Find out bulk modulus, Mechanical Engineering

Assignment Help:

Find out bulk modulus:

A steel bar of 25 mm diameter was tested on a gauge length of 250 cm in tension and in torsion. A tensile load of 50 kN generated an extension of 0.13 mm and a torque of 200 N-m produced in twist, Find out :

(a) the modulus of elasticity (b) the modulus of rigidity (c) The Poisson's ratio (d) the bulk modulus

Solution

d = 25 mm = 0.025 m

A = (π/4 ) d 2  = 4.9 × 10- 4 m2

J =  (π /32) d 4  = 3.8 × 10- 8 m4

l = 25 cm = 0.25 m

P = 50 kN = 50 × 103 N

Δ l = 0.13 mm = 0.13 × 10- 3 m

T = 200 N-m

θ = 1o = 0.017 radians

Δ l =  Pl  /A E

 0.13 × 10- 3 = (50 × 10 × 0.15)/ (4.9 × 10- 4 × E)

∴          E = 2 × 1011 N/m2 = 2 × 105 N/mm2

                  T/ J = G θ/ l

200 / (3.8 × 10- 8 = (G × 0.017 )/ 0.25

G = 0.77 × 1011 N/m2  = 0.8 × 105 N/mm2

E = 2G (1 + μ)

⇒         2 × 105  =2 × 0.8 × 105 (1 + μ)

∴          μ= 0.25

E = 3K (1 - 2μ)

2 × 105  = 3 × K (1 - 2 × 0.25)

K = 1.33 × 105 N/mm2


Related Discussions:- Find out bulk modulus

Need of a spectrophotometer, Need of a spectrophotometer: The specific...

Need of a spectrophotometer: The specific instructions will differ with other models, but the principles remain. 1. The instrument must have been warm for at least 15 min.

Injection molding, finishing operation of telephone outer body after inject...

finishing operation of telephone outer body after injection molding

Define external broaching - types of broaching, Define External Broaching -...

Define External Broaching - Types of Broaching External broaching is employee for machining a flat surface. The broach is in the form of a small length tool mounted on a slider

Explain the advantages of rack cutter, Explain the Advantages of Rack Cutte...

Explain the Advantages of Rack Cutter? a. A single cutter of any specific pitch can cut gears of any number of teeth having similar pitch. b. The tooth profile produced is m

Eng chemistry, write notes on internal treatement of water

write notes on internal treatement of water

Engine lubrication system , Engine Lubrication System: This system facilit...

Engine Lubrication System: This system facilitates the lubrication of all the engine components, gears and other associated parts.

Parallel foreces, what do you understand by two like and unlike parallel fo...

what do you understand by two like and unlike parallel forces?

Location of safe areas, All equipment that is critical to the plant's safet...

All equipment that is critical to the plant's safety support; should always be located in a Safe Area (e.g. fire pumps, instrument/electrical equipment and an Emergency Assembly Ar

Find out the deflection at mid-span - cantilever beam, Find out the deflect...

Find out the deflection at mid-span - cantilever beam: A double overhanging beam of 12 m length rests on supports symmetrically, 8 m apart. A load of 80 kN acts at one free en

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