Plastic Moment for Propped Cantilever Calculator

Plastic Moment Formula:

\[ M_{pprop} = \frac{W_u \times a_1 \times a_2}{l + a_2} \]

Theoretical Load (W_u):

Distance1 (a₁):

Distance2 (a₂):

Beam Length (l):

Plastic Moment (M_pprop): N·m

1. What is Plastic Moment for Propped Cantilever?

Definition: The plastic moment is the maximum moment a beam can resist before it becomes fully plastic and forms a collapse mechanism.

Purpose: It helps structural engineers determine the load-bearing capacity of propped cantilever beams at their plastic limit state.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{pprop} = \frac{W_u \times a_1 \times a_2}{l + a_2} \]

Where:

\( M_{pprop} \) — Plastic moment for propped cantilever (N·m)
\( W_u \) — Theoretical or nominal load (kg)
\( a_1 \) — Distance from support to point load (m)
\( a_2 \) — Distance from point load to other end (m)
\( l \) — Overall length of beam (m)

Explanation: The formula calculates the plastic moment capacity considering the beam's geometry and applied load position.

3. Importance of Plastic Moment Calculation

Details: Accurate plastic moment calculation ensures structural safety by preventing collapse under ultimate loads while optimizing material usage.

4. Using the Calculator

Tips: Enter all required values with ±5% tolerance. The calculator will compute the plastic moment capacity in Newton-meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a propped cantilever?
A: A cantilever beam with one fixed end and one simply supported end, where the support prevents vertical deflection but allows rotation.

Q2: Why is plastic moment important?
A: It determines the ultimate load capacity of a beam when it reaches full plasticity and forms a collapse mechanism.

Q3: How does load position affect the plastic moment?
A: The plastic moment varies with the load position (a1 and a2) as it changes the internal moment distribution.

Q4: What units should I use?
A: Use consistent units: kg for load, meters for distances. The result is in Newton-meters.

Q5: Does this consider material properties?
A: The plastic moment inherently depends on the material's yield strength, which is accounted for in the theoretical load (Wu).