Example 1: Analyze the beam shown in the figure that is subjected to a distributed load and a point force, use the matrix method of stiffness.
EI = Constant
a) Define the degrees of freedom and orientation of the element.
- The beam is not subjected to axial load, therefore two degrees of freedom are defined at each node (shear and moment).
- First we define the free degrees of freedom (green color).
- Second, we define the restricted degrees of freedom (red color).
- Finally, we define the orientation of the element.
b) Assemble the stiffness matrix of each element.
c) Assemble the stiffness matrix of the beam.
d) Partition of the sub matrix K₁₁.
e) Load vector analysis.
f) Displacement vector calculation. |DD| = |K ₁₁|⁻¹ * |Cc|
g) Calculation of reactions. |CD| = |DD| * |K₂₁|
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