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

#title VECTORS, The 70m microwave transmission tower is steadied by three g...

The 70m microwave transmission tower is steadied by three guys cable. Cable AB carries a tension of 12kN. Express the corresponding force on point A as a vector

Define phase, Define Phase. A phase is a quantity of matter that is hom...

Define Phase. A phase is a quantity of matter that is homogeneous during in chemical composition and physical structure. Determine if the matter is all gas, all liquid or all s

Determine the centroidal moment of inertia, Determine the centroidal moment...

Determine the centroidal moment of inertia: Determine the centroidal moment of inertia of a thin flat disc shown in Figure which is having a mass m kg. By using the parallel a

#tTORQUE, HOW TO CALCULATE OUTPUT TORQUE OF HELICAL GEAR BOX

HOW TO CALCULATE OUTPUT TORQUE OF HELICAL GEAR BOX

Find the horizontal hydrostatic force, Question. In the system shown below...

Question. In the system shown below, the force exerted by the free jet issuing from the sharp-edged circular nozzle and impinging on the small circular plate is just su±cient to k

Solids of mechanics, Derive the equation for pure bonding of beam (simply)

Derive the equation for pure bonding of beam (simply)

Equiliubrium, Review questions condition of equilibrium grade 11 unit 7

Review questions condition of equilibrium grade 11 unit 7

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