Section Modulus calculation and optimization

OBJECTIVE:

• To Calculate the section modulus for the previously designed hood and optimized hood.
• To Come up with the new section that has improved section modulus of the previous section.

SECTION MODULUS:

• Section modulus is the geometric property of a given cross-section used in the design of flexural members. Section modulus depends only on the cross-section shape of the beam or structure.
• For symmetric sections, the value of section modulus is the same for both above and below of centroid of the cross-section. An asymmetric section has two values for the top and bottom of the centroid, the maximum section modulus (S_max) and minimum section modulus (S_min).

There are two types of section modulus:

• Elastic section modulus(S).
• Plastic section modulus(Z).

Significance of Section Modulus:

• Section modulus is an important factor for designing beams and flexural members.
• Higher the section modulus, higher will be the resistance to bending.
• Easier to calculate strength and stresses in beams.
• If two beams are made of the same material and the section modulus of two beams are being compared and vice versa, the beam with larger section modulus will be tougher and more capable to withstand larger loads.

We know that stress (σ) in a beam or structure is given by

σ=M⋅yIσ=M⋅yI...................(1)

Where I = Moment of Inertia

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

M = the moment about the neutral axis

Section Modulus is given by

S=IyS=Iy.......................(2)

From equations (1) and (2),

σ=MSσ=MS........................(3)

Thus from equation (3), it can be said that higher the section modulus, higher will be the resistance to bending.

DESIGN 1: Section Modulus of Initial Hood Design

From the above analysis, following minimum and maximum moment of inertia are obtained

I_max = 7289806.34 mm⁴

I_min = 23539.5194 mm⁴

y = 880.23/2 = 440.115 mm

S_max = I_max / y = 7289806.34 / 440.115 = 16563.412 mm³

S_min = I_min / y = 23539.5194 / 440.115 = 53.484 mm³

DESIGN 2: Section Modulus of Optimized Hood design

What changes I made and Why?

Section Modulus can also be represented as

S = Σ m_iA_i² / y where A is the area of the section and M is the mass of the body

From the above equation, it can be observed that the section modulus of the body is directly proportional to the sectional area of the body.

Here the section area is increased by reducing the embossing depth and offsetting the outer panel by 3 mm. This increases the value of section modulus.

From the above analysis, following minimum and maximum moment of inertia are obtained

I_max = 4901199.43 mm⁴

I_min = 15406.5614 mm⁴

y = 440.115 mm

S_max = I_max / y = 4901199.43 / 440.115 =11136.179 mm³

S_min = I_min / y = 15406.5614 / 440.115 = 35.005 mm³

CONCLUSION:

• By comparing the values we can say that section modulus of the optimized hood (#Design 2) is increased by 1 %.
• MOI increases with the increase of section area.
• MOI increases with the increase of section length.
• If we increase the gap between the inner and outer panel of hood eventually section length will increase thus MOI will increase.