Q$.2($a$)$ What do you mean by factor of safety?

$($b$)$ Write short note on maximum shear stress theory and maximum distortion energy

theory,

Q$.3$ Define equivalent twisting moment and equivalent bending moment. State when

these two terms are used in design of shafts.

$($b$)$ A cylindrical shaft made of steel of yield strength $700$ MPa is subjected to static

loads consisting of a bending moment of $10$kN$-$m and a torsional of $30$kN$-$m$.$

Determine the diameters of the shaft using two different theories of failure and

assuming a factor of safety of $2.$

Q$.4$ The force acting on a bolt consists of two components an axial pull of $12$ kN and a

transverse shear force of $6$ kN $.$ The bolt is made of steel having S$\_($y$)=310$N$//$mm$^(2)$ and

factor of safety is $2\mathrm{.}5.$ Determine the diameter of the bolt using maximum shear

stress theory of failure?

Q$\mathrm{.}5)($a$)$ A rectangular steel plate is welded as a cantilever to a vertical columnand supports

a single concentrated load P $,$ as shown in the figure. Determine the weld size if

shear stress in the same is not to exceed $140$ MPa.

$($b$)$ A $200$ xx$150$ xx$10$mm angle is to be welded to a steel plate by fitlet welds as shown in

the figure. If the angle is subjected to a static load of $200$ kN $,$ find the length of

weld at the top and bottom. The allowable shear stress for static loading may be

taken as $75$ MPa $.$

Q$.6($a$)$ Explain any two of the following terms of the spring:

$($i$)$ Free length;

$($ii$)$ Spring index;

$($iii$)$ Solid height;

$($iv$)$ Spring rate.

$($b$)$ A helical compression spring made of eil empered carbon steel, is subjected to a

load which varies from $400$ N to $1000$ N $.$ The spring index is $6$ and the design

factor of safety is $1\mathrm{.}25.$ If the yieldstress in shear is $770$ MPa and endurance stress

in shear is $350$ MPa $.$ Find: i$.$ Size of the spring wire, ii$.$ Diameter of the spring, iii.

Number of turns of the spring, and iv$.$ Free length of the spring. The compression

of the spring at the maximum load is $30$ mm $.$ The modulus of rigidity for the spring

material may be taken a $580$kN$//$mm$^(2).$

$($a$)$ Discuss the different types of brakes giving at least one practical application for

$($b$)$ With the teip of neat sketches, differentiate between single and multi$-$plate

Q$.8($a$)$ Gtassify the rivet heads according to Indian Standard specifications.

$($b$)$ Eind the efficiency of the following riveted joints:

$($ii$)$ having a pitch of $50$ mm

$($ii$)$ Double riveted lap joint of $6$ mm plates $20$ mm diameter rivets having

a pitch of $65$ mm

Assume permissible tensile stress in plate as $120$ MPa $,$ permissible shearing stress

in rivets as $90$ MPa $,$ permissible crushing stress in rivents as $180$ MPa

$($compressive$).$

Q$.9$ A rotating bar made of steel having S$\_($uI$)=620$N$//$mm$^(2)$ is subjected to a completely

reversed bending stress. The corrected endurance limit of the bar is $310$N$//$mm$^(2).$

Calculate the fatigue strength of the bar for a life of $100000$ cycles.