Deflection In Beam Calculator

Cantilever Beam Deflection Formula:

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

Load (P):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam that is fixed at one end and free at the other when subjected to a load. The deflection represents how much the beam bends under the applied force.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

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

Where:

\( \delta \) — Deflection (m)
\( P \) — Applied load (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the free end of a cantilever beam with a point load at the free end. The deflection increases with the cube of the beam length.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams don't deflect excessively under load, which could lead to structural failure or serviceability issues.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a structural element that is fixed at one end and free at the other, commonly used in bridges, balconies, and aircraft wings.

Q2: What are typical modulus of elasticity values?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~20-30 GPa, Wood: ~10 GPa (varies by species and grade).

Q3: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For common shapes like rectangles and circles, standard formulas are available in engineering handbooks.

Q4: Does this formula work for distributed loads?
A: No, this formula is specifically for a point load at the free end. Different formulas apply for uniformly distributed loads or multiple point loads.

Q5: What is considered acceptable deflection?
A: Deflection limits vary by application, but common standards limit deflection to L/360 for floors and L/240 for roofs under live loads.