IBC 2006 /2009

Response Spectra Analysis

On the Loads – Load Cases command in RAM Frame, the IBC 2006/2009 modal Response Spectra Analysis can be obtained using the ASCE 7-05 Response Spectra option.

General Procedure Response Spectrum given in Section 11.4 of ASCE 7-05 defines response spectra curve for the dynamic analysis.

To define the design response spectra curve as shown in Figure 11.4-1, 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 Figures 1613.5(1) through 1613.5914) of IBC 2006 (or from Figures 22-1 to 22-14 in ASCE 7-05)
S₁	Maximum considered Earthquake acceleration at 1 second period from Figures 1613.5(1) through 1613.5914) of IBC 2006 (or from Figures 22-1 to 22-14 in ASCE 7-05)
T_L	Long-period transition period (s) given in Figures from 22-15 to 22-20 in ASCE 7-05.

The structure period T is not approximated with T_α and it is not limited by T ≤ C_uT_α. Also note from Figure 11.4-1 that a new branch is added to Response Spectra curve, designated with T_L. This new part is constant-displacement part of the curve and it governs the seismic response of the structures with periods beyond T_L.

Equivalent Static Lateral Force

IBC 2006 and 2009 refers to Section 11 and 12 of ASCE 7-05 for the seismic provision. Section 12.8 refers to Equivalent Lateral Force Procedure, which is implemented.

In the Loads – Load Cases command the IBC 2006/2009 Seismic option is referred to as ASCE 7-05 / IBC 06/09 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 Figures 1613.5(1) through 1613.5(14) of IBC 2006 (or from Figures 22-1 to 22-14 in ASCE 7-05)
S₁	Maximum considered Earthquake acceleration at 1 second period from Figures 1613.5(1) through 1613.5(14) of IBC 2006 (or from Figures 22-1 to 22-14 in ASCE 7-05)
T_L	Long-period transition period (s) given in Figures from 22-15 to 22-20 in ASCE 7-05.
R	Response Modification Factor from Table 12.2-1 in ASCE 7-05.
I	Seismic Importance Factor from Table 11.5-1 in ASCE 7-05.

In order to comply with the requirements of IBC 2009 the option to Apply Requirements of Supplement No.2 must be selected.

Values for S_s and S₁ in the Figures are given for site class B with 5% damping. For other sites, they are modified as follows:

S_MS = F_αS_s

(Eq. 11.4-1)

S_M1 = F_vS₁

(Eq. 11.4-2)

where F_α and F_v are determined based on Tables 11.4-1 and 11.4-2. Design spectral response acceleration parameters are calculated from:

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

(Eq. 11.4-3)

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

(Eq. 11.4-4)

The Seismic Design Category is defined in Section 11.6 of ASCE 7-05 and it is specified in Tables 11.6-1 and 11.6-2. It is based on Occupancy Category (Table 1-1),S_DS and S_D1 and it can be determined directly from the user input. The user can either designate that the program determines 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.

Note also that if a structure is assigned to Seismic Design Category A, Section 11.7 in ASCE 7-05 precedes and forces at each level are calculated according to

F_x = 0.01w_x

(Eq. 11.7-1)

where F_x and w_x are the design lateral forces applied at story x, and the portion of the total dead load of the structure, D, located or assigned to level x, respectively. The program uses Eq. 11.7-1 if the structure is assigned to Seismic Design Category A.

The fundamental period (i.e., T) of the structure can be entered by user or it can be calculated by the program. In the latter case, the program runs an Eigenvalue 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. 12.8-7)

where C_t and x are defined in Table 12.8-2. Only C_t is required from the user and corresponding value of x is determined by the program. The value of h_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. 12.8-8)

in which N is the number of stories. Certain limitations apply for Equation 12.8-8 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 12.8-9 but this is also not implemented.

An upper limit is defined by the provision such that T ≤ C_uT_α and this is enforced. The term C_u is read from Table 12.8-1 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 12.8.1 and it is calculated from

V = C_sW

(Eq. 12.8-1)

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. 12.8-2)

and the following limitations apply:

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

for T ≤ T_L

(Eq. 12.8-3)

C_{S} \leq \frac{S_{D 1} T_{L}}{T^{2} (\frac{R}{I})}

for T > T_L

(Eq. 12.8-4)

Also C_s shall not be less than

C_s = 0.01

(Eq. 12.8-5)

If the option to apply the requirements of Supplement No. 2 is selected, Eq. 12.8-5 is modified to be:

C_s = 0.044S_DSI ≥ 0.01

(Eq. 12.8-5)

In addition, for structures located where S₁ is equal to or greater than 0.6g, C_s shall not be less than

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

(Eq. 12.8-6)

The vertical distribution is given by

F_x = C_vxV

(Eq. 12.8-11)

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. 12.8-12)

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.