Matrix of Stiffness Coefficients

The coefficients that determine spring stiffness are calculated as below equations (units are force/length).

where,

Undeformed Length

Enter the undeformed length of the beam along the x-axis.

Young’s Modulus

Specify the young's modulus of elasticity for the beam material (unit is force/length^2).

Shear Modulus

Specify the shear modulus of the beam (unit is force/length^2).

Moment of Area

Enter the torsional constant

This value is calculated automatically using Library

Enter the area moments of inertia about the neutral axes of the beam cross sectional areas (y-y and z=z).

These values are calculated automatically using Library

Shear Area Ratio

Enter the shear area ratio for shear deflection in the y direction for Timoshenko beams.

This value is calculated automatically using Library

Enter the shear area ratio for shear deflection in the z direction for Timoshenko beams.

This value is calculated automatically using Library

Area of Cross Section

Enter the uniform area of the beam cross-section geometry.

This value is calculated automatically using Library

Damping Coefficient (matrix)

Enter the coefficient that determines the damping force given the velocity of the beam end points (units are force-time/length).

If the matrix for structural damping is selected, the upper triangular matrix for the damping should be entered since the damping matrix is symmetric.

Viscous Damping Coefficient (ratio)

The damping coefficient matrix is calculated as

Displacements

Translational and rotational displacements of the action marker with respect to the base marker

Velocities

Translational and rotational velocities of the action marker with respect to the base marker