Tanvesh
Tanvesh
Masters in Structural Engineering | Research Interest - Artificial Intelligence and Machine learning in Civil Engineering | Youtuber | Teacher | Currently working as Research Scholar at NIT Goa

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Free online stiffness matrix calculator for beam element and frame element.

How to use calculator

  1. Select the units from dropdown.
  2. Select stiffness matrix for beam element or stiffness matrix for frame element.
  3. Enter length of beam or frame element.
  4. For a frame element cross sectional area is must, for beam element it can be kept as optional.
  5. Enter youngs modulus of the material.
  6. Enter area moment of inertia for the element.
  7. Flexural rigidity will be calculated automatically, user can change the units of each quantity separately as and how required.
  8. The units of the results can also be changed.

Stiffness matrix for beam element

\left[\begin{array}{cccc} \frac{12 E I}{L^{3}} & \frac{6 E I}{L^{2}} & \frac{-12 E I}{L^{3}} & \frac{6 E I}{L^{2}} \\ \frac{6 E I}{L^{2}} & \frac{4 E I}{L} & \frac{-6 E I}{L^{2}} & \frac{2 E I}{L} \\ \frac{-12 E I}{L^{3}} & \frac{-6 E I}{L^{2}} & \frac{12 E I}{L^{3}} & \frac{-6 E I}{L^{2}} \\ \frac{6 E I}{L^{2}} & \frac{2 E I}{L} & \frac{-6 E I}{L^{2}} & \frac{4 E I}{L} \end{array}\right]

Stiffness matrix for frame element

\left[\begin{array}{cccccc} \frac{A E}{L} & 0 & 0 & \frac{-A E}{L} & 0 & 0 \\ 0 & \frac{12 E I}{L^{3}} & \frac{6 E I}{L^{2}} & 0 & \frac{-12 E I}{L^{3}} & \frac{6 E I}{L^{2}} \\ 0 & \frac{6 E I}{L^{2}} & \frac{4 E I}{L} & 0 & \frac{-6 E I}{L^{2}} & \frac{2 E I}{L} \\ \frac{-A E}{L} & 0 & 0 & \frac{A E}{L} & 0 & 0 \\ 0 & \frac{-12 E I}{L^{3}} & \frac{-6 E I}{L^{2}} & 0 & \frac{12 E I}{L^{3}} & \frac{-6 E I}{L^{2}} \\ 0 & \frac{6 E I}{L^{2}} & \frac{2 E I}{L} & 0 & \frac{-6 E I}{L^{2}} & \frac{4 E I}{L} \end{array}\right]
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