Deflection At Section For Strut Subjected To Compressive Axial And Uniformly Distributed Load Calculator

Formula Used:

\[ \delta = \frac{-M_b + q_f \times \left( \frac{x^2}{2} - \frac{l_{column} \times x}{2} \right)}{P_{axial}} \]

Bending Moment in Column (M_b):

N·m

Load Intensity (q_f):

Distance of deflection from end A (x):

Column Length (l_column):

Axial Thrust (P_axial):

Deflection at Section (δ):

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1. What is the Deflection at Section Formula?

The deflection at section formula calculates the lateral displacement at a specific point along a strut or column that is subjected to both compressive axial load and uniformly distributed load. This is essential for structural analysis and design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \frac{-M_b + q_f \times \left( \frac{x^2}{2} - \frac{l_{column} \times x}{2} \right)}{P_{axial}} \]

Where:

\( \delta \) — Deflection at Section (m)
\( M_b \) — Bending Moment in Column (N·m)
\( q_f \) — Load Intensity (Pa)
\( x \) — Distance of deflection from end A (m)
\( l_{column} \) — Column Length (m)
\( P_{axial} \) — Axial Thrust (N)

Explanation: The formula accounts for the combined effects of bending moment, distributed load, and axial compression on the deflection of a structural member.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design code requirements for columns and struts under combined loading conditions.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, Newtons for force, Pascal for pressure). Ensure axial thrust is not zero to avoid division by zero error.

5. Frequently Asked Questions (FAQ)

Q1: What types of structural elements does this formula apply to?
A: This formula applies to columns, struts, and other compression members subjected to both axial compressive loads and uniformly distributed lateral loads.

Q2: What are typical deflection limits for columns?
A: Deflection limits vary by building codes and structural requirements, but typically range from L/250 to L/500 of the column length, where L is the column length.

Q3: When is this deflection formula most accurate?
A: This formula provides accurate results for linear elastic materials and small deflections where the principle of superposition applies.

Q4: Are there limitations to this equation?
A: The formula assumes linear elastic behavior, small deflections, and may not account for large deformations, material nonlinearity, or buckling effects.

Q5: How does axial thrust affect deflection?
A: Compressive axial thrust generally increases deflection (reduces stiffness), while tensile axial thrust decreases deflection (increases stiffness) in structural members.