Question $2$: For the plane $(2$D$)$ frame shown below, evaluate transformation matrix $[$T$]$ and nodal

load vector in the local axis system $\{P_L\}$ of the elements. For the evaluation of $\{P_L\},$ resolve the

member loads point load on element $1,2\mathrm{.}25k\frac{N}{m}$ distributed load on element $3$ where

transformation of distributed load follows same rule as that used for point load$)$ in local axis system.

Use these matrices to evaluate the nodal load vector in the structural$/$global axis system $\{P_i\}$ of the

members. Assemble the element nodal load vectors $\{P_G\}$ and the load acting directly at the nodes to

form the overall nodal load vectors of the structure $\{P\}.$

The nodal displacement vector of the structure is:

$4\mathrm{.}32485\mathrm{.}0120-0\mathrm{.}0119320\mathrm{.}00\mathrm{.}00\mathrm{.}0-$ units are in $mm$ and degree $($convert it to radian before use$).$

From this nodal displacement vector of the whole structure, extract the nodal displacement vector

$\{x_G\}$ of element $1.$ Using transformation matrix $T$ of this element, convert $\{x_G\}$ in terms of nodal

displacement vector of the element in its local axis system $\{x_L\}.$ Evaluate the stiffness matrix of the

element in its local axis system $K_L$ and calculate member end forces and member end moments of

the element due to joint displacements and rotations using $K_L$ and $\{x_L\}.$ Superpose these values

with the values of fixed end forces and moments due to the applied member load of $15kN.$ Use

these values to draw the axial force, shear force and bending moment diagram of this element. All

members of the frame have same material $(E=200$GPa$)$ and same cross$-$section which is a hollow

square section $($external dimension $200mm200mm$ and all walls are $6mm$ thick$).$Question $2$: For the plane $(2$D$)$ frame shown below, evaluate transformation matrix $[$T$]$ and nodal

load vector in the local axis system $\{P_L\}$ of the elements. For the evaluation of $\{P_L\},$ resolve the

member loads point load on element $1,2\mathrm{.}25k\frac{N}{m}$ distributed load on element $3$ where

transformation of distributed load follows same rule as that used for point load$)$ in local axis system.

Use these matrices to evaluate the nodal load vector in the structural$/$global axis system $\{P_G\}$ of the

members. Assemble the element nodal load vectors $\{P_G\}$ and the load acting directly at the nodes to

form the overall nodal load vectors of the structure $\{P\}.$

The nodal displacement vector of the structure is:

$4\mathrm{.}32485\mathrm{.}0120-0\mathrm{.}0119320\mathrm{.}00\mathrm{.}00\mathrm{.}0-$ units are in $mm$ and degree $($convert it to radian before use$).$

From this nodal displacement vector of the whole structure, extract the nodal displacement vector

$\{x_G\}$ of element $1.$ Using transformation matrix $T$ of this element, convert $\{x_G\}$ in terms of nodal

displacement vector of the element in its local axis system $\{x_L\}.$ Evaluate the stiffness matrix of the

element in its local axis system $K_L$ and calculate member end forces and member end moments of

the element due to joint displacements and rotations using $K_L$ and $\{x_L\}.$ Superpose these values

with the values of fixed end forces and moments due to the applied member load of $15kN.$ Use

these values to draw the axial force, shear force and bending moment diagram of this element. All

members of the frame have same material $(E=200$GPa$)$ and same cross$-$section which is a hollow

square section $($external dimension $200mm200mm$ and all walls are $6mm$ thick$).$