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  

ANSWER : 

      To calculate the lateral stiffness of the one story frame with an intermediate realistic stiffness of the beam as given below

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

ANSWER : 

• Here we find the number of degree of freedom for dynamic analysis for both (a) and (b)
• Then we want to find the equation of motion
• Finally Calculate their natural frequencies for both given diagrams

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 : 

• Here we want to calculate the natural frequence of propped cantilever beam
• The weight of the beams in comparison with the mass M is very small.
• And also we findout the simply supported beam.

Question 4:

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

ANSWER : 

• Here we given below the effective stiffness for all the given diagrams