Metal Deflection Calculator

Metal Deflection Equation:

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

Force (F):

Length (L):

Elastic Modulus (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Metal Deflection Equation?

The metal deflection equation calculates the amount of bending or deformation a beam experiences under a load. It's a fundamental formula in structural engineering used to determine the deflection (δ) of a cantilever beam with a point load at the free end.

2. How Does the Calculator Work?

The calculator uses the deflection equation:

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

Where:

\( F \) — Applied force (N)
\( L \) — Length of the beam (m)
\( E \) — Elastic modulus of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: The equation calculates the maximum deflection of a cantilever beam with a point load at the free end, considering the material's stiffness and geometric properties.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to ensure beams and structures can withstand loads without excessive deformation that could lead to failure or serviceability issues.

4. Using the Calculator

Tips: Enter force in newtons (N), length in meters (m), elastic modulus in pascals (Pa), and moment of inertia in meters to the fourth power (m⁴). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this equation apply to?
A: This specific equation applies to cantilever beams with a point load at the free end. Different equations are used for other beam types and loading conditions.

Q2: What is elastic modulus (E)?
A: Elastic modulus is a material property that measures its stiffness - the ratio of stress to strain. Higher values indicate stiffer materials.

Q3: What is moment of inertia (I)?
A: Moment of inertia is a geometric property that depends on the cross-sectional shape and size. It measures the beam's resistance to bending.

Q4: Are there limitations to this equation?
A: This equation assumes linear elastic material behavior, small deflections, and applies only to cantilever beams with point loads at the free end.

Q5: How does deflection affect structural design?
A: Excessive deflection can cause serviceability issues, damage to non-structural elements, and in extreme cases, structural failure. Deflection limits are specified in building codes.