Deflection At Top Due To Fixed Against Rotation Calculator

Formula Used:

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

Concentrated Load on Wall (P):

Modulus of Elasticity of Wall Material (E):

Wall Thickness (t):

Height of the Wall (H):

Length of Wall (L):

Deflection of Wall (δ):

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1. What is Deflection at Top due to Fixed against Rotation?

The Deflection at Top due to Fixed against Rotation measures the degree to which a structural wall element is displaced under a concentrated load when the wall is fixed against rotation at its base. This calculation is essential in structural engineering to ensure stability and serviceability of wall structures.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the deflection at the top of a wall that is fixed against rotation at its base, considering the material properties, dimensions, and applied load.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design specifications and building codes.

4. Using the Calculator

Tips: Enter all values in consistent units (N for load, Pa for modulus, m for dimensions). All values must be positive and non-zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What does "fixed against rotation" mean?
A: It means the base of the wall is constrained from rotating, providing full moment resistance at the support.

Q2: What are typical deflection limits for walls?
A: Deflection limits vary by building codes and applications, but typically range from L/240 to L/360 for serviceability requirements.

Q3: How does wall thickness affect deflection?
A: Increased wall thickness reduces deflection, as deflection is inversely proportional to thickness in this formula.

Q4: Can this formula be used for all wall types?
A: This formula is specifically for walls fixed against rotation at the base. Different boundary conditions require different formulas.

Q5: What is the significance of the H/L ratio?
A: The height-to-length ratio significantly influences deflection, with higher ratios resulting in greater deflection under the same load.