MOMENT OF INERTIA

MOMENT OF INERTIAOBJECTIVE: TO DETERMINE THE FORCES ACTING ON THE CROSS SECTIONAL AREA OF A GIVEN GEOMETRICAL FIGUREINERTIAThe tendency of a body at rest to remain at rest unless an external force is acted upon the body.POTENTIAL ENERGYThe tendency of a moving body in linear motion to remain in that state of motion unless an external force is acted upon the body.KINETIC ENERGYThe internal resistance of a body to resist any change in its state of rest or motion in relation to its mass, density and velocity.REACTIONMOMENT OF INERTIAEngineering mechanics (dynamics and statics)DYNAMICSThe kinetic energy of a rotating body about its axis of rotation.The angular velocity of an object about an axis due to rotation.STATICSThe ability of a body to resist rotation about an axis due to an applied load.

MASS MOMENT OF INERTIA

The kinetic energy of an object that is rotating at an angular velocity about an axis t= mv2

t= kinetic energy v = magnitude of force vector

IRREGULAR OBJECTdmEqual to the distance from the centroidAnd the perpendicular distance to the axis of rotationr

rdt= dm( ) 2

vMASS MOMENT OF INERTIA

The kinetic energy of an object that is rotating at an angular velocity about an axis t= mv2

t= kinetic energy v = magnitude of force vector

IRREGULAR OBJECTdmEqual to the distance from the centroidPerpenicular to the axis of rotationr

rdt= dm( ) 2

vr

STRUCTURAL CONCEPTbdIxx = bd3

1_12I = moment of inertia about the X axisb = breadth of the beamd = depth of the beamMOMENT OF INERTIA about the X axisIxxOTHER GEOMETRICAL FIGURESr4(1/36)db3(1/36)bd3(11/2) r4(1/8) r411 r4Known moment of inertia about the centroidal axisPROBLEM 1b=150 MMd=250 MMIxxFind the moment of inertia 0f the given figureNo.IAdI+Ad2195,312,500Ixx = bd3

1_12= (150)(250) 3

1_12Ixx = 195,312,500 mm4

Composite membersNo.IAdI+Ad21(1/12) bd3 of 1bd of 1d1mm42(1/12) bd3 of 2bd of 2d2mm4TOTAL12d1

d2

d

d

bbna

t

c

Ec = 2EtMOMENT OF INERTIA of an area about the centroidal axis

MOMENT OF INERTIA of an area at a given X & Y axis.PARALLEL AXIS THEOREMXyEXERCISESNext topicX At = X1A1+ X2A2 +XNANFormula in finding the distance from the neutral axis to the distance d1 and d2.Next topicX At = X1A1+ X2A2 +XNANFormula in finding the distance from the neutral axis to the distance d1 and d2.