Question $1$

For the beam shown below, $L=9m.$

$(1)$ Analyse the beam assuming $El$ is constant.

$(2)$ Determine the deformed shape and bending moment diagram of the beam, as well as the

relevant values at the "strategic" points.

Part a$)$ Task $1$:

Which joint$($s$)$ should be locked and unlocked? $($you can choose more than one joint$)$

B

$B$ and $C$

$C$

A and $D$

Part a$)$ Task $2$:

Determine the bending stiffness $($please present with three decimal places$)$:

Flexural stiffness: $k_{AB}=k_{BA}=$

$EI,k_{BC}=k_{CB}=$

$EI,k_{CO}=k_{OC}=$

End rotational stiffness: $S_{BA}=$

$k_{BA}=$

$El,S_{BC}=$

$k_{BC}=$

EI

$k_{CD}=$

El Part a$)$ Task $3$:

Determine the distribution factor $($DF$)($absolute value; please present with four decimal places$)$:

$D{F}_{BA}=$

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

$,D{F}_{CB}=,D{F}_{CD}=$

Determine the Fixed End Moment $($FEM$)($kNm$)($assuming anti$-$clockwise positive; please

present with two decimal places$)$:

$FE{M}_{AB}=$

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

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

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

CEM... $-$

Fill in the table below $($actual values; please DO NOT present the values in traction$)$: Part a$)$ Task $4$:

Determine all support reactions $($fill in with absolute values$)$:

Vertical reaction at $A$:$V_A=,kN$

uarr

Vertical reaction at $B$:$V_B=,kN$

Vertical reaction at $C$:$V_C=,kN$

Vertical reaction at $D$:$V_0=,kN$

What is the local maximum moment between A and $B($absolute value$)?$

What is the local maximum moment between B and C $($absolute value$)?$

What is the local maximum moment between $C$ and $D($absolute value$)?$

kNmPart c$)$ Task $2$:

Bending force diagram of the beam: