Section Modulus calculation and optimization

Aim:- To explain & find a Section Modulus of a Hood and Optimize a best section modulus for hood by increasing/ decreasing the cross section area.

SECTION MODULUS:-

A section modulus is a direct measure of the strength of the component. It doesn’t represent anything physically. A component that has a larger section modulus than another will be stronger and capable of supporting greater loads.

A section modulus of a component is can be defined as a ratio of a Moment of Inertia about the bending axis to A distance between the neutral axis and the extreme end of the object.

Section modulus is generally denoted by Z.

Therefore , Z = I / Y_max

where, I = Moment of inertia of a section.

Y_max = Distance of the outer most fibre of the object from the neutral axis.

Area moment of Inertia:

The area moment of inertia of a beams cross sectional area measures the beam ability to resist bending.  The larger the moment of inertia less will be the bend.

Neutral axis: When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibres of the beams are subjected to maximum tension.

A Section modulus can also be defined by using the simple bending theory as,

we know that,  σ / Y= M / I

Therefore, Z = M / σ

i.e, section modulus is also expressed as the ratio of bending moment to the bending stress of a given object within the elastic limit.0

Significance of section modulus

1. Section modulus is the important factor for design of component and flexural member
2. Higher the value of section modulus, higher will be the resistance of member to bending
3. It is required to calculate stresses in component.
4. It is used to calculate strength of the steel structure
5. More the section modulus, it can withstand more load and it is also considered to be more tougher.
6. Cross section Shape

Steps to calculate section modulus :-

• Step 1:-Find location of centroid of given cross section.
• Step 2:-Find moment of inertia about neutral axis (INAINA)
• Step 3:-Find YmaxYmax from neutral axis.
• Step 4:-Find elastic section modulus using the formula provided above.

Calculation of Section Modulus of a Hood :-

Here the sectional modulus of hood design before optimization

Momemt of inertia is calculated by NX-CAD software

 

 

^{Case 2 After Optimization}

The hood inner panel’s curve is offset by 0.5mm outwards and section inertia analysis is done same as case 1 for a closed curve.

 

MOI (max) = 5.224913282e+06 (mm^4)

MOI (min) = 1.489963570e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =904.458mm

Y = 904.458 / 2

= 452.229 mm

Therefore, S = 14899.63570 mm^4/452.229 mm

S= 32.94mm³

^{As we can see by increasing the cross section area the section modulus also increases.}

^{Conclusion :-}

^{Strength of material is directly proportional to the moment of interia, thus increasing the sectional area increase the increases strength of component.}

^{Thus sectional modulus for hood design is calculated and optimized design is also done to increase the section modulus of the hood.}