IBC 2000

Response Spectra Analysis

The IBC response spectra load case can be selected using the Loads – Load Cases command in RAM Frame. It is the IBC 2000 – Response Spectra item in the list of Dynamic load types. IBC Section 1615.1.4, General procedure response spectrum, defines the response spectra curve to be used for the dynamic analysis.

The curve is given in Figure 1615.1.4. In order to calculate those values the following values are specified by the user:

Setting	Description
Site Class	from Table 1615.1.1
S_s	from Figures 1615(1) through 1615 (10)
S₁	from Figures 1615(1) through 1615 (10)

As identified in Table 115.1.2(1) and its footnote, in some cases a site-specific response spectra curve may be required for Site Classes E and F.

The structure period, T, used is that calculated for the structure. It is not the approximate T_α nor T limited by C_uT_α

Equivalent Static Lateral Force

The IBC 2000 seismic force load case can be selected using the Loads – Load Cases command in RAM Frame. The equivalent lateral force procedure is defined in IBC Section 1617.4, Equivalent lateral force procedure for seismic design of buildings.

The following input values are required:

Setting	Description
R	Response modification factor from Table 1617.6
I_E	Seismic Importance factor, from Table 1604.5
Site Class	from Table 1615.1.1
S_s	from Figures 1615(1) through 1615 (10)
S₁	from Figures 1615(1) through 1615 (10)

An error message is given if Site Class E and values of S_s greater than 1 or S₁ greater than 0.4 are specified, since tabular values of F_α and F_v are not given for those values. Also, Site Class F is not available for selection. In those cases a site-specific response spectra analysis is required.

The Seismic Design Category is specified in Table 1616.3(1) and Table 1616.3(2). It is based on the Seismic Use Group, S_DS, and S_D1 and can be determined directly from the user input described above. 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 user can either enter the fundamental period T or else designate that the program calculate it.

Story\diaphragm forces can be generated as required for Drift, where the upper limit on T of Section 1617.4.2 (T ≤ C_uT_α) does not apply (Section 1617.4.6.1), or those required for determining member design forces. This is specified with the Provisions for: option.

From the input values, the following are calculated:

F_α is determined from Table 1615.1.2(1), based on Site Class and S_s. For values of S_s between the values shown, straight-line interpolation is used to determine F_α.

F_v is determined from Table 1615.1.2(2), based on Site Class and S₁. For values of S₁ between the values shown, straight-line interpolation is used to determine F_v.

S_MS = F_αS_s

(Equation 16-16)

S_M1 = F_vS₁

(Equation 16-17)

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

(Equation 16-18)

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

(Equation 16-19)

The seismic base shear is given by:

V = C_sW

(Equation 16-34)

where:

C_{S} = \frac{S_{D S} I_{E}}{R}

(Equation 16-35)

C_s need not exceed:

C_{S} \leq \frac{S_{D 1} I_{E}}{R T}

(Equation 16-36)

but shall not be taken less than:

C_s ≤ 0.044S_DSI_E

(Equation 16-37)

If Seismic Design Category E or F, or if S₁ ≥ 0.6g, C_s shall not be taken less than:

C_{S} \geq 0.5 S_{1} \frac{I_{E}}{R}

(Equation 16-38)

W is the seismic weight, as currently calculated by the program, based on the Mass Dead Load specified in the Modeler.

The vertical distribution of the shear is given by:

F_x = C_vxV

(Equation 16-41)

Where

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

(Equation 16-42)

And

k = 1 for T ≤ 0.5 s.
k = 2 for T ≤ 2.5 s.
k is linearly interpolated between 1 and 2 for 0.5 < T < 2.5

Limitations

For Seismic Design Category A, an alternate Minimum Lateral Force procedure is permitted, whereby the story force is given as 0.01w_x (Section 1616.4). This has not been implemented. It can easily be done by the user as a user-defined story load case.

In some cases a Simplified analysis procedure is allowed (Section 1617.5) whereby the story force is given as $1.2 \frac{S_{D S} w_{x}}{R}$ . This has not been implemented. It can easily be done by the user as a user-defined story load case.

For regular structures in Seismic Design Categories D, E and F, limits are allowed on S_s and S₁ (Section 1616.6.3). The conditions that allow these limits are not investigated by the program and hence these limits will not be incorporated by the program; the user can directly input the limited S_s and S₁ values when appropriate.