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

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

a

q3

q4

degree of freedom= 1

equation of motion

ma +cv+ku=p(t)

here no damping and external force

so c= 0 t= 0

ma+ku=0

here leg is hinged so

k= 3EI/L3

ma+(3EI/L3) .U= P(T)

NATUREL FREQUENCY fn

as fn= 1/Tn

Tn= 2