Ultimate Moment Calculator

Formula

To calculate the ultimate moment:

\[ Mu = A \times T \times \left(D - \frac{a}{2}\right) \]

Where:

\( Mu \) is the ultimate moment
\( A \) is the cross-sectional area
\( T \) is the tensile strength of the material
\( D \) is the depth of the beam
\( a \) is the depth of the neutral axis

What is an Ultimate Moment?

An ultimate moment is a measure of the total moment acting on a beam at its maximum capacity. It helps in determining the beam's strength.

Example Calculations

Example 1:

Assume the following values:

Cross-Sectional Area (A): 10 in²
Tensile Strength (T): 6000 psi
Depth of the Beam (D): 12 in
Depth of the Neutral Axis (a): 4 in

Using the formula:

\[ Mu = 10 \times 6000 \times \left(12 - \frac{4}{2}\right) = 10 \times 6000 \times 10 = 600,000 \text{ in-lb} \]

The ultimate moment is 600,000 in-lb.

Example 2:

Assume the following values:

Cross-Sectional Area (A): 20 mm²
Tensile Strength (T): 30 MPa
Depth of the Beam (D): 200 mm
Depth of the Neutral Axis (a): 80 mm

Using the formula:

\[ Mu = 20 \times 30 \times \left(200 - \frac{80}{2}\right) = 20 \times 30 \times 160 = 96,000 \text{ N-mm} \]

The ultimate moment is 96,000 N-mm.

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