IBC 2003

Response Spectra Analysis

On the Loads – Load Cases command in RAM Frame, the IBC 2003 modal Response Spectra Analysis is referred to as "IBC 2003 – Response Spectra".

General Procedure Response Spectrum given in Section 9.4.1.2.6 of ASCE 7-02 defines response spectra curve for the dynamic analysis.

To define the design response spectra curve as shown in Figure 9.4.1.2.6, the following information is specified by the user:

Setting	Description
Site Class	Classes A, B, C, D and E are considered. Class F is not available for selection
S_s	Maximum considered Earthquake acceleration at short period from Figure 9.4.1.1(a) - (j)
S₁	Maximum considered Earthquake acceleration at 1 second period from Figure 9.4.1.1 (a) - (j)

The structure period T is not approximated with T_α and it is not limited by T ≤ C_uT_α

Equivalent Static Lateral Force

Seismic provision of IBC 2003 permits use of one of the methods given in Section 9.5.2.5.1 of ASCE 7-02 or the "Simplified Procedure" given in Section 1617.5 of IBC 2003.

The implemented procedure is the "Equivalent Lateral Force Analysis" method given in Section 9.5.5 of ASCE 7-02. Other procedures explained in the reference are not implemented.

In the Loads – Load Cases command the IBC 2003 Seismic option is referred to as ASCE 7-02 / IBC 03 Equivalent Lateral Force.

The following data is entered by the user:

Setting	Description
Site Class	Classes A, B, C, D and E are available. Class F is not available for selection and it is not accounted for this implementation.
S_s	Maximum considered Earthquake acceleration at short period from Figure 9.4.1.1(a) - (j)
S₁	Maximum considered Earthquake acceleration at 1 second period from Figure 9.4.1.1 (a) - (j)
R	Response Modification Factor from Table 9.5.2.2
I	Seismic Importance Factor form Table 9.1.4.

Values for S_s and S₁ in Figure 9.4.1.1(a) - (j) are given for site class B with 5% damping. For other sites, they should be modified as follows:

S_MS = F_αS_s

(Eq. 9.4.1.2.4-1)

S_M1 = F_vS₁

(Eq. 9.4.1.2.4-2)

where F_α and F_V are calculated by the help of Tables 9.4.1.2.4a and 9.4.1.2.4b. The same tables are given in 1615.1.2(1) and 1615.1.2(2) of IBC 2003. Design spectral response acceleration parameters are calculated from:

S_{D S} = \frac{2}{3} S_{M S}

(Eq. 9.4.1.2.5-1)

S_{D 1} = \frac{2}{3} S_{M 1}

(Eq. 9.4.1.2.5-2)

The Seismic Design Category is specified in Tables 9.4.2.1a and 9.4.2.1b. It is based on Seismic Use Group, S_DS and S_D1 and can be determined directly from the user input. The user can either designate that the program determine The Seismic Design Category or else enter it directly; this is only necessary if the user wants to over-ride what the program would otherwise select.

The fundamental period (i.e., T) of structure can be entered by user or it can be calculated by the program. In the latter case, the program runs an Eigen analysis without any eccentricity to find T. In an third option, approximate period T_α can be used for T. The approximate period can be directly defined by the user, or it is calculated from

T_α = C_th_n^x

(Eq. 9.5.5.3.2-1)

where C_t and x are defined in Table 9.5.5.3.2. Only C_t is required from the user and corresponding value of x is determined by the program. The value ofh_n is the height above the base to the highest level of the structure. An alternative equation for T_α is also available to the user:

T_α = 0.1 N

(Eq. 9.5.5.3.2-1a)

in which N is the number of stories. Certain limitations apply for Equation 9.5.5.3.2-1a but these limitations are not checked by the program. Note also that a special equation is given to calculate T_α for masonry and concrete structures as shown in Equation 9.5.5.3.2-2 but this is also not implemented.

An upper limit is defined by the provision such that T ≤ C_uT_α and this is enforced. C_u is read from Table 9.5.5.3.1 by the program. However, this upper limit is not applied if story forces are generated for Drift.

Calculation of seismic base shear is given in Section 9.5.2.2 and it is calculated from

V = C_sW

(Eq. 9.5.5.2-1)

where W is the effective seismic weight of building and it is calculated by the program based on the Mass Dead Load specified in the Modeler. The coefficient C_s is the seismic response coefficient:

C_{S} = \frac{S_{D S}}{\frac{R}{I}}

(Eq. 9.5.5.2.1-1)

and the following limitations apply:

0.044 S_{D S} I \leq C_{S} \leq \frac{S_{D 1}}{T (\frac{R}{I})}

For buildings in Seismic Design Categories E and F:

C_{S} \geq \frac{0.5 S_{1}}{\frac{R}{I}}

The vertical distribution is given by

F_x = C_vxV

(Eq. 9.5.5.4-1)

where C_vx is vertical distribution factor:

C_{v x} = \frac{w_{x} h_{x}^{k}}{\sum_{i = 1}^{n} w_{i} h_{i}^{k}}

(Eq. 9.5.5.4-2)

and w_x and w_i are the portion of total gravity load of W at level i or x, respectively; h_i and h_x are the height from the base to level i or x, respectively; and k is 1 for T ≤ 0.5 seconds, 2 for T ≥ 2.5 seconds and it is linearly interpolated between 1 and 2 if 0.5 < T < 2.5

The generated story\diaphragm forces will be applied at 5% eccentricity of the building dimension if it is specified by the user. In this case, the program runs a separate Eigen analysis and calculates a different fundamental structural period T for each eccentric load cases. Lateral story seismic forces are calculated based on separate values of T.