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

Natural frequency-degree of freedom-conservative system , Natural Frequency...

Natural Frequency: This is the frequency of vibration of a system that is undamped and without external excitation while it is disturbed. Forced Vibration: This is the vibra

Plate shift drum stopper bolt and arm comp, Plate shift drum stopper bolt a...

Plate shift drum stopper bolt and arm comp Shift drum stopper : Ensure that the plate shift drum bolt is tight and in arm shift drum stopper assembly, check stopper arm bolt for to

Repair of surface defects in welds, Repair of surface defects in welds by c...

Repair of surface defects in welds by chipping, grinding and gouging is permitted provided the thickness is not reduced below the minimum required. Removal of defects shall be ver

Explain about the collapsible soils and subsidence, Collapsible Soils and S...

Collapsible Soils and Subsidence There are soils which are quite stable when dry and they show large volume changes on wetting under load. Examples of  these soils are loess (w

Diffrence between external diameter and internal diameter, Diffrence betwee...

Diffrence between external diameter and internal diameter: A compound tube is built by shrinking one tube on another, the ultimate dimension being, 80 mm internal diameter, 16

ISMB 250, WHAT IS LOAD CARRYING CAPACITY ISMB 250 OF 1.2 MTR LENGTH. PL REP...

WHAT IS LOAD CARRYING CAPACITY ISMB 250 OF 1.2 MTR LENGTH. PL REPLY

Describe fire clay and kaolinite binders, Q. Describe Fire clay and Kaolini...

Q. Describe Fire clay and Kaolinite Binders? Fire clay : Fire clay is refractory clay usually found in the coal measures. Kaolinite: Its general composition is al 2 o 3

Road under special conditions, Road under Special Conditions: Roads pa...

Road under Special Conditions: Roads passing through difficult terrain and environmental conditions require special attention in design, construction and maintenance. The foll

Calculate the magnitude and position of the balance mass, The four masses m...

The four masses m1, m2, m3 and m4 having their radii of rotation as 200mm, 250mm, 150mm, 250mm and 300mm are 200kg, 300kg,240kg and 260kg in magnitude respectively. The angles betw

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