Calculation of Stiffness in Structural elements

Solution.1)

Aim: To Compute lateral stiffness of the one story frame with an intermediate realistic stiffness of the beam. The system has 3 DOFs as shown. Assume L = 2h and El_b = El_c  

Procedure:

Result: Lateral Stiffness of the given one storey frame has been calculated = `(96EI_c)/(7h^3)`

Solution.2)

Aim: For the following structures:

• Determine the number of degrees-of-freedom for dynamic analysis
• Establish the equation of motion
• Calculate their natural frequencies

Procedure:

Result: Natural Frequency for the following cases has been calculated:

a) Natural Frequency(f) = `1/(2pi)sqrt((3EI)/(mh^3))`

b) Natural Frequency(f) = `1/(2pi)sqrt((27EI)/(mh^3))`

Solution.3)

Aim: To determine the natural period of the system shown, 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.

Procedure:

Result: Natural Frequency for the given case has been derived succesfully.

Solution.4)

Aim: To determine an expression for the effective stiffness of the following systems:

Procedure:

Result: Expression for the effective stiffness has been found successfully.