Find out the axial moment of inertia, Mechanical Engineering

Find out the axial moment of inertia:

Find out the axial moment of inertia of a rectangular area of base b and height d around centroidal axis GX and the base B1B2.

Solution

With Reference to Figure, where centroidal axis GX divides the area at mid-depth, i.e. d/2.

2295_Find out the axial moment of inertia.png

Figure

For a thin strip, illustrated shaded, of width b and thickness (very small) dy, all of the points on it are at a constant distance y from axis GX,

                                                          ∴ dA = bdy

Letting y as positively upward from centroidal axis GX: for elements below

GX, y shall be treated as negative.

                                                        ∴ ∫   A dy = 0

1152_Find out the axial moment of inertia1.png

                                                                         =bd3 /12

Likewise, referring to y axis through centroid G,

                                                       IGY  =   db3 /12

Moment of inertia around base B1 B2 may be computed either directly or by utilizing parallel axis theorem.

Direct approach is as. Referring to Figure,

I B1 B2   = ∫ dA × ( y′)2

1459_Find out the axial moment of inertia2.png

On the other hand, using theorem of parallel axis, we have

I B1 B2 = IGX  + A ( y1 )2

Where y1  =  d/2 = perpendicular distance between GX and B1B2.

= b d 3/12 + b d (d/2)2           ?

= b d 3/ 3

Posted Date: 1/29/2013 1:18:17 AM | Location : United States







Related Discussions:- Find out the axial moment of inertia, Assignment Help, Ask Question on Find out the axial moment of inertia, Get Answer, Expert's Help, Find out the axial moment of inertia Discussions

Write discussion on Find out the axial moment of inertia
Your posts are moderated
Related Questions
BOILER CLASSIFICATION : (1 )  According to Tube Contents:   Boilers can be water tube or fire tube type. In water tube boilers water flows in tubes and in Fire Tube Boilers h

Military and Civil Aircraft: Military aircraft can be of several types such as : (a) Cargo carriers, with capacity to carry heavy loads, such as trucks and tanks. (b) Fi

Rich Mixture: It generally ranges from approximately 7 : 1 to 13 : 1 proportion of air to fuel by weight. To get a high power rich mixture is required. In fact to start the e

Drynes s Fraction of Steam: Dryness fraction of steam is factor which used to specify the quality of steam. It can be defined as the ratio of weight of dry steam W d s pr

why the pressure will reduce when the velocity increases

Define the Abrasive Jet Cutting Machines 1. Abrasive jet cutting machines which are used to cut sheet materials or to remove materials of work piece from a surface by generatin



Q. What do you mean by Bunds and Dikes ? A bund (or dike) is an embankment or wall of brick, stone, concrete or other impervious material, which surrounds the entire perimeter

Q. Positive Material Identification Testing? Any physical evaluation or a test of a material to confirm that the material which has been or will be placed into service is consi