Challenge

Calculation of Stiffness in Structural elements

DOF=3

k=96/7 EIc/h^3

(a)

DOF= 1

Equation of motion is,

Mu+ku=0

Substitute k=3EI/H^3mu+(3EI/H^3)u=0

Let natural frequency be Wn(omega n),

Wn= root(k/m)

Wn=root((3EI/H^3)/m)

(b)

DOF=1

Equation of motion is,

Mu+ku=0

Substitute k=12EI/H^3+12EI/H^3=24EI/H^3

mu+(24EI/H^3)u=0

Let natural frequency be Wn(omega n),

Wn=root(k/m)

Wn=root((24EI/H^3)/m)

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

Let natural frequency be Wn(omega n). Then,

Wn=root(k/m)=root((6EI/H^3)/m)

Time period, Tn =2π/Wn

Tn=2π/root(6EI/H^3)

a) Effective stiffness is 3EI/H^3.

b)Effective stiffness is 3EI/H^3 + 3EI/H^3 = 6EI/H^3

c)Effective stiffness is 3EI/H^3 + 3EI/H^3 = 6EI/H^3

Ship work like this
in your own course.