Maximum Deflection Of Simply Supported Beam Carrying Triangular Load With Max Intensity At Center Calculator

Formula Used:

\[ \delta = \frac{q \cdot l^4}{120 \cdot E \cdot I} \]

Uniformly Varying Load (q):

N/m

Length of Beam (l):

Elasticity Modulus of Concrete (E):

Area Moment of Inertia (I):

m⁴

Deflection of Beam (δ):

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1. What is Maximum Deflection of Simply Supported Beam Carrying Triangular Load with Max Intensity at Center?

The maximum deflection of a simply supported beam carrying a triangular load with maximum intensity at the center is a critical parameter in structural engineering. It represents the maximum vertical displacement that occurs at the center of the beam under this specific loading condition.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \frac{q \cdot l^4}{120 \cdot E \cdot I} \]

Where:

\( \delta \) — Deflection of Beam (m)
\( q \) — Uniformly Varying Load (N/m)
\( l \) — Length of Beam (m)
\( E \) — Elasticity Modulus of Concrete (Pa)
\( I \) — Area Moment of Inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam subjected to a triangular load distribution with maximum intensity at the center.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for ensuring structural integrity, serviceability, and compliance with building codes. Excessive deflection can lead to cracking, vibration issues, and discomfort for occupants.

4. Using the Calculator

Tips: Enter all values in consistent units (N/m for load, m for length, Pa for modulus, and m⁴ for moment of inertia). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a triangular load with max intensity at center?
A: This is a load distribution where the intensity varies linearly from zero at the supports to a maximum value at the center of the beam.

Q2: Where does maximum deflection occur in this loading condition?
A: For a simply supported beam with triangular load (max at center), the maximum deflection occurs at the center of the beam.

Q3: What are typical deflection limits for beams?
A: Most building codes limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.

Q4: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (E) will have less deflection under the same loading conditions.

Q5: Can this formula be used for other beam types?
A: No, this specific formula applies only to simply supported beams with triangular load distribution (max at center).