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

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

Base Shear

Definition

Base shear is the horizontal force at the base of a structure due to seismic or wind loads. It represents the total lateral force that a building foundation must resist during an event like an earthquake.

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

Definition

Deflection refers to the displacement of a structural element under load. Excessive deflection can compromise structural integrity and occupant comfort.

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 and depends on the total weight and seismic coefficient.
- Deflection is a displacement and depends on material properties and geometry.

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Conclusion

·       Base shear and deflection are fundamental in the design of earthquake-resistant structures.

·       Accurate calculations using proper design codes ensure safety and functionality.

·       By understanding these principles, engineers can create structures that are resilient and efficient under lateral forces.