Equivalent Lateral Force Method: When Can It Be Used?

The equivalent lateral force method represents the earthquake with static forces distributed over the height of the building. It is fast and can be checked by hand. But it is not valid for every building — and even where it is, the period found by the analysis program cannot be trusted as is.

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1. What the method assumes

The equivalent lateral force method assumes that the seismic response of the building is dominated by a single mode of vibration: the building sways in one shape from foundation to roof. Under this assumption the earthquake becomes a set of horizontal static forces distributed over the height. Their sum is the base shear:

V_tE = m_t · S_aR(T_p) ≥ 0.04 · m_t · g · I · S_DS (Equation 4.19)

The assumption works well for low, regular buildings. In tall buildings higher modes matter; in irregular buildings forces are distributed in plan and height very differently from a single mode. The method therefore has an applicability limit.

2. Table 4.4: for which buildings?

TBDY Table 4.4 defines where the method may be used, by seismic design class (DTS, TBDY-04) and building height class (BYS). There are two rows:

Regular buildings (η_bi ≤ 2.0 and no B2 irregularity): BYS ≥ 4 for DTS 1–2a, BYS ≥ 5 for DTS 3–4a.
All other buildings: BYS ≥ 5 for DTS 1–2a, BYS ≥ 6 for DTS 3–4a.

Remember: the smaller the BYS number, the taller the building. An irregularity therefore lowers the tallest building for which the method may be used by one class. The two irregularities involved appear earlier in the series: torsion (TBDY-05) and soft storey B2 (TBDY-03).

3. Examples

Computed with the site's engine:

DTS	BYS	η_bi,max	B2 present?	Required BYS	Equivalent lateral force method
1a	7	—	no	≥ 4	allowed
1	4	—	no	≥ 4	allowed
1	4	2.5	no	≥ 5	not allowed
3	5	—	yes	≥ 6	not allowed
3	6	—	yes	≥ 6	allowed

The first row is the site's three-storey school block (DTS 1a, BYS 7). Rows two and three are the same building; the only difference is a torsional irregularity with η_bi = 2.5 in the third, which makes the method unusable.

4. The period cap: 1.4·T_pA

The period T_p used in the method usually comes from the analysis program. TBDY caps it (Clauses 4.7.3.2 and 4.7.3.4):

T_pA = C_t · H_N^0.75 (Equation 4.27) T_p ≤ 1.4 · T_pA

C_t depends on the structural system: 0.1 for RC frames, 0.08 for steel frames, 0.07 for other systems (RC wall buildings have a separate relation). For a 20 m RC frame, T_pA = 0.1 × 20^0.75 = 0.946 s and the cap is 1.324 s.

Why a cap? In the long-period range spectral acceleration decreases with period. An assumption that makes the model softer than reality (over-cracked sections, unmodelled members) lengthens the period and artificially lowers the acceleration and the design force. The empirical relation, derived from periods measured in real buildings, is a "reality check".

5. Effect of the cap on the design force

A 20 m RC frame with total mass 2000 t; S_DS = 1.2, S_D1 = 0.60, R = 8, D = 3, I = 1. Suppose the analysis program gives T₁ = 1.8 s. With the site's engine:

	Period used T (s)	S_ae (g)	V_tE (kN)	Minimum (kN)	Design V_t (kN)
With the period cap	1.324	0.453	1111.4	941.8	1111.4
Without the cap	1.800	0.333	817.5	941.8	941.8

Without the cap, the computed force would fall below the minimum and the design would use 941.8 kN. With the cap, the period is reduced to 1.324 s and the design force becomes 1111.4 kN: 18% larger. Hand check: 2·10⁶ × 9.81 × (0.60/1.324) / 8 = 1111.4 kN.

Note: the period cap and the minimum base shear apply to forces. Neither is applied in the storey drift check (TBDY-06).

6. Summary of series A

With this article, series A has covered in order the questions to ask before a building's seismic calculation begins: What is the soil (TBDY-02)? Which class is the building in (TBDY-04)? How much can the force be reduced (TBDY-01)? Are there irregularities (TBDY-03, TBDY-05)? Which method may be used (this article)? And finally: are the drifts acceptable (TBDY-06)?

Try it on the site: the TBDY base shear tool applies the period cap and the minimum base shear automatically and shows which one governs.

References

TBDY 2018 — Table 4.4 (analysis methods), Clauses 4.7.3.2 and 4.7.3.4, Equations (4.27) and (4.28), Equation (4.19). Official Gazette, 18.03.2018, No. 30364 (repeated).
Applicability computed with edyApplicable() in engine/tbdy-assessment.js; period and base shear with baseShear() in engine/seismic-tr.js.

The numbers in this article were produced by the site's engines; code values are given with their clause numbers.

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