Section Modulus calculation and optimization
SECTION MODULUS CALCULATION AND OPTIMIZATION
SECTION MODULUS
Section modulus is a geomentric property for a given cross section used in the design of beams or flexural members or other gemontric properties used in the design included area for the tension or the shear.it does not represent anything physically.
FORMULA FOR THE SECTON MODULUS
It can be defined as the ration of the total moment resisted by the secton to the stress in the extreme fiber which is equal to yeild stress.
which means,
s=i/y
where.,
s= section modulus
i= Moment of inertia
y= Distance between the netural axis and the outer most edge of the component
AREA MOMENT OF INERTIA
Area moment of inertia is said to be the mesure of the flexural stiffness of a beam it is an important property that is used to mesure the resistance offered by a beam to bending or in calculating the beam definition.
the larger the moment of inertia the less the beam will bend.
M= Bending moment
I= Area moment of inertia
E=youngs modulus
R= Radius of gyration
steps to calculate
1.find the location of the center of the given cross section
2.find the moment of inertia
3.find the total length
4. find the section modulus by using the formula provided
CALCULATION
BEFORE OPTIMIZATION
the hood which is already created is imported and the section of inertia is already done we have to make sure that the curve obtained is single and closed curve.
MOI(max)=1.588145454e+07[mm^4]
MOI(min)=1.380764639e+05[mm^4]
as per the equation
s=i/y
I= MOI (min) value is considred
y= total distance/2
y=488.91/2
y=244.455
therefore,
s= 1.380764639e+05[mm^4]/244.455
=564.8338MM^4
AFTER OPTIMIZATION
The hood inner pannels curve is offseted by 3 mm outwards and section of inertia is done as the same as before optimization.
MOI(max)=1.588145454e+07[mm^4]
MOI(min)=1.664562110e+05[mm^4]
as per the equation
s=i/y
I= MOI (min) value is considred
y= total distance/2
y=488.91/2
y=244.455
therefore,
s= 1.664562110e+05[mm^4]/244.455
=680.9278MM^4
conclusion:
by looking at the before optimization and the after optimization in after optimization the moment of inertia and the section modulus is increased by increasing the section area which means the strength of the material is also increased.