Optimization of section modulus of the front hood of a car.

Material of the hood:

Stainless steel AISI 302- cold-rolled, Y = 520 Mpa

Section Modulus:

• Section modulus is an important factor for beam and flexural member design.
• Higher the section modulus, higher will be the resistance to bending.
• It is easier to calculate stresses in beam and an exact measure of strength of steel.
• If two beams are made of same material and comparing the “section modulus” of two beams, the beam with bigger section modulus will be tougher and more capable to withstand larger loads.

It is termed as the ratio of second moment of area and distance from N.A (Neutral axis) to the extreme fiber. Also it is the measure of strength of given member. It is indicated by S.

We know that the bending equation is,

σ / y = M / I (1)

Where,

σ = Bending stress

y = Distance between the neutral axis (where the max stress could cause failure) and the section’s most extreme fiber.

M = Bending moment about the section’s neutral axis (mass moment of inertia)

I = Second moment of area (area moment of inertia)

From equation (1),

σ = (M . y) / I (2)

Section modulus is,

S = I / y (3)

From equation (2) & (3),

σ = M / S (4)

Thus from equation (4) it is shown that, higher the section modulus, higher will be the resistance to bending.

Calculation

Section modulus calculation for the initial hood design

Figure 1: cross-section of initial hood design

From the above analysis, following inertia are obtained

I_max = 7.185*10⁸ mm⁴

I_min = 1.634*10⁶ mm⁴

y = 833.242/2 mm

From equation (3),

S_max = I_max / y = 7.185*10⁸ / 416.621 = 1724589.014 mm³

S_min = I_min / y = 1.634*10⁶ / 416.621 = 3922.03 mm³

Section modulus calculation for the optimized hood design

Section modulus is represented as,

S = I / y

Where,

I is the area moment of inertia. When the area increases, the area moment of inertia also increases. If area moment of inertia increases then the section modulus also increases

From the equation (3), it is shown that the section modulus is increases by increase in the sectional area.

Here the cross-section area is increased by offsetting the outer panel by 3 mm. So the cross-section area gets increased

Figure 2: Cross-section of optimized hood design

From the above analysis, following inertia are obtained

I_max = 9.61*10⁸ mm⁴

I_min = 2.41*10⁶ mm⁴

y = 834.733/2 mm

From equation (3),

S_max = I_max / y = 9.61*10⁸ / 417.3665 = 2302532.67 mm³

S_min = I_min / y = 2.41*10⁶ / 417.3665 = 5774.3 mm³

Table 1: Comparing the Hood design before and after optimization

	Initial Hood			Optimized Hood
	Inertia (mm4)	Y distance (mm)	Section modulus (mm3)	Inertia (mm4)	Y distance (mm)	Section modulus (mm3)
Max	7.185*108	416.621	1724589.014	9.61*108	417.3665	2302532.67
Min	1.634*106	416.621	3922.03	2.41*106	417.3665	5774.3

From the above table, it has been seen that, when the cross-section area increases the section modulus along with that the bending resistance also increases.