Calculation of Stiffness in Structural elements

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 Elb= Elc

if U{1} = 1

U{1} = 24 * (E*Ic)/(h^3)

U{2} = 6 * (E*Ic)/(h^2)

U{3} = 6 * (E*Ic)/(h^2)

1 st equation :

24 * (E*Ic)/(h^3) + 6 * (E*Ic)/(h^2) + 6 * (E*Ic)/(h^2)

if U{2}=1

U{1} = (6*E * Ic)/(h ^ 2)

U{2} = (4E * Ib)/(2h) + (4E * Ic)/h

U{3} = (2E * Ib)/(2h)

2nd equation:

(6*E * Ic)/(h ^ 2) + (4E * Ib)/(2h) + (4E * Ic)/h + (2E * Ib)/(2h)

if U3=1

U{1} = (6*E * Ic)/(h ^ 2)

U{3} = (4E * Ib)/(2h) + (4E * Ic)/h

U{2} = (2E * Ib)/(2h)

3rd equation:

(6*E * Ic)/(h ^ 2) + (2E * Ib)/(2h) + (4E * Ib)/(2h) + (4E * Ic)/h

*According to stiffness matrix method:

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

The degree of freedom is 1

*as the beam is rigid (i.e flexural rigidity M.I infinity

*Equation of motion = mu + fd+fs= p(t) = mu + ku = P(t)

B)

3)

4)

a)

b)

c)