Plastic Moment for SSB with load at distance Calculator

Plastic Moment Formula:

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

Theoretical Load (W_u):

Distance 1 (a₁):

Distance 2 (a₂):

Beam Length (l):

Plastic Moment (M_psx): N·m

1. What is Plastic Moment for SSB with Load at Distance?

Definition: This calculator determines the plastic moment capacity of a simply supported beam when a concentrated load is applied at a specific distance from one support.

Purpose: It helps structural engineers analyze beam behavior at plastic limit states where the entire cross-section yields.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( M_{psx} \) — Plastic moment capacity (N·m)
\( W_u \) — Theoretical or nominal load (kg)
\( a_1 \) — Distance from load to left support (m)
\( a_2 \) — Distance from load to right support (m)
\( l \) — Overall length of beam (m)

Explanation: The formula calculates the maximum moment when the beam forms plastic hinges at the load point and supports.

3. Importance of Plastic Moment Calculation

Details: Plastic moment analysis is crucial for understanding ultimate load capacity and designing ductile structural systems.

4. Using the Calculator

Tips: Enter the theoretical load, both distances (a1 and a2), and beam length. All values must be > 0. Results have ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between elastic and plastic moment?
A: Elastic moment considers yield at extreme fibers only, while plastic moment accounts for full cross-section yielding.

Q2: Why are there two distances in the formula?
A: The two distances (a1 and a2) represent the load's position relative to both supports (a1 + a2 = l).

Q3: What does the ±5% tolerance mean?
A: It accounts for material variability, workmanship, and other practical factors affecting actual capacity.

Q4: Can this be used for multiple point loads?
A: No, this formula is specifically for a single concentrated load on a simply supported beam.

Q5: How does plastic moment relate to beam failure?
A: When plastic moment is reached, the beam forms a collapse mechanism but may not immediately fail.