Use the stiffness method to analyse the structure shown below.

For the beam ABC,$E=2*{10}^8$kPa,$A=,I=1\mathrm{.}2e-4m^4..$

For the truss member $DB,E=200000000$kPaA$=0\mathrm{.}002m^2.$

Also, take $L=2\mathrm{.}4m$ and $=38k\frac{N}{m}$

Calculate the the bending moment at Joint $B$ following the steps below:

Part $1$:

Assemble the global structure stiffness matrix. Note that ABC is infinitely rigid in the axial direction.

Calculate:

a$)K_{11}=$

b$)K_{22}=$

c$)K_{23}=$

d$)K_{44}=$

Part $2$:

Specify the load vector.

Provide your answers with two decimal places.

$P=$

Part $3$:

Calculate the displacements.

Provide your answers with three significant figures: $($For example, if your answer is $0\mathrm{.}00001236$ then insert $1\mathrm{.}24$ e $-5)$

a$)u_1=$

rad

b$)u_2=$

m

c$)u_3=$

rad

d$)u_4=$

rad

Part $4$:

Finally, calculate the absolute value of the moment at joint $B.$

Provide your answer with two decimal places.

$M_B=$

KNm