User:Plicjo

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Given:


Find:

Find the displacements of the three bodies and the forces ( tensile/compressive) in the springs. What are the reactions at the walls? Assume only horizontal translation.

Solution:

The nodes and elements are labeled in the problem. Create a connectivity table.

C:\Users\Josh\Desktop\Problem 6---Connectivity Table.png


Construct Elemental equilibrium equations for all 6 elements.

Here is a sample equilibrium equation for element 3:


The notation for : The superscript parenthesis signifies the element number, while the subscript signifies the associated node number.

With element forces calculated, a node equilibrium can be established.



Start with a free-body diagram of each node, and then create the equation:



Make sure all forces are positive and modeled in tension.


Combine your elemental equilibrium equations with your nodal equilibrium equations for the global stiffness correlation:

Solving with MATLAB: