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

Cscc in gas streams, Q. CSCC in Gas Streams? Due to process upset of FW...

Q. CSCC in Gas Streams? Due to process upset of FWKO or Treater, there may be chance of chloride carry over into the gas lines. Depending on the chloride contents of formation

Question, A28) cm diameter pipe carries oil of sp. gr. 0.9 at a velocity of...

A28) cm diameter pipe carries oil of sp. gr. 0.9 at a velocity of 3 m/s . At another section diameter is 20 cm. find the velocity at this section and also mass rate of flow of oil.

How is varignons theorem useful in engineerin mechanics, how is varignons t...

how is varignons theorem useful in engineering mechanics

Energy method, A semi circular frame of flexural rigidity EI is built at A ...

A semi circular frame of flexural rigidity EI is built at A and caries a vertical load W at B. calculate the magnitude of the vertical and horizontal deflection at B and hence the

Define the polyhedra and euler formula, Polyhedra and Euler's Formula T...

Polyhedra and Euler's Formula The b-rep of a polyhedra that are holomorphic to a sphere are topologically valid if they satisfy the following equations : F - E + V - L = 2 (

Files tool and equipment , Files: Files are used to remove excess metal by...

Files: Files are used to remove excess metal by cutting action. These can be classified according to their length, shape, cross-section.

Define the components in the step standard, Define the components in the ST...

Define the components in the STEP standard There are many components in the STEP standard. (i) The first component discusses the purpose of the standard. It contains :  (

Gear torque output, what is the different torque rating of a helical gear o...

what is the different torque rating of a helical gear one direction verses the other

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