Maximum bending moment given max deflection for strut subjected to uniformly distributed load Calculator

Formula Used:

\[ M = -(P_{axial} \times C) - \left(\frac{q_f \times l_{column}^2}{8}\right) \]

Axial Thrust (P_axial):

Maximum initial deflection (C):

Load Intensity (q_f):

Column Length (l_column):

Maximum Bending Moment (M): N·m

1. What is Maximum Bending Moment Calculator?

Definition: This calculator determines the maximum bending moment in a strut subjected to both axial thrust and uniformly distributed load.

Purpose: It helps structural engineers analyze and design columns or struts under combined loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M = -(P_{axial} \times C) - \left(\frac{q_f \times l_{column}^2}{8}\right) \]

Where:

\( M \) — Maximum bending moment (N·m)
\( P_{axial} \) — Axial thrust (N)
\( C \) — Maximum initial deflection (m)
\( q_f \) — Load intensity (Pa)
\( l_{column} \) — Column length (m)

Explanation: The formula accounts for both the bending due to axial thrust and the bending due to distributed load.

3. Importance of Maximum Bending Moment Calculation

Details: Accurate calculation ensures structural integrity, prevents buckling, and helps in proper material selection.

4. Using the Calculator

Tips: Enter all values in consistent units (N, m, Pa). The calculator will provide the maximum bending moment in N·m.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of initial deflection?
A: Initial deflection accounts for imperfections in the column that affect its bending behavior under load.

Q2: How does axial thrust affect bending moment?
A: Axial thrust amplifies the bending effect due to the P-Δ (P-delta) effect, increasing the total moment.

Q3: What's the typical range for initial deflection?
A: Initial deflection is often taken as L/500 to L/1000 of the column length, depending on construction tolerances.

Q4: Can this be used for both steel and concrete columns?
A: Yes, but material properties will determine the allowable stresses and safety factors to apply.

Q5: What if my column has different end conditions?
A: This formula assumes pinned ends. For other conditions, different moment equations apply.