Question $1$

For the frame shown below, $q=1k\frac{N}{m}$ and $L=9m.$

$(1)$ Analyse the trame assuming thean $=21$ and $I_{\text{c}\text{o}\text{u}\text{m}}=1.$

$(2)$ Determine the deformed shape and BMD of the frame. In BMD$,$ determine $($a$)$ relevant values :

the 'strategic' points; $($b$)$ magnihude$($s$)$ and location$($s$)$ of the local maximum or minimum moment$|$

and $($c$)$ location of contraflexural point$($s$).($Hint make use of the principie of supepposition.$)$

Part a$)$ Task $1$:

Symmetric frame:

The boundary condtion at $H$ is:

Free enct

Hinge

siding roter

Determine the bending stftress:

Flexural stimess: $K_{\text{e}\text{x}\text{t}}=$

El$,K_{aE}=$

El$,K_{0e}=$

End rotational atithess: $S_{94}"$

$k_{64}=$

E$.$

Part a$)$ Task $2$:

Symmetric frame:

Determine the distribution factor $($DF$)($absolute value: beteste prestnt win foor debimes placest:

$D{F}_{BS}=,D{F}_{BC}=,D{F}_{BI}=$

Determine the Ftred End Moment $($FEM$)($kNm$)($assuming antloclockwise positive: please

present with two decimal piaces$)$

$FE{M}_{AB}=,FE{M}_{GA}=,FE{M}_{BE}=,,FE{M}_{5H}=,$FEM $=$

$FE{M}_{Fs}=$

$El,S_{et}=,K_{et}=,E1,s_{eH}=$

$Ke{n}^{?}=$

EI

EI Part a$)$ Task $3$:

Symmetric frame:

FII in the table below $($actual values: plesse DO NOT present the values in fraction$)$: Part a$)$ Task $4$:

Antivymmetric trame.

The boundary concison at $H$ is:

$0$ Fiee end

Hinge

Slsing roller

Deiermine the bending stithess:

Flenurar stthesa: Kus $=$

El$,$ Kec:

El$,$ Kos$=$

El

End rotational stheew: Sa$4,"$

$k_{6a}=$

EI$,$ See $=$

EI

$K_{ar}=$

El

Part a$)$ Task $5$:

Antisymmetric frame:

Determine the distribution tactor $($DF$)($absolyte valutipletse pretent weh Soor ghalmar plictt$)$:

$D{F}_{Aa}=$

DFe $m$

$,O{F}_{B-}=$

Determine the Flxed thd Moment $($FEM$)($KNm$)($assuming antboplockwist posither:plemt

present with tho decimel placestc

$FE{M}_N=$

$,FC{M}_{DA}=$

$,FE{M}_{LC}=$

$E$

kec$=$

$FE{M}_{CD}=$

Part a$)$ Task $6$:

Antisymmetric frame:

Fill in the table below $($estual walues: pleese DO NOT poesent me walues in cretion$)$: Member end moment at $E$:$M_{Fn}=$

kNm

$1$

$\frac{N}{A}$

Member end moment at $C$:$M_n=$

$kNm$

$-$

$-$

$\frac{N}{A}.$

Member end moment at C: M $M_{CD}=$Member end moment at $D$:$M_{DC}=,kNm$

$-$

$0-$

O N$/$A

$-$

$0$

$-$

N$/$A

Member end moment at $C$:$M_{CF}=$

Part b$)$ Task $1$:

O N$/$A

$kNm$

Member end moment at $C$:$M_{CF}=,kNm$

Member end moment at $F$:$M_{FC}=,kNm$

$0{}^1$

For column BE$,$ the location of the contraflexure point $($CP$)$ from E:

For column CF$,$ the location of the contrafexure point $($CP$)$ from F;

Part b$)$ Task $2$:

Bending moment dagram of the frame: $+$