What is Base Shear and Deflection and its calculation in excel sheet download.

Base Shear

Base shear denotes the horizontal force applied to the building' s foundation by seismic or wind pressure. It is the entire lateral force that the foundation of a building must resist in the event of an earthquake, for example

Formula for Base Shear

The base shear (V_b) is commonly calculated using seismic design codes such as IS 1893 (India), ASCE 7 (USA), or Eurocode 8. The general formula is:

V_b = C_s · W
Where:
- C_s: Seismic coefficient, determined by factors like site location, building importance, and response spectrum.
- W: Total seismic weight of the building.

Steps for Calculation

1. Determine Seismic Weight: Include the total dead load and applicable live loads.
2. Evaluate Seismic Coefficient:
   - Based on soil type, zone factor (Z), response reduction factor (R), and importance factor (I).
   - C_s = (Z · I) / R
3. Calculate Base Shear: Multiply C_s by W.

Example

Problem: Calculate the base shear for a 5-story building with the following parameters:
- Zone factor, Z = 0.16
- Importance factor, I = 1.2
- Response reduction factor, R = 5
- Seismic weight, W = 5000 kN

Solution:
C_s = (Z · I) / R = (0.16 · 1.2) / 5 = 0.0384
V_b = C_s · W = 0.0384 · 5000 = 192 kN

Thus, the base shear for the building is 192 kN.

Deflection

Deflection refers to the displacement of a structural element under load. Cracking or visible movement signals that a member's stress is near its allowable level. Excessive deflection can put structural integrity and occupant comfort at risk.

Types of Deflection

1. Lateral Deflection - Horizontal displacement caused by wind or seismic forces.

2. Vertical Deflection - Downward bending of beams or slabs under gravity loads.

Formula for Lateral Deflection

For seismic loads, deflection (Δ) can be calculated using:

Δ = (V · H^3) / (12 · E · I)

Where:
- V: Applied lateral load
- H: Height of the structure
- E: Modulus of elasticity
- I: Moment of inertia of the section

Example

Problem: Calculate the lateral deflection for a single-story building with:
- Lateral load, V = 50 kN
- Height, H = 5 m
- Modulus of elasticity, E = 25000 MPa
- Moment of inertia, I = 0.02 m^4

Solution:
Δ = (V · H^3) / (12 · E · I)
Δ = (50 · 5^3) / (12 · 25000 · 0.02)
Δ = (50 · 125) / 6000 = 1.04 mm

The lateral deflection is 1.04 mm.

Comparison of Base Shear and Deflection

Base Shear is a force which depends on the total weight, and a coefficient depends upon seismic conditions.

Deflection is the displacement of an object and depends on both material properties as well as geometric shape.

Conclusion

Base shear and deflection are essential in the design of earthquake-proof structures.

Efficient calculations enabled by the use of correct design codes make certain that safety and function are not compromised.

Knowing these principles, it is possible for engineers to construct structures which can resist the forces which slide from left to right.

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