Base Shear Calculation as per IS 1893:2016 — Worked Example

Base shear is the total horizontal force an earthquake is assumed to push into a building at its base. For ordinary regular buildings in India it is worked out by the equivalent static method of IS 1893 (Part 1):2016, and it is the first number you need before you can size shear walls, check frames, or write the seismic load combinations.

This guide walks through the method step by step, with a fully worked example for a seven-storey RC frame with brick infill in Zone IV. To try your own building, use the free seismic base shear calculator, which shows every intermediate value.

The method in four steps

The design base shear comes from four quantities: the building's approximate natural period, the spectral acceleration for that period, the design horizontal acceleration coefficient, and the seismic weight.

Step 1: approximate fundamental period, Ta (Cl 7.6.2)

• h: height of the building (m)
• d: base dimension of the building at plinth level in the direction of the earthquake considered (m)

Step 2: spectral acceleration, Sa/g (Cl 6.4.2(a))

For the equivalent static method at 5% damping, Sa/g is flat at 2.5 up to a corner period that depends on the soil, then falls off as c/T up to 4 s:

Beyond 4 s the value stays at 0.25, 0.34 or 0.42. The 1 + 15T ramp below 0.1 s that you may have seen belongs to the response spectrum method, Cl 6.4.2(b), and is not used in the static method.

Step 3: design horizontal acceleration coefficient, Ah (Cl 6.4.2)

Ah = (Z / 2) × (I / R) × (Sa / g)

• Z: zone factor from Table 3 (0.10, 0.16, 0.24, 0.36 for Zones II to V)
• I: importance factor (1.0, 1.2 or 1.5 in the calculator)
• R: response reduction factor (3 for an ordinary moment-resisting frame, 5 for a special moment-resisting frame)

Step 4: design base shear, Vb (Cl 7.6.1)

Vb = Ah × W

W is the seismic weight of the whole building: its dead load plus the part of the imposed load that IS 1893 asks you to include. It is not the same as the factored gravity load you use to design columns.

Vb may not be less than the minimum design lateral force of Cl 7.2.2 (Table 7), ρW, where ρ is 0.7%, 1.1%, 1.6% and 2.4% of W for Zones II to V.

Worked example: seven-storey RC frame with brick infill, Zone IV

• Seismic zone IV, so Z = 0.24
• Soil type III (soft)
• RC frame with masonry infill, height h = 21 m
• Base dimension in the direction considered d = 18 m
• Importance factor I = 1.2 (taken by the designer from Table 8)
• Special moment-resisting frame, R = 5
• Seismic weight W = 36,000 kN

1. Period. With infill, Ta = 0.09 × 21 / √18 = 1.89 / 4.243 = 0.445 s.
2. Sa/g. For soft soil the flat part runs to 0.67 s, and 0.445 s is inside it, so Sa/g = 2.5.
3. Ah. (0.24 / 2) × (1.2 / 5) × 2.5 = 0.12 × 0.24 × 2.5 = 0.072.
4. Minimum check. For Zone IV, ρ = 1.6% = 0.016. 0.072 is larger, so the spectrum value governs.
5. Base shear. Vb = 0.072 × 36,000 = 2,592 kN.

Why the period formula matters

Suppose the same building is entered as a bare RC frame, ignoring the infill:

• Ta = 0.075 × 21^0.75 = 0.736 s, past the 0.67 s corner
• Sa/g = 1.67 / 0.736 = 2.270
• Ah = 0.12 × 0.24 × 2.270 = 0.0654
• Vb = 0.0654 × 36,000 = 2,353 kN

Choosing the bare-frame formula for a building that will have brick walls understates the base shear by 239 kN, about 9%. Stiff infill shortens the period, and in this range a shorter period means more force.

The choice of R matters even more. With R = 3 (an ordinary frame) the same building gets Ah = 0.12 and Vb = 4,320 kN. R = 5 is only valid if the frame is detailed as a special moment-resisting frame.

Reference table: the same building in every zone

The table keeps everything from the example (soft soil, infill, I = 1.2, R = 5, W = 36,000 kN) and changes only the zone.

For this short-period building the spectrum value is well above the minimum in every zone. The minimum tends to control for tall, flexible buildings in low zones, where Sa/g has dropped a long way.

Common mistakes

• Using the bare-frame period for an infilled building. If the frame will have masonry infill, use 0.09h/√d, and use d in the direction you are checking. A building has two values of d and so two periods.
• Applying the 1 + 15T ramp in the static method. For the equivalent static method Sa/g is 2.5 right down to T = 0.
• Forgetting the minimum lateral force. Always compare Ah with ρ for the zone.
• Taking R = 5 without ductile detailing. The higher R assumes a special moment-resisting frame. If the frame is not detailed for ductility, R = 3 applies and the base shear rises by two-thirds.
• Using factored gravity load as W. Seismic weight uses only part of the imposed load and no load factors.
• Treating Vb as a storey force. Vb is the total at the base. It still has to be distributed up the height before you can design any floor.

How CivilTech Studio does this

The seismic base shear calculator asks for the zone, importance factor (1.0, 1.2 or 1.5), R (3 or 5), soil type, the period formula (RC frame, steel frame or frame with infill), the height h, the base dimension d where needed, and the seismic weight W. It then shows:

• Ta from Cl 7.6.2 and Sa/g from the static spectrum of Cl 6.4.2(a)
• Ah = (Z/2)(I/R)(Sa/g), and whether the Table 7 minimum governs
• the design base shear Vb = Ah × W

It refuses to give a result if h is zero, or if d is zero with the infill formula, instead of printing a meaningless 2.5. It does not calculate W for you, distribute Vb over the storeys (Cl 7.6.3), check torsion, or scale response spectrum results (Cl 7.7.3).

Once you have Vb, use the load combination generator to write out the combinations that include the earthquake load, and the wind pressure calculator to see whether wind or seismic governs the lateral design. For the walls that carry the force, see shear wall design, and for the clauses in plain English, the Code Clause Compass.

FAQ

How to calculate base shear as per IS 1893:2016?

Find the period Ta from Cl 7.6.2, read Sa/g for that period and the soil type, work out Ah = (Z/2)(I/R)(Sa/g), check it against the Table 7 minimum, and multiply by the seismic weight: Vb = Ah × W. A 21 m infilled frame in Zone IV on soft soil with I = 1.2, R = 5 and W = 36,000 kN gives Vb = 2,592 kN.

What is the value of Sa/g for a low-rise building?

For the equivalent static method, Sa/g is 2.5 whenever the period is below the corner period of the soil: 0.40 s on rock, 0.55 s on medium soil and 0.67 s on soft soil. Most low-rise buildings fall in this range, so they take the full 2.5.

What is Ah in IS 1893?

Ah is the design horizontal acceleration coefficient, the fraction of the seismic weight applied as horizontal force. It equals (Z/2) × (I/R) × (Sa/g) and may not be less than the Table 7 minimum for the zone.

Which period formula should I use for a building with brick infill walls?

Use Ta = 0.09h/√d. For the example building it gives 0.445 s, against 0.736 s with the bare RC frame formula, and the shorter period leads to a 9% higher base shear on soft soil.

What are the zone factors in IS 1893:2016?

Table 3 gives Z = 0.10 for Zone II, 0.16 for Zone III, 0.24 for Zone IV and 0.36 for Zone V. The equation for Ah uses Z/2.

What is the difference between R = 3 and R = 5?

R = 3 is for an ordinary moment-resisting frame and R = 5 for a special moment-resisting frame with ductile detailing. Because R divides the force, the same building with R = 3 gets five-thirds of the base shear it would get with R = 5: 4,320 kN instead of 2,592 kN in the example.

Educational reference. Always confirm against IS 1893 (Part 1):2016 and your project's structural design basis.