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

Ans.

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

Ans.

The DOF for Dynamic analysis will be 1.

Equation of motion is

then mu+ku=0

substitute the value of k as 3EI/H^3

mu+3EI/H^3U=0

Natural frequency

wn(omega n)= root k/m

root(3EI/h^3/M)

ANS.

The DOF for dynamic analysis will be 1

Equation of motion is mu+ku=0

Substitute the value of k as 12EI/H^3+12EI/H^3

MU+24EI/H^3U=0

Nature of frequency

wn(omega n) root k/m

root(24Ei/h^3/m)

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.

ANS,.

wn =root (k/m)

k for simply supported beam is 6EI/H^3

so the natural period is =root (6EI/H^3/M)

Question 4

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

ANS. a).

Here the expression for effective stiffness will be

3EI/H^3

b). Here the expression for effective stiffness will be

3EI/H^3 + 3EI/H^3

6EI/H^3

c). Here the expression for effective stiffness will be

3EI/H^3 + 3EI/H^3

6EI/H^3