Calculate Bending Stress In Cantilever Beam

Bending Stress Formula:

\[ \sigma_{max} = \frac{w L^2}{2} \times \frac{h}{2} \div I \]

Uniform Load (w):

N/m

Beam Length (L):

Beam Height (h):

Moment of Inertia (I):

m⁴

Maximum Bending Stress (σ_max):

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1. What is Bending Stress in Cantilever Beams?

Bending stress is the internal stress induced in a beam when an external load is applied, causing the beam to bend. In cantilever beams with one fixed end and one free end, maximum bending stress occurs at the fixed support where the bending moment is highest.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

\[ \sigma_{max} = \frac{w L^2}{2} \times \frac{h}{2} \div I \]

Where:

\( \sigma_{max} \) — Maximum bending stress (Pa)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Length of the cantilever beam (m)
\( h \) — Height of the beam cross-section (m)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: The formula calculates the maximum stress at the fixed end of a cantilever beam subjected to a uniformly distributed load, considering the beam's geometric properties.

3. Importance of Bending Stress Calculation

Details: Calculating bending stress is essential for structural engineering to ensure beams can withstand applied loads without failure. It helps in selecting appropriate materials and cross-sectional dimensions for safe design.

4. Using the Calculator

Tips: Enter the uniform load in N/m, beam length and height in meters, and moment of inertia in m⁴. All values must be positive numbers greater than zero.

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 various mechanical applications.

Q2: Where does maximum stress occur in a cantilever beam?
A: Maximum bending stress occurs at the fixed support where the bending moment is greatest.

Q3: What is moment of inertia (I)?
A: Moment of inertia is a geometric property that measures a beam's resistance to bending, depending on its cross-sectional shape and dimensions.

Q4: Can this calculator be used for point loads?
A: No, this specific calculator is designed for uniformly distributed loads. Different formulas apply for point loads or other load configurations.

Q5: What units should I use for inputs?
A: Use consistent SI units: Newtons per meter (N/m) for load, meters (m) for length and height, and meters to the fourth power (m⁴) for moment of inertia.