Calculate Deflection Of A Beam

Beam Deflection Formula:

\[ \delta_{max} = \frac{q L^4}{30 E I} \]

Distributed Load (q):

N/m

Length (L):

Elastic Modulus (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. It's a critical factor in structural engineering that determines how much a beam will bend when subjected to forces. The triangular load deflection formula calculates the maximum deflection for a beam with a triangular distributed load.

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

\[ \delta_{max} = \frac{q L^4}{30 E I} \]

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( q \) — Distributed load intensity (N/m)
\( L \) — Length of the beam (m)
\( E \) — Elastic modulus of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: This formula calculates the maximum deflection for a beam with triangular distributed load, fixed at one end and free at the other.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is essential for ensuring structural integrity, preventing excessive deformation, and meeting building code requirements. Excessive deflection can lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter the distributed load in N/m, length in meters, elastic modulus in Pascals, and moment of inertia in m⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula applies to cantilever beams with triangular distributed load, fixed at one end and free at the other.

Q2: What is the significance of moment of inertia?
A: Moment of inertia represents the beam's resistance to bending. Higher values indicate stiffer beams that deflect less under the same load.

Q3: How does material affect deflection?
A: Materials with higher elastic modulus (E) deflect less under the same load. Steel has a higher E value than wood, making it stiffer.

Q4: What are acceptable deflection limits?
A: Deflection limits vary by application and building codes. Typically, deflection should not exceed L/360 for floors or L/240 for roofs under live loads.

Q5: Does this formula account for shear deflection?
A: This formula calculates bending deflection only. For short, deep beams, shear deflection may need to be considered separately.