MKE-FDocumentation / GNU Octave

Additional chapter 14 · two-element frame

Stiffness and mass matrices

Illustrative Example 11.1: local matrices of two frame elements, rotation into global axes, 9×9 assembly, fixed supports and transition to the equation Mffü + Kffu = F(t).

Reference contents

Structural model and degrees of freedom

Three frame nodes give nine global DOFs. The outer nodes are fixed; the middle node is free.

Step 1 of 8

Structural model

Two 100 in elements

Two-element plane frame An inclined frame element connects fixed node 1 to free node 2. A horizontal element connects node 2 to fixed node 3. F(t) 1 2 3 e₁ · 45° · L=100 e₂ · 0° · L=100 u₁=v₁=θ₁=0 u₃=v₃=θ₃=0

Global DOF map: [uₓ, uᵧ, θ] at each node

Area A6 in²
Modulus E10⁷ lb/in²
Density ρ0.7 lb·s²/in⁴
Second moment I100 in⁴
Length L100 in
Free DOFs[4, 5, 6]

Local stiffness matrix coefficients

Global stiffness matrix K

zero initialization · 9 × 9

K = 0
Select a nonzero cell to see its origin.

Note: Mario Paz published this dataset as a modal example. Here the same verified K and M are used in the undamped transient equation and Newmark effective matrix.

Bibliography: Structural Dynamics. Theory And Computation, 5th ed., Mario Paz, William Leigh, 2004.