China GB50011-2001

Response Spectra Analysis

Design acceleration response spectrum (i.e., seismic influence coefficient curve) is given in Design Acceleration Response Spectrum (China GB50011-2001) , where the following parameters are used:

η_{1} = 0.02 + \frac{0.05 - ξ}{8} \geq 0

η_{2} = 1 + \frac{0.05 - ξ}{0.06 + 1.7 ξ} \geq 0.55

γ = 0.9 + \frac{0.05 - ξ}{0.5 + 5 ξ}

and ξ is damping coefficient (user defined value in the dialog). It is can be also summarized as follows:

α = {\begin{matrix} (0.45 + \frac{η_{2} - 0.45}{0.1} T) α_{\max} & T \leq 0.1 \\ η_{2} α_{\max} & 0.1 < T \leq T_{g} \\ {(\frac{T_{g}}{T})}^{γ} η_{2} α_{\max} & T_{g} < T \leq 5 T_{g} \\ [η_{2} {0.2}^{γ} - η_{1} (T - 5 T_{g})] α_{\max} & 5 T_{g} < T \leq 6 \end{matrix}

where α_max is maximum acceleration, and it is determined from the following Table 5.1.4-1 in the building code:

Design Acceleration Response Spectrum (China GB50011-2001)

Table 1. Maximum value of horizontal seismic influence coefficient (α_max)
	Intensity 6	Intensity 7	Intensity 8	Intensity 9
Frequently EQ	0.04	0.08 (0.12)	0.16 (0.24)	0.32
Rarely EQ	-	0.50 (0.72)	0.90 (1.20)	1.40

Note that the values in the brackets are used for the regions which design basis earthquake acceleration values are 0.15g or 0.30g.

The parameter T_g (characteristic period) is determined according to Table 5.1.4-2 in the building code:

EQ Group	Soil Site Class
EQ Group	I	II	III	IV
1	0.25	0.35	0.45	0.65
2	0.30	0.40	0.55	0.75
3	0.35	0.45	0.65	0.90

Note: According to Section 5.1.4, the values given in the above table for T_g shall be increased by 0.05 seconds for rarely earthquake of Intensity 8 and 9,whichis enforced in the current implementation.

Equivalent Static Lateral Force

In the following discussion, GB50011-2001 seismic is referred for base shear calculations and other related topics.

Seismic base shear according to the Chinese code is calculated as follows:

F_EK = α₁G_eq

where

α₁	=	seismic influence coefficient
G_eq	=	Equivalent gravity load (seismic weight) of building

In calculation of G_eq, the followings are considered:

When the structure is modeled as a single-mass system, the representative value of the total gravity load shall be used
When the structure is modeled as a multi-mass system, the 85% of the representative value of the total gravity load may be used.

The calculated base shear is distributed among stories based on the following equation:

F_{i} = \frac{G_{i} H_{i}}{\overset{n}{\sum_{j = 1}} G_{j} H_{j}} F_{E k} (1 - δ_{n})

where

i	=	1,2,…,n
F_i	=	applied story load at i^th story
G_iH_i	=	seismic weight and height of the i^th story, respectively
δ_i	=	additional seismic action factor at the top story of building

A graphical interpretation of these quantities is shown in the figure below:

China Seismic Load Case Vertical Load Distribution

Note that the additional load ΔF_n applied at the top story is computed based on

ΔF_n = δ_nF_EK

The following options are provided to calculate δn:

it is not considered (i.e., ΔF_n =0)
δn is provided by the engineer
it is directly read from the Table 5.2.1 of GB50011-2001.

In the Table 5.2.1, T is the building fundamental period for a given loading direction and T_g is characteristic period determined from soil site class category and EQ group (both parameters should be defined in the dialog). The term T_g is read from Table 5.1.4-2 and it is increased by 0.05 seconds for rarely earthquake of Intensity 8 and 9.

The term α₁ is referred to as seismic influence coefficient, and it is a function of building period ( T ) and design acceleration response spectrum (or also known as seismic influence coefficient curve). The design acceleration response curve is defined as follows

α = {\begin{matrix} (0.45 + \frac{η_{2} - 0.45}{0.1} T) α_{\max} & T \leq 0.1 \\ η_{2} α_{\max} & 0.1 < T \leq T_{g} \\ {(\frac{T_{g}}{T})}^{γ} η_{2} α_{\max} & T_{g} < T \leq 5 T_{g} \\ [η_{2} {0.2}^{γ} - η_{1} (T - 5 T_{g})] α_{\max} & 5 T_{g} < T \leq 6 \end{matrix}

where

η_{1} = 0.02 + \frac{0.05 - ξ}{8} \geq 0

η_{2} = 1 + \frac{0.05 - ξ}{0.06 + 1.7 ξ} \geq 0.55

γ = 0.9 + \frac{0.05 - ξ}{0.5 + 5 ξ}

and ξ is damping coefficient. The above information can be also expressed on a single curve:

Design Acceleration Response Spectrum (GB50011-2001)

Note: α_max is maximum value of horizontal seismic influence coefficient and it is determined from Table 5.1.4-1.

Once the seismic loads are computed for each diaphragm, the following check is also enforced in this implementation:

V_{E k i} > λ \sum_{j = 1}^{n} G_{j} V_{E k i} > λ \sum_{j = 1}^{n} G_{j}

where

λ	=	the minimum seismic shear factor , obtained from Table 5.2.5
G_j	=	the seismic weight at j^th floor

where λ is the minimum seismic shear factor , obtained from Table 5.2.5 and G_j is seismic weight at j^th floor.