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

What is a coated tool, (a) What is a coated tool? What are its advantages? ...

(a) What is a coated tool? What are its advantages? What types of coatings are used in cutting tool. Discuss. (b) Discuss different types of cutting fluids, their properties and

Projection welding, Projection Welding Projection welding is similar to...

Projection Welding Projection welding is similar to spot welding but for the fact that the welding takes place at the projections on the surface of the metals and flat shaped e

MOS., WHY SHEAR STRESS IS NOT MAXIMUM AT THE NEUTRAL AXIS IN TRIANGLE...ITS...

WHY SHEAR STRESS IS NOT MAXIMUM AT THE NEUTRAL AXIS IN TRIANGLE...ITS MAX IN ALL OTHER CASES BUT Y NOT IN TRIANGLE?#

#flow rate in turbochargers, What is the amount of air is supplied to engin...

What is the amount of air is supplied to engine via turbochargers and how their sizes vary from engine to engine ?

Deflection, determine the vertical deflection at end A neglecting shear

determine the vertical deflection at end A neglecting shear

Evaluate the motion of system, Evaluate the motion of system: Q : Blo...

Evaluate the motion of system: Q : Block A and B are connected by a rigid horizontally bar planed at each end are placed on the inclined planes as shown in the figure giv

Determine the value of shunt connected capacitance, An electric heating ele...

An electric heating element is rated at 4.0kW when connected to a single phase 240Vrms, 50 Hz AC supply, and is known to have a power factor of 0.833 lagging. 1. Calculate the c

Age-hardening of aluminium alloys, Age-hardening of Aluminium Alloys I...

Age-hardening of Aluminium Alloys In specific alloys precipitation from a single phase may arise. The precipitate phase might be in form of determine sub-microscopic particles

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