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

Trusses, Differentiate between perfect, deficient and redundant trusses

Differentiate between perfect, deficient and redundant trusses

Simply supported beam, Simply Supported Beam: Simply Supported Beam: ...

Simply Supported Beam: Simply Supported Beam: The beam on which both ends are supported, either by point load or hinged or roller support.

Metals, what effects do external factors have on engineering metals

what effects do external factors have on engineering metals

Internal parts of boiler, Internal Parts of boiler: P r essu r e ...

Internal Parts of boiler: P r essu r e Gauge :   For indicating steam pressure W ater Level Indicator : for indicating water level. Steam Stop Valve : Permits fl

Explain selective inventory control, Write short notes on following terms:-...

Write short notes on following terms:- (i) Total quality management (ii) Method study (iii) Selective Inventory Control (iv) Break Even analysis (v) Merits Rating an

Withworth quick return mechanism, its definition, principle, explanation, a...

its definition, principle, explanation, application, and a diagram

Induction pressure welding, Induction Pressure Welding In this process,...

Induction Pressure Welding In this process, the current is induced by high frequency induction process in the job. Due to electrical induction the job is heated. When a suitabl

Molding process, why compression molding process is impractable for thermop...

why compression molding process is impractable for thermoplastics?

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