SECTION A

1 A Solid Cimular Stad rad 6mm in diameter and 500mm long is rigully fastened to the end of square brass bar 25mm on a side and 400mm long, this geometric noves of the looms be along the same time An axial tensile force of 5tent is applied at each of the. extreme ands Butermine the total elongation of the assembly. For sted, I = 200GPa and for bra, E=900P

Given:

d = 6 mm

a=25 mm

L1= 500 mm,L2= 400 mm, P = 5 kN = 5000 N

$E1_.steel$ = 200 Gpa = 200 x $10^3$ ${N}/{mm^2}$

$E2_.brass$ = 90 Gpa = 90 x $10^3$ ${N}/{mm^2}$

A1 (Area of steel) = $\frac{πd^2}{4}$ = 9 π $mm^2 $

A2 (Area of brass) = $a^2$ = 625$mm^2 $

The total elongation :
$\delta$ = $\frac{PL1}{E1A1}$ + $\frac{PL2}{E2A2}$

= P$\left(\frac{L1}{E1A1} +\frac{L2}{E2A2}\right)$

= 5000$\left(\frac{500}{2 × 10^5 × 9π } +\frac{L2}{9×10^4×625}\right)$

≈ 0.478 mm