Wall Thickness Given Deflection At Top Due To Fixed Against Rotation Calculator

Formula Used:

\[ t = \frac{P}{E \cdot \delta} \cdot \left( \left( \frac{H}{L} \right)^3 + 3 \cdot \left( \frac{H}{L} \right) \right) \]

Concentrated Load on Wall (P):

Modulus of Elasticity of Wall Material (E):

Deflection of Wall (δ):

Height of the Wall (H):

Length of Wall (L):

Wall Thickness (t):

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1. What is Wall Thickness Given Deflection At Top Due To Fixed Against Rotation?

This calculation determines the required wall thickness based on the deflection at the top of a wall that is fixed against rotation. It considers the concentrated load, material properties, and wall dimensions to ensure structural stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \frac{P}{E \cdot \delta} \cdot \left( \left( \frac{H}{L} \right)^3 + 3 \cdot \left( \frac{H}{L} \right) \right) \]

Where:

\( t \) — Wall Thickness (m)
\( P \) — Concentrated Load on Wall (N)
\( E \) — Modulus of Elasticity of Wall Material (Pa)
\( \delta \) — Deflection of Wall (m)
\( H \) — Height of the Wall (m)
\( L \) — Length of Wall (m)

Explanation: The formula calculates the required wall thickness to limit deflection at the top for a wall fixed against rotation, considering the applied load and material properties.

3. Importance of Wall Thickness Calculation

Details: Proper wall thickness calculation is crucial for structural integrity, ensuring walls can withstand applied loads without excessive deflection while maintaining stability and safety.

4. Using the Calculator

Tips: Enter all values in appropriate units (N for load, Pa for modulus, m for dimensions). Ensure all values are positive and within reasonable ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What does "fixed against rotation" mean?
A: It means the wall is constrained from rotating at its supports, typically at the base, providing additional stability against applied loads.

Q2: When is this calculation typically used?
A: This calculation is used in structural engineering for designing walls, partitions, and vertical structural elements that need to resist concentrated loads with limited deflection.

Q3: What factors affect wall thickness requirements?
A: Load magnitude, material stiffness, wall dimensions, and allowable deflection all influence the required wall thickness.

Q4: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior, small deflections, and specific boundary conditions. It may not be accurate for very thick walls or non-uniform loading conditions.

Q5: How does wall height-to-length ratio affect thickness?
A: Higher H/L ratios generally require greater wall thickness to maintain stability and limit deflection under applied loads.