Calculation of Stiffness in Structural elements
Aim :
Question 2
For the following structures:
- Determine the number of degrees-of-freedom for dynamic analysis
- Establish the equation of motion
- Calculate their natural frequencies
Procedure : The system has single degree of freedom
2. It has fixed end at bottom
the expression will be as folows
k = 3EI/h3
The expression is attached below
Question 2 (b)
Answer:
The first two column are fixed at bottom and third column is pinned
Position of Element can be described by 1 coordinate only u(t)
The System has single degree of freedom.
Aim : Question 3
Consider the propped cantilever shown in the figure below. The beams are made from the same steel section and have lengths as shown on the diagram. Determine the natural period of this system if a large mass, M, is placed at the intersection of the beams at point A. The weight of the beams in comparison with the mass M is very small.
Answer :
Both elements have same material and section. That means same modulous of Elasticity but the length is different
When mass M is Applied at the point both element will respond simultanously. They are connected in parellel.
The Expression for stiffness of system is given below in the Attachment
Aim : Question 4
Determine an expression for the effective stiffness of the following systems:
The Expression for the above question is given below