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

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

Posted Date: 1/29/2013 1:33:15 AM | Location : United States







Related Discussions:- Find out the product of inertia of a rectangular area, Assignment Help, Ask Question on Find out the product of inertia of a rectangular area, Get Answer, Expert's Help, Find out the product of inertia of a rectangular area Discussions

Write discussion on Find out the product of inertia of a rectangular area
Your posts are moderated
Related Questions
Describe carburetion. What are the basic different air-fuel mixture on which an engine can be operated ? Write a short note on sterling cycle. In an engine working on inlet pres

Define Cutting Parameters - Depth of Cut It is the thickness of metal removed by grinding wheel in one traverse stroke (lengthwise) t=depth of cut  =D 1 -D 2 / 2

Q. Stress analysis reporting? • Stress sketch with all node points, dimensions, pipe schedule, weights of non-standard components, e.g., control valves and actuators, insulatio

(a) Compare otto, Diesel and Dual combustion cycle on the basis of compression ratio, same compression ration and same Heat input and constant maximum pressure and heat supplied.

Determine the maximum bending stresses: A rectangular beam of breadth 100 mm & depth 200 mm is simply supported over a span of 4 m. The beam is loaded with a uniformly distrib


Types of Holons The four major types of holons are: Order holons Product holons Resource holons Staff holons Considering the cooperative aspect of the

If Engine Keeps on Running after Ignition is Switched Off Causes of Problem Remedy Pre-ignition due to very hot spark plug used

Components of power plant &it''s functions

Compute amplitude and frequency of the particle: The displacement of a particle is described by x = 5 + 3 cos 3 t. Determine the position of the particle at t = 3 seconds. Com