Section Modulus calculation and optimization
SECTION MODULUS :
SECTION MODULUS IS NOTHING BUT THE RATIO OF AREA MOMENT OF INERTIA AT THE NEUTRAL AXIS AND THE CENTER OF GRACITY DISTANCE FROM THE NUTRAL AXIS TO THE OUTERMOST OBJECT .
WE HAVE SQUARE SECTION , RECTANGULAR SECTION AND CIRCULAR SECTION
FOR ALL OF THE ABOVE WE HAVE DIFFERENT FORMULA TO FIND THE AREA MOMENT OF INERTIA (I) AND CENTER GRAVITY DISTANCE FROM THE AXIS TO THE OUTERMOST EDGE (Y) .
USUALLY SECTION MODULUS IS DEFINED AS Z , BUT HERE WE ARE TAKING SECTION MODULUS AS S.
S = I/y
Where,
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
SQUARE SECTION :
I= a^4/12 , y = a/2
S = a^3/6
RECTANGULAR SECTION:
I = bd^3/12 , y = d/2
S= bd^2/6
CIRCULAR SECTION:
I = πD^4/64 , y = D/2
S= πD^3/32
BENDING EQUATION = M/I = σ/y = E/R
M- MOMENT OF INERTIA WHICH DEPENDS ON THE MASS AND THE VELOCITY
I - INERTIA WHICH ONLY BELONGS TO THE MASS
σ - BENDING STRESS
y - CG DISTANCE FROM THE AXIS TO THE OUTERMOST EDGE
E- YOUNG'S MODULUS
R- CURVATURE OF THE PARTICULAR BENDING
TO CALCULATE MOMENT OF INERTIA (M) - WE NEED TO USE THE FOLLOWING FORMULA
M = (I/y) * σ
CALCULATED SECTION MODULUS FROM EXISTING HOOD DESIGN CURVES :
DETAILED VIEW OF THE SECTION INERTIA ANALYSIS :
I = 2.897192085e+05 MM^4
y = 876.5191/2 MM
y= 438.25955 MM
S = I/y
S = 661.0676447324422 MM^3
NOW I AM GOING TO INCREASE THE DISTANCE BETWEEN INNER AND OUTER PANEL :
EXISITING THICKNESS : 0.75 AND NOW ADDING 0.5 MM
THEN THE BELOW IT THE RESULT
I = 3.128611758e+05 MM^4
y= 876.5191/2 MM
y= 438.25955 MM
S= I/y
S= 713.8718957750036 MM^3
DETAILED VIEW OF THE SECTON INERTIA ANALYSIS :
THUS THE SECTION MODULUS VALUE GOT INCREASED BY INCREASING THE THICKNESS/ DISTANCE BETWEEN THE INNER AND THE OUTER PANEL . THE AREA MOMENT OF INERTIA IS THE DYNAMIC HERE. THE DIFFERENCE BETWEEN THE INERTIA 1 AND INERTIA 2 IS GIVEN BELOW.
I1 = 2.897192085e+05 MM^4
I2 = 3.128611758e+05 MM^4
I2>I1
SO THAT WE HAVE DIFFERENCE IN THE SECTION MODULUS . THE STRENGHTH OF THE DESIGNED PART'S STRUCTURE IS BASED ON THIS SECTION MODULUS.