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AS 1170.4-2007

Response Spectra Analysis

In this section, response spectra analysis referring to Section 7 of AS 1170.4-2007 is explained.

Horizontal design spectrum (Cd) values for a known period T is calculated as follows:
C d ( T ) = k p Z ( S p μ ) C h ( T )
where
kp
=
probability factor (Section 3, Table 3.1 of the building code)
Z
=
hazard factor (Section 3, Table 3.2 of the building code)
Sp
=
spectral performance factor (Section 6.5 of the building code)
μ
=
structural ductility factor (Section 6.5 of the building code)
Ch(T)
=
spectral shape factor value (Section 6, Table 6.4 of the building code)

The equation for response spectra curves based on different type of soil are

  Soil Ae Soil Be Soil Ce Soil De Soil De
0 < T ≤ 0.1 0.8 + 15.5 T 1.0 + 19.4 T 1.3 + 23.8T 1.1 + 25.8 T 1.1 + 25.8
0.1 < T ≤ 1.5 0.704/T but ≤2.35 0.88/T but ≤2.94 1.25/T but ≤3.68 1.98/T but ≤3.68 3.08/T but ≤3.68
T > 1.5 1.056/T2 1.32/T2 1.874/T2 2.97/T2 4.62/T2

The above equations are portrayed graphically as shown below. Note that the spectral shape factor, Ch(T), is simply ordinate value in this function.

Normalized Response Spectra (AS 1170.4-2007)

The parameters Sp and Sp (spectral performance factor and structural ductility factor, respectively) is defined in Table 6.5(A) and 6.5 (B), based on lateral resisting framing type.

It should be noted that accidental torsional effects are included in this implementation based on "± 0.1b", where b is the width of building perpendicular to application of loads.

Equivalent Static Lateral Force

Equivalent Static Analysis Procedure, given in Section 6 of AS 1170.4-2007 is implemented ant the followings refer to aforementioned building code.

Earthquake Base Shear

Building base shear is given in Eq. 6.2(3):
V = [ k p Z C h ( T 1 ) S p μ ] W t 6.2(3)
where
V
=
building base shear
kp
=
probability factor (Section 3, Table 3.1 of the building code)
Z
=
hazard factor (Section 3, Table 3.2 of the building code)
Ch(T1)
=
spectral shape factor value (Section 6, Table 6.4 of the building code)
Sp
=
spectral performance factor (Section 6.5 of the building code)
μ
=
structural ductility factor (Section 6.5 of the building code)
Wt
=
seismic weight of the building

Vertical Distribution of Horizontal Forces

Horizontal equivalent static design force Fi at each level is calculated according to the following equation:
F i = w i h i k ∑ j = 1 n w j h j k V 6.3(2)
where
n
=
the number of levels
h
=
the height of level " i "
W
=
the seismic weight of structure at level " i "
k
=
a coefficient defined as follows:
k = { 1.0 for T < 0.5 2.0 for T ≥ 2.5 Determined by linar interpolation between 1 and 2

Natural Period of Structure (T1)

Three options are provided to user for natural period of structure in X- and Y-directions:
  • Either it is directly calculated by the program
  • Or it is directly provided by user
  • Or it is calculated according to Eq. 6.2(7):

    T1 = 1.25kthn0.75 6.2(7)

    where kt is defined as follows:

    Frame Type kt
    Moment-resisting steel frames 0.11
    Moment-resisting concrete frames 0.075
    Eccentrically braced steel frames 0.06
    All other structures 0.05

    The base shear obtained using either calculated by the program or user entered shall not be less than 80% of the value obtained with T1 according to above equation. Thus, the user needs to enter kt for each direction for fulfilling this requirement. This check is enforced in the program.

Normalized Response Spectra Curve Equations

The equation for response spectra curves based on different type of soil are given in the following table.

  Soil Ae Soil Be Soil Ce Soil De Soil De
0 < T ≤ 0.1 0.8 + 15.5 T 1.0 + 19.4 T 1.3 + 23.8T 1.1 + 25.8 T 1.1 + 25.8
0.1 < T ≤ 1.5 0.704/T but ≤2.35 0.88/T but ≤2.94 1.25/T but ≤3.68 1.98/T but ≤3.68 3.08/T but ≤3.68
T > 1.5 1.056/T2 1.32/T2 1.874/T2 2.97/T2 4.62/T2

The above equations are portrayed graphically as shown below. Note that the spectral shape factor, Ch(T1), is simply ordinate value in this function.

Normalized Response Spectra (AS 1170.4-2007)

Structural Performance Factor (Sp)

This factor is defined in Table 6.5(A) and 6.5 (B), based on lateral resisting framing type.

Structural Ductility Factor (μ)

This factor is defined in Table 6.5(A) and 6.5 (B), based on lateral resisting framing type.

Torsional Effects

Calculated story level forces can be applied to diaphragm with eccentricities. Some of the generated load cases include eccentric loads. A value of " ± 0.1b ", where b is the width of building perpendicular to application of loads, is used in the implementation. Also, user can generate load cases based on "100% and 30%" orthogonal effects.

Storey Drift Computation

The program is able to compute storey drift values at any location of diaphragms. Note that the Equation 6.7(1) is not implemented.

P-Delta Effects

P-delta effects can be considered directly in the analysis. Note that stability coefficient factor (Eq. 6.7(2)) is not implemented. Also, calculated base shears, story forces or deflections are not modified according to Section 6.7.3.2.

Parent topic: Story Forces: Seismic/Dynamic