Find out the product of inertia of a rectangular area, Mechanical Engineering

Assignment Help:

Find out the product of inertia of a rectangular area:

Find out the product of inertia of a rectangular area b × d with respect to its sides as illustrated in Figure

Solution

Let sides OA and OB is the reference axes of area for the needed product of inertia.

 ∴ I x,y (0)  = ∫ dA xy

551_Find out the product of inertia of a rectangular area.png

= b2  d 2 /4

If G is the centroid of the area, then I xy (G) = 0 by virtue of symmetry.

On the other hand,

 I x,y (0)  =  I xy (G )  +  A xG  yG

where, obviously

x G        =  b/2

y G        =  d /2

I x y (0)                    =   bd × (b/2) × ( d/2)

= b2  d 2/ 4

Though, product of inertia w. r. t. axes BC and Y is negative as illustrated below.

I x y (B)  = I xy (G )  +  A xG′ yG′

where with respect to B,

xG′ =  b/2 ;  yG′ = ( -  d/2)

∴  I x y (B)  = (bd ) (b/2)(-d/2)= - b2 d 2/4


Related Discussions:- Find out the product of inertia of a rectangular area

The dimension text edit command-autocad, The Dimension Text Edit command is...

The Dimension Text Edit command is used to modify the text position of any single dimension.                                    The command can be used to position the tex

Atomic hydrogen welding, Atomic Hydrogen Welding In this process, an a...

Atomic Hydrogen Welding In this process, an arc is struck between two tungsten electrodes using AC power supply.The Streams of hydrogen gas are passed from orifices around the

What are interconnecting pipe racks, Q. What are Interconnecting pipe racks...

Q. What are Interconnecting pipe racks? Interconnecting pipe racks carry the main process inlet, export and transfer lines and utility distribution lines to and from process an

Chemistry, scale and sludge formation

scale and sludge formation

PUMP, We have a reciprocating compressor operating at 800 rpm. Suction pre...

We have a reciprocating compressor operating at 800 rpm. Suction pressure and discharge pressure are held constant by other systems that have nothing to do with the compressor. W

Connected rod - part of combustion engine, Connecte d Rod: It is att...

Connecte d Rod: It is attached to piston at its small end by means of gudgeon pin. The big end bearing is connected to crank pin. It is made up of forged steel.

What are methods used in rating for time study, a)What are methods used in ...

a)What are methods used in rating for time study. Illustrate them. b) Write down principles of motion economy.

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