Group $2$

$4b-$A SDOF $($single degree of freedom system$)$ with a stiffness $k={10}^{5}k\frac{N}{m},$ mass

$M=160$ ton, damping ratio $=25\%,$ initially at rest, is subjected to the action of a force

with the following variation along time.

Write de equation that allows the calculation of the displacement of the system at instant $t=8s$

Consider the following structure. The beams are rigid and the columns axially undeformable,

therefore, for dynamic analysis, the system can be modelled as having one degree of freedom,

the horizontal displacement on top. The diagonal bars are cables, that only work under tensile

forces $($this is$,$ the cables don't work simultaneously, only one at a time$).$ The damping factor

of the structural material is $=5\%$

$5-$ If the structure is acted upon by an imposed sinusoidal displacement with maximum

acceleration of $a_{\text{m}\text{a}\text{x}}=2\frac{m}{s^2}$ and angular frequency $=12ra\frac{d}{s},$ calculate the

maximum bending moment on the upper columns $($consider only the steady state response

of the structure$)$

$6-$ If the structure is acted upon by an earthquake to which corresponds the response spectrum

indicated, calculate the maximum force in the cables.

Group $2$

$4$ b $-$ A SDOF $($single degree of freedom system$)$ with a stiffness $k={10}^{5}k\frac{N}{m},$ mass

$M=160$ ton, damping ratio $=25\%,$ initially at rest, is subjected to the action of a force

with the following variation along time.

Write de equation that allows the calculation of the displacement of the system at instant $t=8s$

Consider the following structure. The beams are rigid and the columns axially undeformable,

therefore, for dynamic analysis, the system can be modelled as having one degree of freedom,

the horizontal displacement on top. The diagonal bars are cables, that only work under tensile

forces $($this is$,$ the cables don't work simultaneously, only one at a time$).$ The damping factor

of the structural material is $=5\%$

$5-$ If the structure is acted upon by an imposed sinusoidal displacement with maximum

acceleration of $a_{\text{m}\text{a}\text{x}}=2\frac{m}{s^2}$ and angular frequency $=12ra\frac{d}{s},$ calculate the

maximum bending moment on the upper columns $($consider only the steady state response

of the structure$)$

$6-$ If the structure is acted upon by an earthquake to which corresponds the response spectrum

indicated, calculate the maximum force in the cables.