Deflection At Any Point On Simply Supported Beam Carrying UDL Calculator

Formula Used:

\[ \delta = \left( \frac{w' \cdot x}{24 \cdot E \cdot I} \right) \cdot \left( l^3 - 2 \cdot l \cdot x^2 + x^3 \right) \]

Load per Unit Length (w'):

N/m

Distance x from Support:

Elasticity Modulus of Concrete (E):

Area Moment of Inertia (I):

m⁴

Length of Beam (l):

Deflection of Beam (δ):

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1. What is Beam Deflection?

Beam deflection is the degree to which a structural element is displaced under a load. It refers to the movement of a beam from its original position due to the forces and loads being applied to it.

2. How Does the Calculator Work?

The calculator uses the deflection formula for simply supported beams carrying uniformly distributed load:

\[ \delta = \left( \frac{w' \cdot x}{24 \cdot E \cdot I} \right) \cdot \left( l^3 - 2 \cdot l \cdot x^2 + x^3 \right) \]

Where:

\( \delta \) — Deflection of beam (m)
\( w' \) — Load per unit length (N/m)
\( x \) — Distance from support (m)
\( E \) — Elasticity modulus of concrete (Pa)
\( I \) — Area moment of inertia (m⁴)
\( l \) — Length of beam (m)

Explanation: This formula calculates the deflection at any point along a simply supported beam carrying a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams don't deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, Newtons per meter for load, Pascals for modulus, and meters to the fourth power for moment of inertia). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A simply supported beam is supported at both ends, with one end having a pinned support and the other having a roller support.

Q2: What is uniformly distributed load (UDL)?
A: UDL is a load that is distributed evenly along the length of the beam, measured in force per unit length.

Q3: Where does maximum deflection occur?
A: For a simply supported beam with UDL, maximum deflection occurs at the center of the beam.

Q4: What factors affect beam deflection?
A: Deflection is affected by load magnitude, beam length, material properties (modulus of elasticity), and cross-sectional properties (moment of inertia).

Q5: Why is deflection limited in structural design?
A: Excessive deflection can cause cracking in supported elements, discomfort to occupants, and visual concerns, even if the beam is structurally sound.