Calculation of Stiffness in Structural elements

1.

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

CALCULATIONS:

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

ANSWER:

3:

AIM: 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.

ANSWER:

Lateral stiffness of the cantilever beam Kc= 3EI/Lc^3

Lateral stiffness of the simply supported beam Kb= 48EI/Lb^3

Total stiffness of the beams K= Kc+Kb

Natural frequency (fn)=1/Tn

4.

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

ANSWER:

1. The stiffness of cantilever beams with mass "m" is K=3EI/L^3
2. The stiffness of of the support is K=[(3EI/L^3)+(3EI/L^3)]= 6EI/L^3
3. Expression of effcetive stiffness of figure is K= [(12EI/L^3) +(12EI/L^3)]=24EI/L^3