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

Explain the height adjustment and extension of augers, Normal 0 ...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Replace the two parallel forces by single force, Replace the two parallel f...

Replace the two parallel forces by single force: Replace the two parallel forces acting on the control lever by a single equivalent force R.   Sol.: Since single equ

Calculate the magnitude and position of the balance mass, The four masses m...

The four masses m1, m2, m3 and m4 having their radii of rotation as 200mm, 250mm, 150mm, 250mm and 300mm are 200kg, 300kg,240kg and 260kg in magnitude respectively. The angles betw

Evaluate young modulus of elasticity - ultimate stress, Evaluate Young modu...

Evaluate Young modulus of elasticity - Ultimate stress: Q:   The following observations were made during tensile test on mild steel specimen 40 mm in diameter and 200 mm long

Estimate what fraction of heat loss by the fin, A tube assembly constructed...

A tube assembly constructed of Cu with an inside diameter of 1.25 cm, wall thickness of 0.8 mm and circumferential fins around the periphery. The fins have thickness of 3 mm, and a

Explain commutator- dc generator, Commutator The function of a commutat...

Commutator The function of a commutator is to change alternating current induced in the armature into unidirectional current. The commutator is of cylindrical shape and is made

What do you mean by contractility, Q. What do you mean by Contractility? ...

Q. What do you mean by Contractility? Heart being a muscular pump the ability to eject blood depends on the ability to contract. Another factor is the resistance in the vascula

Applied chemistry, hardness of bore well water is less than sea water .just...

hardness of bore well water is less than sea water .justif

Diesel cycle - thermodynamics, Diesel Cycle - Thermodynamics: Diesel c...

Diesel Cycle - Thermodynamics: Diesel cycle is also called as the constant pressure cycle as all addition of heat takes place at constant pressure. The cycle of operation is s

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