Cantilever Beam Bending Stress Calculator

Cantilever Beam Bending Stress Formula:

\[ \sigma_{max} = \frac{P \cdot L \cdot c}{I} \]

Force (P):

Length (L):

Distance to Extreme Fiber (c):

Moment of Inertia (I):

m⁴

Maximum Bending Stress (σ_max):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Cantilever Beam Bending Stress?

The maximum bending stress in a cantilever beam occurs at the fixed end and is calculated using the formula σ_max = (P·L·c)/I. This stress represents the highest normal stress experienced by the beam material due to bending moments.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

\[ \sigma_{max} = \frac{P \cdot L \cdot c}{I} \]

Where:

\( \sigma_{max} \) — Maximum bending stress (Pa)
\( P \) — Applied force (N)
\( L \) — Length of the cantilever beam (m)
\( c \) — Distance from neutral axis to extreme fiber (m)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum normal stress at the fixed end of a cantilever beam subjected to a point load at the free end.

3. Importance of Bending Stress Calculation

Details: Calculating maximum bending stress is crucial for structural design and analysis. It ensures that beams can safely support applied loads without exceeding material yield strength, preventing structural failure.

4. Using the Calculator

Tips: Enter force in newtons (N), length in meters (m), distance to extreme fiber in meters (m), 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 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 end of the cantilever beam, at the outermost fibers of the cross-section.

Q3: What is the 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: What units should I use for input values?
A: Use consistent SI units: newtons (N) for force, meters (m) for length and distance, and meters⁴ (m⁴) for moment of inertia.

Q5: How does beam cross-section affect bending stress?
A: Different cross-sections (rectangular, circular, I-beam) have different moment of inertia values, which directly affect the calculated bending stress for the same loading conditions.