Evaluate elongation of wire, Mechanical Engineering

Assignment Help:

Evaluate Elongation of wire:

An aerial copper wire (E =1 x 105 N/mm2) 40 m long is having cross sectional area of 80 mm2 and weighs 0.6 N per meter run. If wire is suspended vertically, calculate

(a) Elongation of wire because of self weight,

(b) Total elongation when a weight of 200 N is attached to the lower end of it, and

(c) Maximum weight which this wire can support at the lower end if limiting value of stress is 65 N/mm2.

Sol.:  (a) Weight of wire W = 0.6 × 40 = 24 N The elongation because of self weight is,

δL =   L2/2 E; where ω  is the specific weight (weight per unit volume)

In the terms of total weight W =       ωAL

δL = WL2/E = 24 × (40 × 103)/2 × 80 × (1 × 105)

= 0.06 mm                                                                               .......ANS

(b) Extension because of weight P attached at lower end,

δL = PL/2E

= 200 × (40 × 103)/80 × (1 × 105)

= 1.0 mm

Total elongation of wire = 0.06 + 1.0 = 1.06 mm

(c) Maximum limiting stress = 65 N/ mm2

Stress because of self weight equals that produced by a load of half its weight applied at the end. That is

Stress because of self weight = (W/2)/A = (24/2)/80 = 0.15 N/ mm2

Remaining stress = 65 - 0.15 = 64.85 N/mm2

Maximum weight that the wire can support = 64.85 × 80 = 5188 N


Related Discussions:- Evaluate elongation of wire

Determine the value of the maximum shear stress, Determine the value of the...

Determine the value of the maximum shear stress: A circular beam of 100 mm diameter is subjected to a shear force of 5 kN. Determine the value of the maximum shear stress & al

Determine the magnitude and nature of the force, A frame PQRSTU is hinged t...

A frame PQRSTU is hinged to a rigid support at P and is simply supported at T. It is loaded as indicated in the figure below. Determine the magnitude and nature of the force in the

Elastomers, define elastomer.explain in details?

define elastomer.explain in details?

Determine the number of cycles - crack propagation, Determine the number of...

Determine the number of cycles - crack propagation: The plate of above Example  contained a crack of 50 mm length in the centre before it was subjected to cyclic stress. Deter

Internal combustion engines, During a test on a Lister engine in a thermal ...

During a test on a Lister engine in a thermal laboratory, following parameters were measured; crank shaft speed=1,750rpm Load on dynamometer=220N Radius of dynamometer=1.5m Fuel co

Evaluate the centroid of an area, Evaluate the centroid of an area: De...

Evaluate the centroid of an area: Determine the centroid of an area shown in Figure (a). Solution This problem may be attempted in two ways as illustrated in Figu

Co2 gas supply-co2 welding, CO 2 Gas Supply The CO 2 shielding gas is...

CO 2 Gas Supply The CO 2 shielding gas is supplied cylinders at high pressure (140 kg / cm 2 ). Therefore pressure regulator and flow meter are connected to reduce the pressu

Determine the permissible shear stress, A helical compression spring is use...

A helical compression spring is used to take the shock. The initial compression of the spring is 30 mm and it is further compressed by 50 mm while absorbing the shock. The spring i

Explain concept of counter bore in radial drilling machine, Explain concept...

Explain concept of Counter Bore and countersink in radial drilling machine Counter Bore :- This operation uses a pilot to guide the cutting action to accommodate the heads

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd