Section Modulus calculation and optimization

SECTION MODULUS OF AN HOOD

• 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 • 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, ie 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

Importance:

• It is significant for beam and flexural member design.
• More the section modulus, the more the member is resistant to the bending of the beam.
• It is easier to calculate stresses in the beam and an exact measure of the strength of steel.
• If two beams are made of the same material and comparing the "section modulus" of two beams, the beam with bigger section modulus will be tougher and more capable to withstand larger loads.

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

• Section of hood panel

• Moment of inertia was calucated by using NX-CAD software

MOI(max) = 8.1314e+05 mm^4

MOI(min) = 5.5028e+03 mm^4

Y = 483.2753 mm

Section modulus (S) : I/Y

= 8.1314e+05/483.2753

=1682.5606 mm^3 (max)

Section modulus(S) : I/Y

=5.5028e+03/ 483.2753

=11.3865 mm^3 (min)

Strength of hood varies from 11.3865 mm^3 to 1682.5606 mm^3

Now one more trailis that, here offsetting inner panel curve outside 1mm i,e. increase in the c/s area, as result shown below,

MOI(max) = 8.0844e+05 mm^4

MOI(min) = 5.9386e+03 mm^4

Y = 483.3761 mm

Section modulus (S) : I/Y

= 8.0844e+05/483.3761

=1672.4865 mm^3 (max)

Section modulus(S) : I/Y

=5.9386e+03/ 483.3761

=12.2857 mm^3 (min)

Strength of hood varies from 12.2857 mm^3 to 1672.4865 mm^3

• So, here when comparing both the hoods there is changes in both MAX and MIN strength values,what i came to know that when i increased sectional area by 1mm the value of minimum strength was increased from 11.3865 mm^3 to 12.2857 mm^3 , Hence with increase in cross sectional area results in increase in strength.
• But, when we seen the value of maximum strength its slightly decreases from1682.5606 mm^3 to 1672.4865 mm^3 , 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 have increase in overall mass of an object hence have increase in strength.