Section Modulus calculation and optimization
OBJECTIVE:
Use the section of hood design and calculate the section moduus using the formula S=I/Y
S=Section modulus
I=Moment of inertia
Y=Distance between the neutral axis and extreme end of the object.
Create a new section that has improved the section modulus of the previous section.
Consider stainless steel AlSl 302-cold-rolled-y=520MPa
THEORY:
Section Modulus:
It is a geomentric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness.
There are two types of section moduli,the elastic section modulus and the plastic section modulus.
For general design, the Elastic section modulus is used, applying up to the yeild point for most metal and other common material.The elastic section modulus is defined as S=I/Y, Where I is the second moment of area(or area moment of interia, not to be confused with moment of interia)and Y is the distance from the netural axis to any given fibre.
It is also often used to determine the yield moment(My), such that My=S×σy, where σy is the yeild strength of the material which is maximum allowable load in a mechanical component.
The plastic section modulus is used for material where elastic yeilding is acceptable and plastic behavior is assumed to be an acceptable limit.
Procedure:
In the hood design case we use Elastic section modulus. Model preparation as below.
Copied two parts of hood outer panel and inner panel in another nwe part model which is named as section modulus, then create the section geometry of the outer most geometry of hood outer panel and loewr most geomentry of hood inner panel and joined them with lines as we need closed profile to measure the interia, then later using "Measure the interia" option in catia noted the moment of interia 'I' value and then proceeded with the calculation to measure the allowable strength of the section1.
See the below the images and calculation taken from catia model of for your reference.
Section 1:
Calculation for section 1:
lox=2.025e-006m4=2025000mm4(lo×G value from above image)
Y=430.17mm(Measured value from image 1)
S=I/Y=2025000mm4/430.17mm=4707.44mm3
Yield moment My=s×σy,where σy is the yeild strength of the material which is 520 MPa or N/mm2 as mentioned in question.
M=s×σy=4707.44mm×520N/mm2=2447868.8Nmm=2.4e6Nmm.
To increase the strength of the above section, l increased 3mm the distance between the outer panel geometry to inner panel geometry then repeated the above said procedures then we have got much better strength value. see below section 2 calculation part and images.
Section 2:
Calculation for section 2:
lox=2.556e-006m4=2250000mm4(lo×G value from above image)
Y=430.17mm(Measured value from image 1)
S=I/Y=2550000mm4/430.17mm=5927.8mm3
Yield moment My=s×σy,where σy is the yeild strength of the material which is 520 MPa or N/mm2 as mentioned in question.
M=s×σy=5927.8mm3×520N/mm2=3082456Nmm=3.08e6Nmm.
Conclusion:
Thus by increasing the distance between the inner and outer panel of the hood assembly we got the higher value of section modulus hence the strength also increased.