# Combining Horizontal and Vertical Earthquake Effects

Many engineers are confused how to combine the effects of horizontal and vertical earthquake ground motion, here below we will try to clarify it in accordance to the American standard.

The IBC defines E by reference to Section 12.4 of ASCE 7. As shown below, this section provides load combinations that account for vertical earthquake effects by increasing the dead load factor in the additive seismic load combination by considering vertically downward earthquake effects and by decreasing the dead load factor in the counteractive load combination by considering vertically upward earthquake effects. In each case, that is the conservative thing to do.

Additive load combinations are where gravity effects add to earthquake effects. For example, gravity causes negative bending moments at the support section of a beam; earthquake forces also cause negative moments at the same support section of the same beam. Counteractive load combinations are where gravity effects counteract earthquake effects.

For example, gravity still causes negative moment moments at the same support section of the same beam, but earthquake forces have now reversed themselves; they now cause negative bending moments at the same location. Please note that the above requirement makes the dead load factor of the IBC/ASCE 7 a function of the seismicity (value of S_{DS}) at the site of the structure.

**Strength Design Basic Load Combinations:**

**a.** 1.2D + L + 0.2S + E ……where E = ρQ_{E }+ 0.2S_{DS}D

→ (1.2 + 0.2S_{DS})D + L + 0.2S + ρQ_{E}

**b.** 0.9D + 1.6H + E ……where E = ρQ_{E }– 0.2S_{DS}D

→ (0.9 – 0.2S_{DS})D + 1.6H + ρQ_{E}

**Allowable Stress Design Basic Load Combinations:**

**a.** D + H + F + 0.7E ……where E = ρQ_{E }+ 0.2S_{DS}D

→ (1.0 + 0.14*S _{DS}*)

*D*+

*H*+

*F*+ 0.7ρ

*Q*

_{E}**b.*** D* + *H* + *F* + 0.75*L* + 0.75(*L _{r}* or

*S*or

*R*) + 0.75(0.7E) ……where E = ρQ

_{E }+ 0.2S

_{DS}D

→ (1.0 + 0.10*S _{DS}*)

*D*+

*H*+

*F*+ 0.75

*L*+ 0.75(

*L*or

_{r}*S*or

*R*) + 0.525ρ

*Q*

_{E}**c.** 0.6D + 1.6H + E ……where E = ρQ_{E }– 0.2S_{DS}D

→ (0.6 – 0.14*S _{DS}*)

*D*+

*H*+ 0.7ρ

*Q*

_{E}**Strength Design Basic Load Combinations with Overstrength Factor:**

**a.** 1.2D + L + 0.2S + E_{m} ……where E_{m} = Ω_{0}Q_{E }+ 0.2S_{DS}D

→ (1.2 + 0.2S_{DS})D + L + 0.2S + Ω_{0}Q_{E}

**b.** 0.9D + 1.6H + E_{m} ……where E_{m} = Ω_{0}Q_{E }– 0.2S_{DS}D

→ (0.9 – 0.2S_{DS})D + 1.6H + Ω_{0}Q_{E
}

*Credit to: S.K. Ghosh Associates*

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(May 22, 2016 - 10:08 AM)Interesting..