Section Modulus calculation and optimization
AIM:- section modulus calculation and optimization of designed car hood.
concept:- section modulus is a geomertic property of a beam, columm or any other strutural member. Its used to measure the strenght and stiffness of the member against bendind and torsion. The section modulus is defined as the ratio of the moment of inertia of the cross section of the member to the distance from the neutral axis of the cross section to the top notch fiber or point of the section. It is denoted by the symbol and has units of lenght cubed(mm^3, cm^3).
the section modulus are two type
1. Elastic section modulus ( Bending modulus); it is calculated based on the elastic properties of material. Itis used to determine the maximum bending stress a structure can withstand before it exceed its elastic limit and experiance permanent defprmation.
2. plastic section modulus : it is calculated based on the plastic deformation. it is used to determine the maximum bending stress a structure can withstand before it reaches its yeild point and undergoes plastic deformation.
mathameticaly, secton modulus Z = I/y ;
where 'I' is the moment of inertia of the shape about the neutral axis and
'y' is the destance from the neutral axis to the most distant point in the section.
there sre some section modulus equation for deffrent type cross sectional shape given below.
CALCULATION FOR SECTION MODULUS OF HOOD
here the moment of inertia was calculated by using NX-softwere obtained values given below
case 1
initial hood cross section design and its moment of inertia
in this hood design, we take minimum moment of inertia(MO Imin) is 7.107363453e+03mm^4
and distance form neutral axis y/2= 486.82/ 2; = 243.41 mm
putting that value in formula z = i/ y;
z = 7.107336*10^3/ 243.41
z= 29.19 mm^3
this is the result of section modulus of our intial hood design.
Now, trial 2 (inner panel curve offseting outside by 2mm )
case 2 : section modulus of optimized hood , we increasess 2mm in cross section in inner panel
MOI min = 7.974578997e+03mm^4
y = 243.41mm
putting the value in formula
Z=I/y
Z =7.97457*10^3/ 243.41
Z= 32.76mm^3
so here we can see that the section modulus is increased by 2mm the minimum load carrying capicity or strenght is also increase
conclusion : the strength of the material is directly proportional to the moment of inertia, hence , increase in cross section area there is have increase in overall mass of an object, hence increase in strenght.
Regards
udaysinghbaghel