Calculation of Stiffness in Structural elements

Question -1

u1 = 24 EI/h3

u2= 6EI/h3

u3 = 6EI/h3

Question -2

a) DOF = 1

Equation of motion is mu+ku =0

Lateral stiffness k= 3EI/h3

mu + ( 3EI/h3) u = 0

Natural Frequency = wn = k/m

k =3EI/h3

wn = ( 3EI/h3) / m

b) DOF =1

Equation of motion is mu + ku =0

Lateral stiffness K= 24EI/h3

mu + (24EI/h3) u = 0

Natural Frequency = wn = (k/m)

Lateral stiffness k = 24EI/h3

Natural frequency wn = (24EI/h3) / m

Question -3

Lateral Stiffness K= (6EI/h3)

Natural frequency wn = k/m

wn = (6EI/h3) / m

Natural vibration period Tn = 2 TT / wn

Tn = 2TT / (6EI/h3)

Question-4

a) Effective stiffness = 3EI/h3

b) Effective stiffness = (3EI/h3) + ( 3EI/h3) = 6EI/h3)

c) Effective Stiffness = (3EI/h3) + (3EI/h3) = (6EI/h3)