Formula To Calculate Deflection Of Simply Supported Beam

Maximum Deflection Formula:

\[ \delta_{max} = \frac{P L^3}{48 E I} \]

Point Load (P):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is the Maximum Deflection Formula?

The maximum deflection formula calculates the greatest displacement of a simply supported beam with a center point load. This formula is fundamental in structural engineering for assessing beam performance under load.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta_{max} = \frac{P L^3}{48 E I} \]

Where:

\( P \) — Point load at center (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula shows that deflection increases with the cube of beam length and is inversely proportional to both the modulus of elasticity and moment of inertia.

3. Importance of Deflection Calculation

Details: Calculating maximum deflection is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design specifications in construction and engineering applications.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure positive values for all inputs. The calculator provides the maximum deflection at the center of the beam.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula applies specifically to simply supported beams with a single point load at the center.

Q2: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (E) values (like steel) deflect less than materials with lower E values (like wood) under the same load.

Q3: What is the significance of moment of inertia?
A: Moment of inertia represents the beam's resistance to bending. Beams with higher I values (deeper sections) deflect less than those with lower I values.

Q4: Are there deflection limits in building codes?
A: Yes, most building codes specify maximum allowable deflections, typically as a fraction of the span length (e.g., L/360 for floors).

Q5: How does distributed load deflection differ from point load?
A: Distributed loads produce different deflection patterns and typically result in less maximum deflection than an equivalent point load at the center.