Section Modulus calculation and optimization

SECTION MODULUS:

IT IS THE RATIO OF AREA MOMENT OF INERTIA ABOUT THE NEUTRAL AXIS TO THE DISTANCE OF THE OUTERMOST FIBRE FROM THE NEUTRAL AXIS.

Z=I/Y

Z-SECTION MODULUS

I-AREA MOMENT OF INERTIA

Y-DISTANCE OF THE OUTERMOST FIBRE FROM THE NEUTRAL AXIS

NEUTRAL AXIS:THERE WILL BE TENSION or COMPRESSION

AREA MOMENT OF INERTIA:RESIST BENDING OFFERED BY THE CROSS SECTION

I=bd3/12

BENDING EQUATION:

M/I=σ/Y=E/R

M-BENDING MOMENT

σ-STRESS DUE TO BENDING

E-YOUNGS MODULUS

R-CURVATURE OF BEND

WE ARE TAKING FIRST TWO TERMS,

M/I=σ/Y

BENDING MOMENT(M)=I(σ)/Y [Z=I/Y]

M=Z(σ)

THEREFORE M IS DIRECTLY PROPORTIONAL TO AREA MOMENT OF INERTIA (OR) SECTION MODULUS

IN ORDER TO INCREASE RESIST TO BENDING ,AREA MOMENT OF INERTIA SHOULD BE HIGH or SECTION MODULUS SHOULD BE HIGH.

IN THIS HOOD WE HAVE TO CONSIDER THE MIN MOI AS THE VALUE DUE TO SAFTEY FACTOR

CASE 1:

FIRST CREATE A DATUM PLANE AT THE CENTRE OF THE HOOD BY USING %ARC LENGTH AS 50% .THEN TAKE INTERSECTION OF THE HOOD AND DATUM PLANE.CREATE SKETCH AND PROJECT THE INTERSECTION CURVE.SO WE GOT THAT CURVE IN OUR SKETCH.HIDE THAT INTERSECTION CURVE AND USE PROJECTED CURVE.NOW TO MAKE SECTION INTERTIA ANALYSIS WE HAVE TO CLOSE THE GAPS.CLOSE ALL THE GAPS(HERE I USED LINE AND STUDIO SPLINE TO CLOSE THE GAPS).NOW USE SECTION INTERTIA ANALYSIS .

MIN(MOI) I 1=2.60

CASE 2:

USE THE SAME DATUM PLANE.NOW OFFSET THE INNER PANEL CURVE FOR 0.5mm.NOW PROJECT THE INTERSECTION CURVE.SO WE GOT THAT CURVE IN OUR SKETCH.HIDE THAT INTERSECTION CURVE AND USE PROJECTED CURVE.NOW TO MAKE SECTION INTERTIA ANALYSIS WE HAVE TO CLOSE THE GAPS.CLOSE ALL THE GAPS(HERE I USED LINE AND STUDIO SPLINE TO CLOSE THE GAPS).NOW USE SECTION INTERTIA ANALYSIS .

MIN(MOI) I 2=2.64

CASE 3:(ALSO I HAVE CHECKED THE INERTIA FOR 0.4mm OFFSET):

USE THE SAME DATUM PLANE.NOW OFFSET THE INNER PANEL CURVE FOR 0.4mm.NOW PROJECT THE INTERSECTION CURVE.SO WE GOT THAT CURVE IN OUR SKETCH.HIDE THAT INTERSECTION CURVE AND USE PROJECTED CURVE.NOW TO MAKE SECTION INTERTIA ANALYSIS WE HAVE TO CLOSE THE GAPS.CLOSE ALL THE GAPS(HERE I USED LINE AND STUDIO SPLINE TO CLOSE THE GAPS).NOW USE SECTION INTERTIA ANALYSIS .

MIN(MOI) I 3=2.67

FROM THE ABOVE CASES I CONCLUDE THAT AREA MOMENT OF INERTIA IS HIGH IN CASE 3

I 3>I 2>I 1

I3 HAS AREA MOMENT OF INERTIA AS 2.67