Section Modulus calculation and optimization

OBJECTIVE:

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

What is 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).

Importance of Section Modulus:

• Section modulus is an important factor in designing beams and flexural members.
• The higher the section modulus, the higher will be the resistance to bending.
• Easier to calculate the 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 a 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 the higher the section modulus, the higher will be the resistance to bending.

# DESIGN 1: Section Modulus of Original Hood Design

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

I_max = 5147652 mm⁴

I_min = 16851.33689 mm⁴

y = 450 mm

S_max = I_max / y = 5147652/450= 11,439.2266 mm³

S_min = I_min / y = 16851.33689/450= 37.44741 mm³

# DESIGN 2: Section Modulus of Hood design after 8mm offset of the inner panel to the outer panel.

What changes have 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 I increase the depth of the inner panel and its emboss about 8 mm.

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

I_max = 5167242.08 mm⁴

I_min = 18560.07844 mm⁴

y = 450 mm

S_max = I_max / y = 5167242.08/450= 11,482.76017 mm³

S_min = I_min / y = 18560.07844/450= 41.2446195 mm³

# CONCLUSION:

• By comparing the values we can say that section modulus of the improved hood (#Design 2) is increased.
• 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.