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

Thermodynamics, what are causes of hotness of a body?

what are causes of hotness of a body?

Explain design factors influencing cost of a print project, Problem: (a...

Problem: (a) What is the best paper to use when printing metallic inks? Explain your answer. (b) A multiple page printed document such as a book, brochure or booklet needs f

Flange assembly with bolt elongation measurement, Q. Flange Assembly with B...

Q. Flange Assembly with Bolt Elongation Measurement? Bolt elongation measurement may be used, with COLT engineering approval, at flanges where Hydraulic Bolt Tensioners are imp

Determine the origin of step, Determine the Origin of STEP Considerable...

Determine the Origin of STEP Considerable progress has been made in vector data exchange over the recent past. Initially, some CAD/CAM vendors offered direct translator softwar

Calculate the displacement of a particle, Calculate the displacement of a p...

Calculate the displacement of a particle: The displacement of a particle is given by the equation, x = 10 t 3  - 7 t 2   + 6 t + 2       I.            Calculate its d

Water overflow in the sink, Water flows into the sink shown in figure 5 at ...

Water flows into the sink shown in figure 5 at a flow rate of 8 L/min. If the drain is closed, the water will eventually flow through the overflow drain holes rather than over the

Gasket installation in module site installation, Q. Gasket Installation in ...

Q. Gasket Installation in Module site installation? Gasket will be installed after modules are set. Normally RTJ flanges require mating flanges to be spread with jacks and then

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