Maximum Deflection Of Cantilever Beam Carrying Uvl With Maximum Intensity At Free End Calculator

Formula Used:

\[ \delta = \frac{11 \cdot q \cdot l^4}{120 \cdot E \cdot I} \]

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 the Maximum Deflection Formula?

The formula calculates the maximum deflection of a cantilever beam carrying a uniformly varying load with maximum intensity at the free end. This is important for structural engineering applications to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta = \frac{11 \cdot q \cdot l^4}{120 \cdot E \cdot I} \]

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 free end of a cantilever beam subjected to a triangular load distribution.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams don't sag or deform excessively under load, which could compromise structural integrity and serviceability.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure all inputs are positive values. The calculator will compute the maximum deflection at the free end of the cantilever beam.

5. Frequently Asked Questions (FAQ)

Q1: What is a uniformly varying load?
A: A uniformly varying load is a load whose magnitude varies linearly along the length of the beam, creating a triangular load distribution.

Q2: What are typical deflection limits for beams?
A: Deflection limits vary by application but are typically L/240 to L/360 for live loads and L/180 to L/240 for total loads, where L is the span length.

Q3: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (stiffer materials) will deflect less under the same loading conditions.

Q4: What is area moment of inertia?
A: Area moment of inertia is a geometric property that measures a beam's resistance to bending. It depends on the cross-sectional shape and size.

Q5: Can this formula be used for other beam types?
A: No, this specific formula applies only to cantilever beams with uniformly varying load and maximum intensity at the free end.