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

Trignometric, what is sin2P ,if angle q is 90 degree.

what is sin2P ,if angle q is 90 degree.

Define what is nose radius, Define What is Nose Radius? The nose radius...

Define What is Nose Radius? The nose radius is provided to increase finish and strength of the cutting tip of the tool. Small radii will produce smooth finish and are used on t

Fluid mechanics, What is differential approach (differential formulation) i...

What is differential approach (differential formulation) in fluid mechanics? What are velocity and acceleration fields, give examples. Find, study and write down the differential f

Single direction pump, Can I have a quote for answers relating to this ques...

Can I have a quote for answers relating to this question (6 and 7) on my paper. Thanks

Difference between upstream and downstream in a refinery, The total process...

The total process of a the refining business begins at the oil field or gas field and runs all the way to the sending of processed hydrocarbon to a final user. Upstream applies

Matlab program of location a point with respect a line, matlab program of l...

matlab program of location a point with respect a line

IDE101, Polygon law of forces

Polygon law of forces

Analysis of trusses, State the assumptions in pin joined trusses?

State the assumptions in pin joined trusses?

Physics, difference brtween parallel and unlike parallel forces

difference brtween parallel and unlike parallel forces

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