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
Sweep Representations  The simplest form of sweep is that produced by sweeping a two-dimensional area along an axis perpendicular to its plane. This form of sweep is most usefu

Backup Purge Backup purge gas can also be used to protect the under side of the weld and its adjacent base metal surfaces from oxidation on the time of welding . Uniformity

Ensure all low points on steam mains and equipment have drip trap assembly. High pressure condensate to be taken to flash tanks, provide detail of flash tank. Use minimum 24" (610

Cemented Carbide These are minute pieces along with cutting edges and mechanically jointed or brazed to tool shank. This Carbide tool tips are generated by process of powder m

Define rpm

for an otto cycle, compression ratio=8.5:1,air inlet=15degree celsius and pressure=101.3kpa, maximum cycle temperature= 1800degree celsius, what is temperature after compression,te


Dear Sir, I wish to know the equation for finding the resultant of the axial stress and bending stress for beams. Can you please help me. thanx in advance, Krishna.

what is tooling economics, machine economics and optimization