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

Ideal fluids in motion, In hydrostatic we consider that fluids were at rest...

In hydrostatic we consider that fluids were at rest. Now we relax this consideration but with caution. We will discuss the flow of an real fluid. There are the assumptions about pe

Heavy traffic areas in pumps, Q. Heavy traffic areas in pumps? These ar...

Q. Heavy traffic areas in pumps? These are areas around pumps, filters, control valves, PSV's and other equipment requiring frequent maintenance or servicing. Piping attache

How to calculate coupling factor?, Q. Two coils with self inductances 1H an...

Q. Two coils with self inductances 1H and 4H have a mutual inductance of 1H. The RMS value of current flowing in the two coils is 4A and 1A respectively. Find  the coupling factor

Comparison of disc and drum type brakes drum brake , Comparison of Disc and...

Comparison of Disc and Drum type Brakes Drum Brake Disc Brake Drum brakes have cooling problem because the friction occurs at internal surfaces,

Concept of continum, in concept of continum what is the meaning of upper cu...

in concept of continum what is the meaning of upper cure

The dimension style command-autocad, The Dimension Style Command The Di...

The Dimension Style Command The Dimension Style command can be used to change appearance of dimensions. The best method  to create a new style before you can start creating dim

Principle of superposition, Principle of superposition: Explain the p...

Principle of superposition: Explain the principle of superposition. Sol.: A machine member is subjected to number of forces acting on its outer edges and also at some

Show the limitations of rigid bed models, Q. Show the Limitations of Rigid ...

Q. Show the Limitations of Rigid bed models? Due to vertical exaggeration, model slope automatically becomes steeper than in the prototype, this slope exaggeration being the sa

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