Section Modulus calculation and optimization

SEC TION MODULUS :

     Section modulus is a direct measure of strength of any  sectional area of an object about an reference axis(neutral axis).

• Strength is nothing but, capable of supporting greater loads, so higher the strength it has a high capable of supporting  greater loads.
• This strength can measured directly from Section modulus formula, and defined by below formula.
• Section modulus represented with a symbol of 'S'.

                                                                                        S=I/Y

                                                                                       where 'I'moment of inertia

                                                                                                 'Y' is the distance from the reference line(neutral axis) to one of the extreme end of an object.

• Moment of inertia is nothing but offering resistance against of moment, bending or twisting, i.e if we applied any external load on the body, how much resistance its offering to tend to deform.
• So, higher the value of moment of inertia , have higher resistance to deform under certain load, hence we can say that moment of inertia directly proportional to the strength of the material , and strength of the material can be calculated with the help of section modulus.
• If we vary the  neutral axis towards positive or negative side the overall strength of the body will decrease , because when nuetral axis line lies on the middle of the section only have higher strength at particular point, so,  here 'Y'  value was inversely proportional to section modulus.

Thats why formula represented as above.

By using the same principle i going to calculate the strength of an hood panel.

ILUSTURATION 1:

M1=2.536e-006m4

M2=8.445e-004m4

LENGTH(Y)=483.493

SECTION MODULUS(S1)=I/Y

S1=8.445*10^8/483.493

S1=1746000

ILUSTRATION 2:

Now, one more trail is that, here the inner panel curve offsetting outside by 1.5mmi.e increasing in cross sectional area,the results shown below.

M1=2.125e-006m4

M2=7.32e-004m4

LENGTH(Y)=438.493

SECTION MODULUS(S2)=I/Y

S2=7.32*10^8/438.493

S2=1669000

 So the strength of an hood varies from 1746000MM TO 1669000MM

SIDE SECTION TEST:

ilustration 1:

M1=7.633e-007m4

M2=1.267e-004m4

LENGTH(Y)=238.086

SECTION MODULUS (S1)=I/Y

S1=1.267*10^8/238.086

S1=532160

ilustration 2:

M1=8.765e-007m4

M2=1.418e-004m4

LENGTH(Y)=238.086

SECTION MODULUS(S2)=I/Y

S2=1.418*10^8/238.086

S2=595584

So the strength of an hood varies from 532160MM TO 595584MM

• So, here when comparing both the hoods there is changes in both MAX and MIN strength values1746000MM TO 1669000MM,what i came to know that when i increased sectional area by 1mm the value of minimum strength was increased from ,Hence with increase in cross sectional area results in increase in strength.
• But, when we seen the value of maximum strength its slightly decreases from532160MM TO 595584MM ,i think this due to design of hood, here what we want to know that when increase in cross sectional area there will be increase in minimum strength or maximum strength or increase in both.
• So Newton's first law also explains that ,if higher the mass , the force required to move the object is also high due to offering more resistance in order to move the object, This resistance we called it as a MOMENT OF INERTIA.
• In case of hood also same principle will work, i.e when increase in cross sectional area by 1mm the minimum load carrying capacity or strength was increased by approximately 8% percentage what we observed from the above discussion.
• The strength of the material also depends upon the composition of material ,thickness and cross sectional area of an object.

CONCLUSION:

The strength of the material is directly proportional to the moment of inertia, hence increase in sectional area there is increase in overall strength of the hood. If The Sectional Area Increases The Moment And Bending Stress Decreases.