Section Modulus calculation and optimization

Section modulas

1. Section modulas is the ratio of total moment resisted by the section to the stress in the extreme fibre.
2. If the section modulas increase the moment of resistance increase and hence its load bearing capacity also.
3. S=I/Y
4. Section modulas gives us idea about how the load given structure can take.

Where;

S= Section modulas

I= Moment of inertia

Y= Distance from neutral axis to any given fibre.

Cross sectional shape:-

Cross-sectional shape	Figure	Equation	Comment
Rectangle			Solid arrow represents neutral axis
doubly symmetric I-section (major axis)			NA indicates neutral axis
doubly symmetric I-section (minor axis)			NA indicates neutral axis
Circle			Solid arrow represents neutral axis
Circular hollow section			Solid arrow represents neutral axis
Rectangular hollow section			NA indicates neutral axis
Diamond			NA indicates neutral axis
C-channel			NA indicates neutral axis

Question:-

Using the section from previous hood design calculation the section modulas and also come up with a new section that has improved the section modulas of previous section and mention what changes made that increased the length.

Case 1 hood design:-

Moment of inertia (MAX)= 4.8427*10^4 MM^4

Moment of inertia (MIN)= 1.2960*10^4 MM^4

Y= 440 MM

Section modulas= MOI (MIN)/Y

= 1.2960*10^4/440

= 29.45 MM^3

Case 2 hood optimised design:-

By adding 0.5 mm offset of hood

Moment of inertia (MAX)= 4.8426*10^4 MM^4

Moment of inertia (MIN)= 1.2959*10^4 MM^4

Y= 440 MM

Section modulas= MOI (MIN)/Y

= 1.2959*10^4/440

= 29.45 MM^3

Case 2 hood optimised design:-

By adding 1.3 mm offset of hood

Moment of inertia (MAX)= 7.098*10^4 MM^4

Moment of inertia (MIN)= 1.9670*10^4 MM^4

Y= 440 MM

Section modulas= MOI (MIN)/Y

= 1.9670*10^4/440

= 44.70 MM^3.

Sectional value increases with increase offset.

Conclusion:-

• By increasing offset value, we can see that sectional value also increase.
• If we increase the gap between inner and outer panel then moment of inertia also increases.
• Moment of inertia also increases by increasing depth of hood.