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
SHIELDED METAL ARC WELDING (SMAW) It also known as Manual Metal Arc Welding (MMAW). The heat required for welding is generated by the electric arc formed between metallic elect

Determine  forces in members of cantilever truss: Determine  forces  in  members   B C   and  BD   of   cantilever truss  shown  in  the figure in the figure given below.

If Equivalent force F and F acting on rigid body are not in line Sol.: If equivalent force of same magnitude 'F' acting on the rigid body are not in line, then there is no c

Q. Safety considerations for storage tanks? Large storage tanks are potential fire hazards and should be located at a lower elevation than other occupancies to prevent liquids

Thrust diagrams for the beam: Illustrate the shear force, bending moment & thrust diagrams for the beam illustrated in Figure Figure Solution Vertical compo

Forecasting: Forecasts play a vital role in determining material needs that constitute inventories and in establishing production plans. In this unit, you have studied the imp

Physical meaning of gradient of 2 nd order tensor?

Metals and Melting Practices - Ladle, Limestone,Ore,Sinter Ladle : A big bucket utilized as a carrier for molten metal. Limestone : A Blast Furnace raw material that elimi

Q. How can you determine velocity by electromagnetic method? In electromagnetic method, a magnetic field is generated by the electric current flowing through a coil fixed below

Factor of Safety: Factor of safety is number used to determine working stress. It is fixed based on experimental works on material. It accounts all uncertainties like, mate