Stiffness Matrix Calculator

Your details

Choose the structural element type. Truss carries axial force only. Beam carries shear and bending. Frame combines all three.
Elastic modulus of the material. Steel is ~200 GPa, concrete ~30 GPa, aluminium ~70 GPa.
Area of the element cross-section. Required for truss and frame elements; ignored for pure beam elements.
Second moment of area about the bending axis. Required for beam and frame elements.
Length of the element between its two nodes.
Angle of the element measured counter-clockwise from the global x-axis. Use 0 for a horizontal element. This is used to compute the transformation matrix and global stiffness matrix.
degrees
Flexural coefficient EI/L^3
7,407,111.1111N/m

Primary bending coefficient driving the shear terms

k[1,1]7,407,111.1111
Local stiffness matrix[7.41e+6, 1.11e+7, -7.41e+6, 1.11e+7] [1.11e+7, 2.22e+7, -1.11e+7, 1.11e+7] [-7.41e+6, -1.11e+7, 7.41e+6, -1.11e+7] [1.11e+7, 1.11e+7, -1.11e+7, 2.22e+7]
Global stiffness matrix[7.41e+6, 1.11e+7, -7.41e+6, 1.11e+7] [1.11e+7, 2.22e+7, -1.11e+7, 1.11e+7] [-7.41e+6, -1.11e+7, 7.41e+6, -1.11e+7] [1.11e+7, 1.11e+7, -1.11e+7, 2.22e+7]
Transformation matrix T[1.000, 0, 0, 0] [0, 1.000, 0, 0] [0, 0, 1.000, 0] [0, 0, 0, 1.000]
Local DOF order[v1, theta1, v2, theta2]
AE/L (axial)-
12EI/L³ (bending)7,407,111.1111

Beam element stiffness matrix assembled successfully.

  • Your element is a 4x4 Euler-Bernoulli beam element. The matrix captures shear forces and bending moments at each end, with four degrees of freedom: transverse displacement and rotation at each node.
  • The primary bending coefficient 12EI/L^3 = 7.407e+6 N/m. This governs transverse shear stiffness at the nodes.
  • The element is horizontal (0 degrees), so the local and global stiffness matrices are identical - no rotation is needed.

Next stepTo analyze a full structure, assemble the individual element global stiffness matrices by adding overlapping DOF entries. Then apply boundary conditions (set known displacements) and solve K * d = F for the unknown nodal displacements.

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