Horizontal Reaction given Moment at Section if One End of Column is Fixed and Other is Hinged Calculator

Horizontal Reaction Formula:

\[ H = \frac{M_t + P \times \delta}{l - x} \]

Moment of Section:

N·m

Column Crippling Load:

Deflection at Section:

Column Length:

Distance b/w Fixed End and Deflection Point:

Tolerance:

Horizontal Reaction (N):

1. What is Horizontal Reaction in Column Analysis?

Definition: Horizontal Reaction is used to balance the bending moment due to vertical reactions and dead load, live load, etc. in structural columns.

Purpose: It helps structural engineers determine the lateral forces that develop when one end of a column is fixed and the other is hinged.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H = \frac{M_t + P \times \delta}{l - x} \]

Where:

\( H \) — Horizontal Reaction (N)
\( M_t \) — Moment of Section (N·m)
\( P \) — Column Crippling Load (N)
\( \delta \) — Deflection at Section (m)
\( l \) — Column Length (m)
\( x \) — Distance between Fixed End and Deflection Point (m)

Explanation: The formula accounts for both the bending moment and the effect of axial load on deflection to determine the horizontal reaction.

3. Importance of Horizontal Reaction Calculation

Details: Proper calculation ensures structural stability, prevents excessive deflection, and helps design appropriate foundations and connections.

4. Using the Calculator

Tips: Enter all required parameters in consistent units. The tolerance field (default ±5%) helps account for material and construction variations.

5. Frequently Asked Questions (FAQ)

Q1: When does this formula apply?
A: Specifically for columns with one fixed end and one hinged end under combined axial and lateral loading.

Q2: What's a typical tolerance value?
A: ±5% is common, but this may vary based on material properties and design requirements.

Q3: How do I determine the column crippling load?
A: It's typically calculated using Euler's formula for column buckling or determined through material testing.

Q4: What if I get a negative horizontal reaction?
A: A negative value indicates the reaction acts in the opposite direction to what was assumed.

Q5: Why include tolerance in the calculation?
A: To account for material variability, construction tolerances, and safety factors in real-world applications.