Section Modulus calculation and optimization

REPORT FOR SECTION MODULUS CALCULATION AND OPTIMIZATION

Aim

To find the section modulus of the hood and optimization to improve the overall section modulus. there is

Section modulus:-

The section modulus (S) is the geometric property of the cross-section used for designing beams and flexural members. It does not represent anything physically.

The formula of Section Modulus:

It may be defined as the ratio of the total moment resisted by the section to the stress in the extreme fiber which is equal to yield stress.

S=I / Ymax

Where,

S = Section modulus (mm^3)
I = Moment of inertia (mm^4)
Y = Distance between neutral axes and outermost fiber (mm)

Moment of inertia:

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body, is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for the desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

Sectional Modulus Calculation and Optimization:

Case 1:

Here is the sectional modulus of hood design before optimization of Front Impact:

Length: Distance between neutral axes and outermost fiber (mm)

Distance between the outermost end to another outermost end (d) = 878.528mm

Case 2: Optimized design

In order to increase the sectional modulus, the cross-sectional area has to be increased. So here is the optimized design:-

Table of Section Modulus Calculation of Front Crash:

	Moment of Inertia (I) before Optimization in moment	Moment of Inertia (I) After Optimizationdistance	Distance (Y=d/2)section	Section Modulus before optimization (S1=I/Y)section	Section Modulus after optimization (S2=I/Y) in mm
Minimum	M1 = 1.759*10^6	M1 = 2.032*10^6	878.528/2 = 439.26	4004.46205	4625.961845
Maximum	M2 = 6.124*10^8	M2 = 6.978*10^8	439.26	1394162.91	1588580.795

Results:

• As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Which is the moment of inertia directly proportional to the strength of the material.

Side Impact:

Case 1:

Here is the sectional modulus of hood design before optimization of Side Impact:

Length: Distance between neutral axes and outermost fiber (mm)

Distance between the outermost end to another outermost end (d) = 485.34mm

Case 2: Optimized design

In order to increase the sectional modulus, cross-sectionalonal area has to be increased. So here is the optimized design:-

Table of Section Modulus Calculation of Side Crash:

	Moment of Inertia (I) before Optimization in moment	Moment of Inertia (I) After Optimizationdistance	Distance (Y=d/2) in mm	Section Modulus before optimization (S1=I/Y) in mm	Section Modulus after optimization (S2=I/Y) in mm
Minimum	M1 = 7.3*10^5	M1 = 8.429*10^5	485.341/2 =242.6705	3008.200437	3473.441299
Maximum	M2 = 1.205*10^8	M2 = 1.362*10^8	242.6705	496559.1132	561256.0267

Results:

• As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Whis ich the moment of inertia is directly proportional to the strength of the material.

Conclusion:

• Hence when comparing case 1 & case 2, Section Modulus the Hood of the car was calculated and optimized section modulus with some changes or optimization and found some better results.
• Which Concludes if front and Side Impact loads will be applied to the Hood, if it is flat then force will not be distributed properly and the hood is weak compared to the embossed one , so that we create primary and secondary embosses, Which Results in increasing the section modulus.As we increase the section modulus increase which means strength increases and stress decreased.