Simple Beam Calculator

Maximum Deflection Formula:

\[ \delta_{max} = \frac{5 q L^4}{384 E I} \]

Uniform Load (q):

N/m

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 maximum vertical displacement for a simply supported beam with uniform distributed load. This is a fundamental calculation in structural engineering to ensure beams meet deflection requirements.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

\[ \delta_{max} = \frac{5 q L^4}{384 E I} \]

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( q \) — Uniform load per unit length (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum deflection at the center of a simply supported beam subjected to a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Deflection calculations are crucial in structural design to ensure that beams and other structural elements do not deflect excessively under load, which could affect functionality, cause cracking, or lead to structural failure.

4. Using the Calculator

Tips: Enter uniform load in N/m, length in meters, modulus of elasticity 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 specifically to simply supported beams with uniform distributed load across the entire span.

Q2: What are typical deflection limits?
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 (like steel) deflect less than materials with lower modulus (like wood) under the same loading conditions.

Q4: What if the load is not uniform?
A: Different formulas are used for concentrated loads, triangular loads, or other load distributions. This calculator is specifically for uniform distributed loads.

Q5: How important is moment of inertia in deflection?
A: Moment of inertia is critically important as it represents the beam's resistance to bending. Beams with larger moment of inertia values deflect less under the same loading.