Section Modulus calculation and optimization
Objective: To calculate the section modulus of the car hood designed by finding the Moment of Inertia using the CATIA V5 and also to optimise the cross section for a required result
Introduction: Section Modulus is a geometric property used in design of flexural members which considers the cross section of the member. It is highly dependant of the shape of the cross section as well as the area of the said section.
There are 2 types of section modulus :
1) Elastic Section Modulus: This is used when the yeild point of the material is considered as the acceptable limit. This is the most commonly used standard whenever a component is designed.
2) Plastic Section Modulus: In this case the elastic yeilding is deemed acceptable and plastic deformation is considered as the limit.
The Elastic Section Modulus is defined as
From This bending moment equation we can calculate the section modulus by below formula
S = I/y where;
I = area moment of inertia
Y = distance from the neutral axis to any given fibre
Usually for calculating the Section Modulus, the most extreme fibre which is the farthest from the neutral axis is considered during the calculations.
The significance of Section Modulus is that it defines the resistance of a body to bending. Higher the value of Section Modulus, the more resistant is the body towards bending.
The procedure for calculating the Section Modulus is as follows:
Calculation:
case -1) Section Modulus of Front Crash Before optimization :
DISTANCE
>Here we are considered the innerpannel section of the to analysis the section inertia analysis after doing the we got the desired results shown in the above image
I (MAX) = 8.143e-04(m^4)
= 8.143*10^8 mm
I (MIN) = 2.374e-06 (m^4)
= 2.374*10^6 mm
As per the section modulus equation,
S = I/Y
I = (max & min) Value is considered
Y = Total distance / 2
Y=442.27 mm
Therefore,
S1(Maximum) = 184.118*10^4 mm. S1(Minimum) = 53.678*10^2 mm.
case -2) Section Modulus of Front Crash after optimization (1.8mm) :
DISTANCE
>Here we are considered an section of inner pannel at the cureved region and by doing the analysis we got the desired results shown below
I (MAX) = 9.239e-04(m^4)
= 9.239*10^8 mm
I (MIN) = 2.766e-06(m^4)
= 2.766*10^6 mm
As per the section modulus equation,
S = I/Y
I = (min & max) Value is considered
Y = Total distance / 2,
Total distance ,Y= 442.27 mm
Therefore,
S2(Maximum)= 208.90*10^2 mm. S2(Minimum)= 62.54*10^2 mm
Calculation:
Section Modulus of Side Crash Before optimization :
DISTANCE
>Here we are considered the innerpannel section of the to analysis the section inertia analysis after doing the we got the desired results shown in the above image
I (MAX) = 1.432e-04(m^4)
= 1.432*10^8 mm
I (MIN) = 8.46*10^-7 (m^4)
= 8.46*10^6 mm
As per the section modulus equation,
S = I/Y
I = (min & max) Value is considered
Y = Total distance / 2
Y=485.278/2
Y=242.639 mm
Therefore,
S1(Maximum) = 590.177*10^3 mm. S1(Minimum) = 3486.67 mm.
case -2) Section Modulus of Side Crash after optimization (1.8mm) :
DISTANCE
>Here we are considered an section of inner pannel at the cureved region and by doing the analysis we got the desired results shown below
I (MAX) = 1.64e-04(m^4)
= 1.64*10^8 mm
I (MIN) = 1.005e-06(m^4)
= 1.005*10^6 mm
As per the section modulus equation,
S = I/Y
I = (min & max) Value is considered
Y = Total distance / 2,
Total distance ,Y= 242.639 mm
Therefore,
S2(Maximum)= 474.95*10^2 mm. S2(Minimum)= 4141.96 mm
Results:
by comparing The results of case 1 & case 2,
We came to the conclusion that the section modulus value of case 1 is higher than the case 2.
If we consider that front and Side Imapct loads will be applied to the Hood , And if the supossably flat then force distribution will not be affective as it will be when we create primary and secondary embosses , Which Results in increasing the section modulus.