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 sand and moulding sands, Q. Explain Sand and moulding sands? Sa...

Q. Explain Sand and moulding sands? Sand according to the amount of clayey matter they contain, the moulding sands are classified as: • Silica sand: Up to 20% clay. •

Mechanical Engineering Careers Incorporating the Outdoors, Are there jobs i...

Are there jobs in the field of Mechanical Engineering that incorporate the outdoors? I am an outdoorsman for one, and a tradesman at heart and am currently a Mechanical engineering

Test, test test teste teste teste tester

test test teste teste teste tester

Calculate the reactive power and current supplied, Question: A series r...

Question: A series resistive inductive load is energised from a 240V (RMS), 50Hz single phase AC supply, such that the load draws 1200W at a power factor of 0.8. a) Calculat

Basic s.i. units and its derived unit - mechanics, Basic S.I. Units and its...

Basic S.I. Units and its derived unit: S.I. stands for "System International Units". There are three quantities in the Standard International Systems as concerned to Mechanics

Explain macroscopic approach - thermodynamics, Explain Macroscopic Approach...

Explain Macroscopic Approach - Thermodynamics 1. In this method a fixed quantity of matter is considered without taking into account the events taking place at molecular level.

Application of cost-volume-profit relationships, Application of Cost-Volume...

Application of Cost-Volume-Profit Relationships: Quality stores open for 10 hours a day. Company is considering decreasing the store hours through one hour. This shall resul

Frictionless pulley, Frictionless pulley: The frictionless pulley A ...

Frictionless pulley: The frictionless pulley A is being supported by two bars AB and AC which are hinged at points B and C to a vertical wall. The flexible cable D

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