General (Section 4.3.3.2.1)

This type of analysis may be applied to buildings whose response is not significantly affected by contributions from modes of vibration higher than the fundamental mode in each principal direction. This requirement is deemed to be satisfied in building if both of the following conditions are met:

1. Fundamental periods of vibration T₁ in the two main directions are smaller than the following values

   $T_1\le \left\{\begin{array}{c}4T_C\\ 2.0 s\end{array}\right.$

   (4.4)

   where

   Tc

   =

   the upper limit of the period of the constant spectral acceleration branch (see Section 3.2.2.2).

2. Building meets the criteria for regularity in elevation (see Section 4.2.3.3).

It should be known that the program does not verify the above two requirements. It is engineer’s responsibility to check validity of analysis method.

Base Shear Force (4.3.3.2.2)

The seismic base shear force F_b, for each horizontal direction in which the building is analyzed, shall be determined using the following expression:

where

Sd(T1)	=	the ordinate of the design spectrum at period T1 (see Section 3.2.2.5)
T1	=	Fundamental period of vibration of the building for lateral motion in the direction considered
m	=	the total mass of the building, above the foundation or above the top of a rigid basement, computed in accordance with 3.2.4(2)
λ	=	the correction factor, the value of which is equal to: $\lambda =\left\{\begin{array}{cc}0.85,& T_1<2T_C\text{ and number of stories}\ge 2\hfill \\ 1.0,& \text{ otherwise}\hfill \end{array}\right.$

For the determination of the fundamental period of vibration T₁ of the building, the program provides several options:

1. It can be obtained from an Eigenvalue analysis such as Subspace iteration, Lanczos method or Load Dependent Ritz Vectors.
2. It can be calculated from the following equation:

   $T_1=C_t{H}^{3/4}$

   (4.6)

   where

   Ct	=	$\{\begin{array}{cc}0.085& \text{moment resistant space steel frames}\hfill \\ 0.075& \text{moment resistant space concrete frames, eccentrically braced steel frames}\hfill \\ 0.050& \text{all other structures}\hfill \end{array}$
   H	=	the height of the building measured from the foundation or from the top of a rigid basement. This is referred to as Method 1 in the load case dialog. Value for the term Ct is provided by engineer.

   For structures with concrete or masonry shear walls, the value C_t in expression (4.6) may be taken as:

   $C_t=\frac{0.075}{\sqrt{A_c}}$

   (4.7)

   where

   Ac	=	the total effective area of the shear walls in the first story of the building (Eqn 4.8) $=\sum \left(A_i\right(0.2+{\left(\frac{l_{wi}}{H}\right)}^2\left)\right)$
   Ai	=	the effective cross-sectional area of shear wall i in the direction considered in the first story of the building
   H	=	the height of the building from the foundation or from the top of a rigid basement.
   $l_{wi}$	=	the length of the shear wall i in the first story in the direction parallel to the applied forces, in m, with the restriction that $l_{wi}/H$ should not exceed 0.9.

   This is referred to as Method 2 in the load case dialog. However, the equation for Ac is not implemented in the program. Instead, engineer is required to provide A_c directly if the Method 2 is selected.

3. Alternatively, T₁ may be estimated from Equation (4.9). This is not implemented. However, you are may enter T₁ directly in the load case dialog.

Distribution of the Horizontal Seismic Forces (Section 4.3.3.2.3)

Seismic actions are determined by applying horizontal forces F_i to all stories in two horizontal directions. The program provides two different methods regarding seismic force distribution over height of building:

1. Mode Shape Distribution:

   $F_i=F_b\frac{s_i{m}_i}{\sum s_j{m}_j}$

   (4.10)

   where

   Fi	=	the horizontal force acting on story i.
   Fb	=	the seismic base shear in accordance with expression (4.5).
   si, sj	=	the displacements of masses mi, mj in the fundamental mode shape.
   mi, mj	=	the story masses computed in accordance with the Section 3.2.4(2)

   The program automatically calculates s_i, s_j and m_i, m_j values from an Eigenvalue analysis.

2. Linear Distribution:

   $F_i=F_b\frac{z_i{m}_i}{\sum z_j{m}_j}$

   (4.11)

   where

   zi, zj

   =

   the heights of the masses mi, mj above the level of application of the seismic action (foundation or top of a rigid basement).

Torsional Effects (Section 4.3.3.2.4)

This section is not implemented. However, it is important to note that followings in the program:

1. a) Inherited torsion caused by having diaphragm mass and stiffness center apart is already directly included in analysis.
2. b) Accidental torsional effects can be additionally included by simply creating load cases with eccentricity. In this case, the program calculates accidental eccentricity according to the following:

   $e_{ai}= \pm 0.05 L_i$

   (4.3)

   The eccentricity value of 0.05 is the default but it can be changed (see Loads > Masses command).

Displacement Calculations (Section 4.3.4)

This section is not implemented. It should be known that displacements obtained from an analysis are elastic displacements (i.e., d_e).