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

Determine minimum value of weigh to cause motion, Determine minimum value o...

Determine minimum value of weigh to cause motion: Determine minimum value of weight W required to cause motion of block, which rests on a horizontal plane. The block weighs 3

Find out the modulus of elasticity, Find out the modulus of elasticity: ...

Find out the modulus of elasticity: A unidirectional FRP is produced with fibre volume ratio of 60%. The density of fibre is 1480 kg/m 3 and that of matrix is 1200 kg/m 3 . C

FEED WATER PUMP, #what is the ratio between thirst pr. and discharge pr.? ....

#what is the ratio between thirst pr. and discharge pr.? ..

Theory of machine, In turning moment diagram. why we start to draw curve fr...

In turning moment diagram. why we start to draw curve from o degree?

A circumferential fin rectangular profile is constructed , A circumferentia...

A circumferential fin rectangular profile is constructed of Cu and surrounds a tube having a diameter of 1.25 cm.  The fin length is 6 mm and its thickness is 0.3 mm. The fin is ex

Ductile mid brittle material, Ductile mid brittle material: A mater...

Ductile mid brittle material: A material that can undergo large permanent deformation in tension, that is, it can be drawn into wires is called as ductile. A material which

What is expansion joints, Q. What is Expansion Joints? Expansion joints...

Q. What is Expansion Joints? Expansion joints are used to accommodate thermal growth in piping and pressure vessel applications. The metal bellows, an integral part of an expan

Derive heat transfer and work transfer expression, Derive heat transfer and...

Derive heat transfer and work transfer expression in an non-flow or closed isothermal and polytropic procedure?

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