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

Strength of material and engineering mechanics, Di fferentiate between str...

Di fferentiate between strength of material and engineering mechanics Sol.: Three primary areas of mechanics of solids are statics, dynamics and the strength of materials.

Kinetic or dynamic friction, Kineti c (Dynamic) Friction: When appli...

Kineti c (Dynamic) Friction: When applied force exceeds limiting friction the body starts moving over the other body and the friction of resistance experienced by the body a

Plate clutch pressure-clutch slipping, Plate clutch pressure:  Check plate...

Plate clutch pressure:  Check plate clutch pressure for any step using a straight edge.

Drag link mechanism, why there is a different angular velocity in the two c...

why there is a different angular velocity in the two cranks of a drag link mechanism?

Kinetic inversion, kinetic Inversion In a mechanism, in a kinematic cha...

kinetic Inversion In a mechanism, in a kinematic chain one of the links is fixed. One can get different mechanisms by fixing in different links in a kinematic chain. This techn

What is, what is soundness of casting.

what is soundness of casting.

__, what is magnetostriction?

what is magnetostriction?

Mechanical efficiency, The following data were obtained from a test on a si...

The following data were obtained from a test on a single cylinder, double acting steam engine fitted with a rope brake. Cylinder diameter 200mm Stroke 250mm Speed 5rev/min Effec

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