Section Modulus calculation and optimization

SECTION MODULUS CALCULATION

Aim:

To find the section modulus of your Hood design and calculate the Section Modulus using the formula

S = I/y,

Were,

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object

Come up with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.

Introduction:

A car hood panel is one of the most important components of the BIW (body in white), it is considered as the closure sheet-metal component. The hood or bonnet is the device that hinged cover over the engine of motor vehicles. It’s can open to allow access to the engine compartment, batteries and etc… for maintenance and repair. The hood also used for better look and attract the people.

Section modulus:

Section modulus is the ratio of bending to the farthest fiber from the natural axis or it is the measure of the strength of beam. Ratio of area moment of inertia to the distance from the natural axis to the point where the bending normal stresses determined.

Section modulus (S) = I/Y

I = moment of inertia of the structure(mm),

Y = Distance between the natural axis and the extreme end of the object(mm).

Area moment of inertia the area moment of inertia of the beams cross section area measure to the beam ability to resist the bending the larger the moment of inertia less will be the bend.

Were,

m = bending moment,

I = area moment of inertia

E = Young’s modulus

R = Radius of gyration.

Natural axis:

when beam is subjected to the pure bending to the top most fibres of the beam are subjected to maximum compression, while the bottom most fibre of the beam is subjected to the maximum tension.

Where yield strength of stainless steel is 520 MPa = 520 N/mm²

Calculation:

CASE 1: Before optimization

In this case we going to measure section modulus of the hood design in previous challenge. In the hood diagram we going to create a inter section plane and cut the plane for cross section diagram. In that diagram we going to measure minimum/maximum of bending stress.

In case,

MOI (max) = 4.896769793e+06 (mm⁴)

MOI (min) = 1.553653622e+04(mm⁴)

As per the section modulus equation,

S = I/Y,

I = MOI (min) value is considered

Y = Total length of the hood / 2

Total length = y/2,

= 876.75 / 2 = 438.38 mm

Therefore, S = 15536.54/ 438.38 = 35.44 mm³

In this case we get a section modulus of 35.44 mm³ and then the second case we increase the area of the inner panel and compare the both section for final design

CASE 2:

In this case we going to measure section modulus of the hood design in previous challenge. In that hood section we going to increase the cross section of the area below the outer panel and Meares the section modulus

MOI (max) = 4.89173629e+06(mm⁴)

MOI (min) = 1.79911310e+04(mm⁴)

As per the section modulus equation,

S = I/Y,

I = MOI (min) value is considered

Y = Total length of the hood / 2

Total length = y/2,

= 876.75 / 2 = 438.38 mm

Therefore, S = 17991.13/ 438.38 = 41.04 mm³

Conclusion:

Hence, the comparison between the two case 1&2, The section modulus of the case 2 higher than the case1.

In those cases, we understood relationship between the cross-section area and moment of inertia. When the section area increases the moment of inertia also increase which means strength and load of the material also increase