Exercise $4$: Lateral loading and Stiffness $($K$)$ of a $2$D frame

For the follow steel $2$D frame system, the beam is supported by the two columns with pins

and the columns are fixed at the foundation level. The follow data are given.

Modulus of Elasticity of the Steel: Es $=200$GPa$=>Es=200\mathrm{.}000$Mpa$=>(Mpa=\frac{N}{m}{m}^2)=>$

$Es=200\mathrm{.}000\mathrm{.}000K\frac{N}{m^2}$

The columns and beam have the same section with Moment of Inertia $($i$)$ in direction of

loading $I=0\mathrm{.}0000225m^4,$

External lateral loading $F=50.KKN,$

$h=3.km,$

$L=4\mathrm{.}0m$

where $k$ the last two numbers of your registration number.

$4\mathrm{.}1.$ Estimate the stiffness of the frame $(Kf$ with the assumption that is consisted by the

summation of the stiffness of the vertical structural elements $(4\%)$

$4\mathrm{.}2.$ Estimate the horizontal displacement $(x)$ of the frame under the lateral loading $($F$)(4\%)$

$4\mathrm{.}3.$ Suggest and sketch three methods for increasing the stiffness of the steel frame. $(4\%)$

$4\mathrm{.}4.$ According to the answer of the previous question, give the term of the stiffness of a

structural system and the parameters influence to that. $(4\%)$

$4\mathrm{.}5.$ The stiffness is one parameter which is involved in the basic principles for the

earthquake resistance design of the structures. Explain in which basic principles has

important role and how we satisfy these principles in the case of $\frac{R}{C}$ building structures and

steel frame structures. $(4\%)$