level

corresponding to the uppermost principle seismic weight and Wp is the weight of the part.

5.3 Motivation

The Equivalent Static Analysis (ESA) method, which is commonly used for seismic design of structures, determines the forces for the lateral force resisting system of the structure. However, this approach does not adequately account for the forces which develop in floor diaphragms. These forces are under predicted due to over strength affects and both higher elastic and inelastic mode actions.

Various researchers, as described in Section 5.2.2.1, have indicated that the ESA method poorly predicts the forces which develop in the lower floors of structures. Findings from both the dual structures study and the moment resisting frame study (described in Chapter 3 and 4) indicate diaphragm forces are higher than the forces predicted by the ESA due to higher mode effects.

Inelastic time history analysis (THA) currently provides the most accurate estimate of the behaviour of a structure in response to earthquake actions. This method requires a considerable amount of information about the details of the structure and a substantial amount of time to carry out the required analyses. Static design approaches provide a simpler, quicker option for regular structures which avoid the sensitivity of the predicted actions to the choice of earthquake records and the hysteretic response relationships assumed for plastic regions, associated with THA procedures.

The first mode reduced method, proposed by Rodriguez et al. (2000), provides an approach with a level of complexity that lies between the ESA and inelastic time history analysis

In document Design Recommendations and Methods for Reinforced Concrete Floor Diaphragms Subjected to Seismic Forces (Page 196-200)