The Direction Combination of Horizontal Seismic Load Effect per ASCE 7-16 with ideCAD

How does ideCAD define the direction combination of the horizontal seismic load effect, according to ASCE 7-16, for two earthquake directions?

Symbols

E_h = Horizontal seismic load effect
Q_E = Combined applied design force on the horizontal seismic effects
Q_EX+AT = Effect of the X direction with accidental torsion
Q_EX-AT = Effect of the X direction with accidental torsion
Q_EY+AT = Effect of the Y direction with accidental torsion
Q_EY-AT = Effect of the Y direction with accidental torsion
ρ = redundancy factor, as defined in Section 12.3.4.

Horizontal Seismic Load Effect

The horizontal seismic load effect, E_h, is calculated in accordance with Eq. (12.4-3) as follows:

Combining Horizontal Earthquake Effects Perpendicular to Each Other

Earthquake is a three-dimensional and dynamic effect. During an earthquake, the earth's crust moves simultaneously in three directions, two horizontal and vertical directions. Therefore, the design of structures should be made with these three-dimensional effects.

If the seismic effect is determined with equations of motion representing dynamic behavior in the time domain, the effects in three directions can be considered at the same time. However, since the effect of the vertical component is very low compared to the horizontal effects, the calculation is made in two horizontal directions. In the time domain, the calculation is not used except for special structures due to various difficulties and especially time savings.

The design acceleration spectrum, which is logically used as earthquake data in the Equivalent Lateral Force Method and Modal Analysis, which are used according to different regulations as per the standard building design, corresponds to the maximum total accelerations calculated for one direction of the earthquake. Therefore, magnitudes such as internal force and displacement determined by calculating separately for both horizontal directions are obtained approximately by direction combination rules developed by statistical studies.

According to C12.5, 30% of the main direction and the other direction are combined. Combining effects for seismic loads in each direction, and accidental torsion in accordance with Sections 12.8.4.2 and 12.8.4.3, results in the following 16 load combinations.

Earthquake effects determined in the horizontal X and Y directions perpendicular to each other are automatically combined according to Section C12.5. It is detailed in the program interface and reports. The horizontal earthquake effect is symbolized by Ex and Ey, it is included in the heading of loading status and loading combinations in the select report. Within the loading combinations, the joining according to the 30% rule is also made and the coefficients of the horizontal directions are specified in the combination. It will be seen in the strength-reinforcement area tab in the reinforced concrete column dialog shown below, for example.

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