Critical Elastic Moment Formula

Fx Copy

LaTeX Copy

Critical Elastic Moment represents the maximum moment a beam can carry in its elastic range before it becomes unstable due to lateral-torsional buckling. Check FAQs

M cr = (\frac{C b \cdot π}{L}) \cdot \sqrt{((E \cdot I y \cdot G \cdot J) + (I y \cdot C w \cdot (\frac{π \cdot E}{{(L)}^{2}})))}

M_cr - Critical Elastic Moment?C_b - Moment Gradient Factor?L - Unbraced Length of Member?E - Elastic Modulus of Steel?I_y - Y Axis Moment of Inertia?G - Shear Modulus?J - Torsional Constant?C_w - Warping Constant?π - Archimedes' constant?

Critical Elastic Moment Example

With values

With units

Only example

Here is how the Critical Elastic Moment equation looks like with Values.

Here is how the Critical Elastic Moment equation looks like with Units.

Here is how the Critical Elastic Moment equation looks like.

6.7919 = (\frac{1.96 \cdot 3.1416}{12}) \cdot \sqrt{((200 \cdot 5000 \cdot 80 \cdot 21.9) + (5000 \cdot 0.2 \cdot (\frac{3.1416 \cdot 200}{{(12)}^{2}})))}

6.7919N*m = (\frac{1.96 \cdot 3.1416}{12m}) \cdot \sqrt{((200GPa \cdot 5000mm⁴/mm \cdot 80GPa \cdot 21.9) + (5000mm⁴/mm \cdot 0.2 \cdot (\frac{3.1416 \cdot 200GPa}{{(12m)}^{2}})))}

6.7919 = (\frac{1.96 \cdot 3.1416}{12}) \cdot \sqrt{((200 \cdot 5000 \cdot 80 \cdot 21.9) + (5000 \cdot 0.2 \cdot (\frac{3.1416 \cdot 200}{{(12)}^{2}})))}

Tip: Use pencil () icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Engineering » Civil » Design of Steel Structures » Critical Elastic Moment

Critical Elastic Moment Solution

Follow our step by step solution on how to calculate Critical Elastic Moment?

FIRST Step Consider the formula

M cr = (\frac{C b \cdot π}{L}) \cdot \sqrt{((E \cdot I y \cdot G \cdot J) + (I y \cdot C w \cdot (\frac{π \cdot E}{{(L)}^{2}})))}

Next Step Substitute values of Variables

∴

M cr = (\frac{1.96 \cdot π}{12m}) \cdot \sqrt{((200GPa \cdot 5000mm⁴/mm \cdot 80GPa \cdot 21.9) + (5000mm⁴/mm \cdot 0.2 \cdot (\frac{π \cdot 200GPa}{{(12m)}^{2}})))}

Next Step Substitute values of Constants

∴

M cr = (\frac{1.96 \cdot 3.1416}{12m}) \cdot \sqrt{((200GPa \cdot 5000mm⁴/mm \cdot 80GPa \cdot 21.9) + (5000mm⁴/mm \cdot 0.2 \cdot (\frac{3.1416 \cdot 200GPa}{{(12m)}^{2}})))}

Next Step Convert Units

∴

M cr = (\frac{1.96 \cdot 3.1416}{1200cm}) \cdot \sqrt{((200GPa \cdot 5E-6m⁴/m \cdot 80GPa \cdot 21.9) + (5E-6m⁴/m \cdot 0.2 \cdot (\frac{3.1416 \cdot 200GPa}{{(1200cm)}^{2}})))}

Next Step Prepare to Evaluate

∴

M cr = (\frac{1.96 \cdot 3.1416}{1200}) \cdot \sqrt{((200 \cdot 5E-6 \cdot 80 \cdot 21.9) + (5E-6 \cdot 0.2 \cdot (\frac{3.1416 \cdot 200}{{(1200)}^{2}})))}

Next Step Evaluate

∴

M cr = 6.79190728759447N*m

LAST Step Rounding Answer

∴

M cr = 6.7919N*m

Critical Elastic Moment Formula Elements

Variables

Constants

Functions

Critical Elastic Moment

Critical Elastic Moment represents the maximum moment a beam can carry in its elastic range before it becomes unstable due to lateral-torsional buckling.

Symbol: M_cr

Measurement: Moment of ForceUnit: N*m