Section Modulus calculation and optimization
AIM:-
To calculate the section modulus of the hood design and to increase the section modulus of the hood from the previous calculated value.
SECTION MODULUS:-
Section modulus is used to calculate the bending stress in a structural member. It is a direct measure of a strength of any cross sectional area of an object about a neutral axis. Section modulus depends only on the cross-section shape or cross-section area of the structure.
S= I/Y (`MM^3`/ `M^3`)
Where S is the section modulus
I is the moment of inertia
Y is the distance from the neutral axis to the extreme end of the object.
Example of section modulus-
In Beam A the load will act perpendicular to the b and the length of the d is higher which means the resistance of the beam A is higher.
In Beam B the load will act perpendicular to the b and the length of the d is smaller when compared to the first case (Beam A) which means the resistance of the beam will be low due to the d value is less than the b value.
So from the above comparision Beam A is considered as the Component which is having high resistance when compared to Beam B.
Section modulus is directly proportional to the resistance of the component which will resist the high amount of load acting over it .
In the above comparision the beam is inverted and changed from 180deg(Beam B) to 90deg(Beam A) hence section modulus is improved due to the improvement in area moment of inertia.
To improve the section modulus of a car hood there are many ways but in this challenge we are going to see one of the method:-
Case1:-
By creating the plane in the middle of the hood and with respect to the plane created an intersection curve.
The intersection curve will have some opening lines which we have to close by creating the studio spline with respect to poles to make it a closed sketch. For that created a sketch in the same plane and projected the curves then closed the open curves using studio spline command.
After that the closed sketch of the hood intersection curve is prepared to find the section modulus of the hood model.
The hood is a hollow structure so giving the hollow type with the thickness value of 0.75mm.
In the above image the section inertia analysis is done and we got the value for maximum and minimum moment of inertia for the hood model.
ie
| MOI(max) | 8.97E+07mm4 |
| MOI(min) | 2.89E+05mm4 |
The distance ymax is
| Length from the neutral axis | 443.0977mm |
The formula for secion modulus calculation is:-
S= I/Y
S= Imaxx/Ymaxx
=`8.97E^+07`/443.097`
`S = 202516.20 mm^3`
S= I/Y
S= Imin/Ymaxx
=`2.89E^+05`/443.097`
`S = 6.53E^+02 mm^3`
Case1 with improved Section modulus (strength) by increasing the area :-
In this case the inner panel is offsetted to the distance of 0.5mm and created a sketch with the help of project curves command and joined the curves to form a closed sketch. The offsetting the inner panel is a method to increase the area of the hood , in industry they will concentrate in hood and its inner panel emboss modification and its cutouts to increase the strength of the hood.
| MOI(max) | 8.96E+07mm4 |
| MOI(min) | 2.93E+05mm4 |
| Length from the neutral axis | 443.0977mm |
The formula for secion modulus calculation is:-
S= I/Y
S= Imaxx/Ymaxx
=`8.96E^+07`/443.097`
`S = 202139.89 mm^3`
S= I/Y
S= Imin/Ymaxx
=`2.93E^+05`/443.097`
`S = 6.61E^+02 mm^3`
Case2:-
In this case the hood is intersected in side view with help of the datum plane created in the side view.
With respect to the plane an intersection curve is created.
Created sketch to make a closed sketch of the hood to calculate moment of inertia.
| MOI(max) | 1.55E+07mm4 |
| MOI(min) | 1.12E+05mm4 |
| Length from the neutral axis | 244.8782mm |
The formula for secion modulus calculation is:-
S= I/Y
S= Imaxx/Ymaxx
=`1.55E^+07`/244.8782`
`S = 63325.48 mm^3`
S= Imin/Ymaxx
=`1.12E^+05`/244.8782`
`S= 4.56E^+02 mm^3`
Case 2 with improved section modulus: -
In this case the inner panel is offsetted to the distance of 0.5mm and created a sketch with the help of project curves command and joined the curves to form a closed sketch. The offsetting the inner panel is a method to increase the area of the hood , in industry they will concentrate in hood and its inner panel emboss modification and its cutouts to increase the strength of the hood.
| MOI(max) | 1.55E+07mm4 |
| MOI(min) | 1.51E+05mm4 |
| Length from the neutral axis | 244.8782mm |
The formula for secion modulus calculation is:-
S= I/Y
S= Imaxx/Ymaxx
=`1.55E^+07`/244.8782`
`S = 63136.48 mm^3`
S= Imin/Ymaxx
=`1.51E^+05`/244.8782`
`S = 6.17E^+02 mm^3`
In Both the cases improved with increasing the area moment of inertia which is directily proportional to the section modulus of the component. To increase the area moment of inertia the area of the component has to be increased for that there are more ways to achieve that by adjusting or modifying the size and depth of the emboss in the hood inner panel or to increase the size of the hood. The motto is from design engineers perspective to improve the section modulus of the hood from the previous model as a comparitive.