Deflection Of Cantilever Beam With Point Load Calculator

Cantilever Beam Deflection Formula:

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

Point 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 when a load is applied at its free end. This calculation is crucial in structural engineering to ensure beams can withstand applied loads without excessive bending that could lead to failure.

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 at the free end (m)
\( P \) — Point load applied at the free end (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of the beam material (Pa)
\( I \) — Moment of inertia of the beam cross-section (m⁴)

Explanation: The formula calculates the maximum deflection of a cantilever beam with a point load applied at its free end, considering the beam's material properties and geometry.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is essential for structural design to ensure safety, prevent excessive deformation, and meet building code requirements. It helps engineers determine appropriate beam dimensions and material selection.

4. Using the Calculator

Tips: Enter the point load in newtons, beam length in meters, modulus of elasticity in pascals, and moment of inertia in meters to the fourth power. 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 fixed at one end and free at the other, commonly used in bridges, buildings, and aircraft structures.

Q2: What is modulus of elasticity?
A: Modulus of elasticity (E) is a material property that measures its stiffness and resistance to elastic deformation under load.

Q3: What is moment of inertia?
A: Moment of inertia (I) is a geometric property that measures how a beam's cross-sectional area is distributed relative to its neutral axis, affecting its resistance to bending.

Q4: Are there limitations to this formula?
A: This formula applies only to point loads at the free end of prismatic beams with constant cross-section and material properties. It assumes small deflections and linear elastic material behavior.

Q5: How does beam length affect deflection?
A: Deflection increases with the cube of the beam length, meaning longer beams are significantly more flexible and prone to larger deflections under the same load.