Maximum Bending Moment Developed in Plate given Total Resisting Moment by n Plates Calculator

Formula Used:

\[ \text{Maximum Bending Stress in Plates} = \frac{6 \times \text{Bending Moment in Spring}}{\text{Width of Full Size Bearing Plate} \times \text{Number of Plates} \times \text{Thickness of Plate}^2} \] \[ \sigma = \frac{6 \times M_b}{B \times n \times t_p^2} \]

Bending Moment in Spring (M_b):

N·m

Width of Full Size Bearing Plate (B):

Number of Plates (n):

Thickness of Plate (t_p):

Maximum Bending Stress in Plates (σ):

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1. What is Maximum Bending Stress in Plates?

Maximum Bending Stress in Plates is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. It represents the highest stress experienced by the material during bending.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma = \frac{6 \times M_b}{B \times n \times t_p^2} \]

Where:

\( \sigma \) — Maximum bending stress in plates (Pa)
\( M_b \) — Bending moment in spring (N·m)
\( B \) — Width of full size bearing plate (m)
\( n \) — Number of plates
\( t_p \) — Thickness of plate (m)

Explanation: This formula calculates the maximum bending stress experienced by plates under a given bending moment, considering the geometric properties of the plates.

3. Importance of Maximum Bending Stress Calculation

Details: Calculating maximum bending stress is crucial for structural design and analysis, ensuring that materials can withstand applied loads without failure and helping engineers determine appropriate plate dimensions for safety and efficiency.

4. Using the Calculator

Tips: Enter bending moment in N·m, width in meters, number of plates (must be at least 1), and thickness in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input values?
A: Use consistent SI units: bending moment in Newton-meters (N·m), width and thickness in meters (m).

Q2: Why is the number of plates important in this calculation?
A: The number of plates distributes the bending moment across multiple plates, reducing the stress on each individual plate.

Q3: What is the significance of plate thickness in bending stress?
A: Thicker plates significantly reduce bending stress since stress is inversely proportional to the square of the thickness.

Q4: How does plate width affect bending stress?
A: Wider plates distribute the bending load over a larger area, reducing the maximum bending stress.

Q5: What are typical maximum allowable bending stresses for different materials?
A: Allowable bending stresses vary by material. Steel typically allows 150-250 MPa, aluminum 80-150 MPa, and wood 5-15 MPa, depending on grade and treatment.