How to use calculator
- Select the units from dropdown.
- Select stiffness matrix for beam element or stiffness matrix for frame element.
- Enter length of beam or frame element.
- For a frame element cross sectional area is must, for beam element it can be kept as optional.
- Enter youngs modulus of the material.
- Enter area moment of inertia for the element.
- Flexural rigidity will be calculated automatically, user can change the units of each quantity separately as and how required.
- 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]
