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

Stress, what is hoop stress

what is hoop stress

What is vertical spoilers, Q. What is Vertical Spoilers? Vertical Spoil...

Q. What is Vertical Spoilers? Vertical Spoilers - Use a three-start system of short vertical spoilers arranged in a helical pattern on the top third of the vessel. The exposed

Ease of operation-factors in clutch design , Ease of Operation : For highe...

Ease of Operation : For higher power transmissions, the operation of disengaging the clutch must not be tiresome to the driver.

Determine a real root of the equation, Determine a real root of the equatio...

Determine a real root of the equation xlog10 x = 1.2 by regula-falsi method correct to four decimal places.

Concept of absolute thermodynamic temperature scale, (a) Illustrate the con...

(a) Illustrate the concept of absolute thermodynamic temperature scale on the basis of second law. (b) In a Steady flow apparatus , 13.5 KJ of work is done by each kg of fluid.

Properties of system - thermodynamics, Define different types of properties...

Define different types of properties: Sol: For defining any system certain parameters are needed. Properties are the observable characteristics of system, which can be emplo

Maximum permissible stress in belt, Maximum permissible stress in belt: ...

Maximum permissible stress in belt: Q: A belt 100mm wide and 8.0mm thick are transmitting power at belt speed of 160m/minute.  The angle of lap for smaller pulley is 165º an

Final project , Hi ... I have a final project I need to finish it soon abou...

Hi ... I have a final project I need to finish it soon about 3 weeks from now ... to design any machine by the Solidworks program .... please feed me back if you can .. thank you

Cam and followers work, how to do work in cam and follower?anser in hindi t...

how to do work in cam and follower?anser in hindi type

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