Calculation of Stiffness in Structural elements

Question 1:

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

Aim:- To compute the lateral stiffness of the given frame.

Introduction:-

Mathematically,We can define stiffness as the force which is required to produce unit deformation is called stiffness (or) The moment which is required to produce unit rotation is called stiffness.

P= KΔ

where, P is the applied force,k is the stiffness and Δ is the deformation

M=Kθ

where, M is the applied moment, K is the stiffness, θ is the unit rotation produced.

Solution procedure:-

The above given frame can be solved by using a displacement method under which Stiffness matrix method is available to compute the lateral stiffness of the frame.

Question 2,a:

For the following structures:

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

Solution procedure are as follows:-

Question 2,b:

For the following structures:

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

Solution procedure are as follows:-

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.

Solution procedure are as follows:-

Question 4

Determine an expression for the effective stiffness of the following systems:

Solution procedure are as follows:-