Cantilever Steel Beam Calculator

Maximum Bending Stress Formula:

\[ \sigma_{max} = \frac{w L^2}{2} \cdot \frac{c}{I} \]

Uniform Load (w):

N/m

Length (L):

Distance to Extreme Fiber (c):

Moment of Inertia (I):

m⁴

Maximum Bending Stress (σ_max):

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1. What is Maximum Bending Stress?

Maximum bending stress (σ_max) is the highest stress experienced by a cantilever steel beam under uniform load. It occurs at the fixed support where the bending moment is maximum and at the extreme fiber of the cross-section.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

\[ \sigma_{max} = \frac{w L^2}{2} \cdot \frac{c}{I} \]

Where:

\( w \) — Uniform load (N/m)
\( L \) — Length of the cantilever beam (m)
\( c \) — Distance to extreme fiber (m)
\( I \) — Moment of inertia (m⁴)

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

3. Importance of Bending Stress Calculation

Details: Calculating maximum bending stress is crucial for structural design to ensure that steel beams can safely support applied loads without exceeding material yield strength, preventing structural failure.

4. Using the Calculator

Tips: Enter uniform load in N/m, length in meters, distance to extreme fiber in meters, and moment of inertia in m⁴. All values must be positive and non-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 engineering applications.

Q2: Where does maximum bending stress occur?
A: Maximum bending stress occurs at the fixed support of the cantilever beam and at the extreme fiber of the cross-section (top or bottom surface).

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

Q4: How does uniform load affect bending stress?
A: Bending stress increases with the square of the beam length and linearly with the uniform load magnitude. Longer beams and heavier loads result in higher stresses.

Q5: What are typical steel yield strengths?
A: Common structural steel has yield strengths ranging from 250-690 MPa. The calculated stress should be compared to the material's yield strength with appropriate safety factors.