Find out the moment of inertia of a triangular area, Mechanical Engineering

Find out the Moment of Inertia of a triangular area:

Find out the Moment of Inertia of a triangular area ABC with base b and height d around its base BC. Therefore or otherwise determine the Moment of Inertia around centroidal axis parallel to the base

Solution

Figure illustrates the triangular area ABC with its centroid G, where perpendicular distance from G to BC is = (d/3).

1436_Find out the Moment of Inertia of a triangular area2.jpg

Let a thin strip LM of thickness dy at distance y from the base BC. Letting similar triangles, ALM and ABC,

LM/(d -  y)      =  BC/ d =  b/ d

∴ LM = (b/ d) (d - y)

= b (1 -   (y/d))

∴ Elemental Area dA = b (1 -   (y/d))dy

2447_Find out the Moment of Inertia of a triangular area.png

= bd 3  ((1 /3)-  (1/4 ))=  bd3/12

By using theorem of parallel axes,

1869_Find out the Moment of Inertia of a triangular area1.png

IGX = I BC  -  A  (d/3)2

b d 3  /12 -(bd/2)(d2/9)

Posted Date: 1/29/2013 1:21:42 AM | Location : United States







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

Write discussion on Find out the moment of inertia of a triangular area
Your posts are moderated
Related Questions
Polymerization Whether similar molecules join in long chain is termed as polymerization and resulting outcome is a polymer in a chemical reaction. Each plastic are polymers. T


Pin-jointed steel structure: Find out the forces in the members of the pin-jointed steel structure. Solution Joint D  Suppose f CD and f DE both as tensile forc

(a) What are the different types of clutches used in modern automobiles? With the help of neat and clean diagram describe the functioning of a diaphragmspring clutch. (b) Explai


Determine the carbon content of steel: A hypoeutetoid steel which was cooled slowly from γ-state to room temperature was found to contain 10% eutectoid ferrite. Suppose no cha

Approximate the tension: A copper tube 38 mm external diameter and 35 mm internal diameter is nearly wound with a steel wire of 0.8 mm diameter. Approximate the tension at whi

A truss of 12 m span is loaded as shown in figure below. Determine the forces in the members of the truss by method of sections.

Gated pattern This is an improvement over the simple pattern where the gating and runner system are integral with the pattern. This would eliminate the hand cutting of the runn

Movement of wire at the signal box: The wire working on railway signal is 5mm in diameter and 300m long. If movement at the signal end is to be 25cm, make calculations for mo