Calculation of Stiffness in Structural elements

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 .}

Answers:-

AIM:-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 .}

RESULT:-

STIFFFNESS COEFFICIENT, K = 96EIc/7h³.

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.

Answers:-

AIM:-

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

a)

RESULT:-

Natural frequency,Fn= ∞

b)

ANSWERS:-

RESULTS:-

Natural frequency,Fn= ∞

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.

ANSWERS:-

AIM:-  To 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.

RESULTS:-

Natural period, Tn = 2π√(u/g) or Tn = 2√(u)

Question 4.

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

Answers:-

(a)

Aim:-To determine an expression for the effective stiffness of the following system.

RESULT:-

Keff= 3EIK/(KL³+3EI)

(B)

Aim:-To determine an expression for the effective stiffness of the following system.

RESULT:-

Keff= 24EI+kh³/(h³)

Answers:-

(c)

Aim:-To determine an expression for the effective stiffness of the following system.

RESULTS:-

Keff= 48EI/L³ + EA/√(h²+l²)