Section Modulus calculation and optimization

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 (Smax) and minimum section modulus (Smin).

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 = 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

Pic.1

Pic.2

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

Imax = 4860152.365mm4

Imin = 15218.533mm4

y = 440.354 mm

Smax = Imax / y = 4860152.365/ 440.354 = 11,036.921 mm3

Smin = Imin / y = 15218.533/ 440.354 = 34.559 mm3

DESIGN 2: Section Modulus of Improved section Hood design

Changes made to improve and optimize the Section modulus

Section Modulus can also be represented as

S = Σ miAi2 / 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.

For the improved section, we are going to increased the section area for the given hood by offsetting the inner panel lines by 0.5mm and then again splitting and joining the lines to form a closed section.

Pic.3

Pic.4

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

Imax = 4868649.084 mm4

Imin = 15023.120 mm4

y = 440.354 mm

Smax = Imax / y = 4868649.084 / 440.354 = 11,056.2163 mm3

Smin = Imin / y = 15023.120/ 440.354 = 34.116 mm3

DESIGN 3: Section Modulus of Improved section Hood design

Changes made to improve and optimize the Section modulus

Like the Design 2 , it can be observed that the section modulus of the body is directly proportional to the sectional area of the body.

S = Σ miAi2 / y where A is the area of the section and M is the mass of the body

For the improved section, we are going to increased the section area for the given hood by giving extra embosses to half hood and then again splitting , joining the lines and mirroring to form a closed section.

Pic.5

Pic.6

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

Imax = 4914891.211 mm4

Imin = 14944.516 mm4

y = 440.354 mm

Smax = Imax / y = 4914891.211 / 440.354 = 11,161.227 mm3

Smin = Imin / y = 14944.516/ 440.354 = 33.937 mm3

CONCLUSION:

• By comparing the values we can say that section modulus of the optimized hood of Design 2 and Design 3 were 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. So,it is quite evident that increasing the gap between the inner and outer panel has a significant impact on increasing the section modulus which in turn it's strength also. But it also depends on the designer to choose the best option from the calculation that gives satisfactory results.