Formula To Calculate Deflection

Beam Deflection Formula:

\[ \delta = \frac{F L^3}{3 E I} \]

Force (F):

Length (L):

Modulus (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is the Beam Deflection Formula?

The beam deflection formula calculates the vertical displacement of a beam under load. This specific formula applies to cantilever beams with point loads at the free end, providing engineers with critical information about structural behavior and safety.

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

\[ \delta = \frac{F L^3}{3 E I} \]

Where:

\( \delta \) — Deflection (m)
\( F \) — Force applied (N)
\( L \) — Length of beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula demonstrates that deflection increases with the cube of beam length and linearly with applied force, while decreasing with higher material stiffness and cross-sectional moment of inertia.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring beams can withstand loads without excessive deformation that could compromise structural integrity or serviceability.

4. Using the Calculator

Tips: Enter force in newtons, length in meters, modulus in pascals, and moment of inertia in meters to the fourth power. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula specifically applies to cantilever beams with a point load at the free end. Different formulas exist for simply supported beams and distributed loads.

Q2: What is typical acceptable deflection?
A: Acceptable deflection varies by application, but common limits are L/360 for live loads and L/240 for total loads, where L is span length.

Q3: How does material affect deflection?
A: Materials with higher modulus of elasticity (like steel vs. wood) result in less deflection under the same load conditions.

Q4: What if the load is distributed instead of point load?
A: Different formulas apply for distributed loads. For uniform distributed load on cantilever, the formula becomes δ = wL⁴/(8EI).

Q5: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior, small deflections, and homogeneous material properties. It may not be accurate for large deformations or composite materials.