Section Modulus calculation and optimization
SECTION MODULUS:-
Section modulus is the Area moment of inertia divided by the maximum distance from the centroid to the outer fiber of a cross section. It measure the strength of any area of an object.,Greater the value of section modulus, greater will be the strength of the section.The section modulus depends upon the moment of inertia which again depends not only on the total area of the cross-section but also on the disposition of the area with respect to neutral axis.
Types of section modules:- 1) Elastic section modulus 2) Plastic section modulus
Elastic Section Modulus
The elastic section modulus is applicable up to the yield point of material.
Section Modulus Formula (S) =I/Y
Where I =Second Moment of Inertia
Y= Distance from the neutral axis to any given fiber
Plastic section modulus
The plastic section modulus is generally used for material in which plastic behavior is observed.The plastic section modulus is the sum of the area of cross section on each side of the plastic natural axis multiplied by the distance from the local centriod of the two ares of the plastic natural axis,
Zp= AcYc+AtYt
Moment of Inertia:-
Inertia is the tendency of the body that resist change. Momnet of inertia is the efficiency of body to resist bending due to load.The more the section modulus the more body resist the load. It depends on density of material, shape and size of body and distribution of mass relative to the axis
Calculation:-
Case 1
MOI(Max): 4.806634884e+06[mm^4]
MOI(Min): 1.400740909e+04[mm^4]
total hood distance= 881.62mm
distance between the end of the hood and neutral axis (Y) = 440.81mm
Section Modulus S= I/Y
= 1.400740909*10^4/440.81
= 14007.40909/440.81
= 31.77mm^3
Case 2
After optimize the section by offsetting the inner panel by 2mm
MOI(Max): 4.804008660+06[mm^4]
MOI(Min): 1.525659735+04[mm^4]
total hood distance= 881.62mm
distance between the end of the hood and neutral axis (Y) = 440.81mm
Section Modulus S= I/Y
= 1.525659735*10^4/440.81
= 15256.599735/440.81
= 34.61mm^3
Conclusion:-
After the modification section modulus has increased,this clearly shows that strength of the material is directly propertional to the moment of inertia if the area increases the section modulus is also increase.