Q$2.$ Bar Element

A stepped bar is subjected to two point forces as shown in Fig$\mathrm{.}2.$

The modulus of elasticity, diameter and length for each element are, $E_1=120$GPA,$E_2=180$GPa,$E_3=240$GPa

$d_1=50mm,d_2=40mm,d_3=25mm$

$L_1=600mm,L_2=400mm,L_3=800mm$

Applied forces are,

$F_1=100kN,F_2=60kN$

Determine,

a$)$ Elemental stiffness matrix

b$)$ Global stiffness matrix

c$)$ Nodal displacements

d$)$ Element forces

e$)$ Reaction forces

Note: Node and element numbering are given in Fig$\mathrm{.}2.$

Figure $2.$ Bar Element