Section Modulus calculation and optimization

Section Modulus calculation and optimization

Objective: - Use the Section from your Hood design and calculate the section modulus using the formula.

Fromula:

S = I/y

S = Section Modulus

I = Moment of Inertia

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

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.

Where,

M=Bending moment

I=Area moment of inerta

E=Youngs modulus

R=Radius of gyration.

Neutral axis:

When a beam is subjected to pure bending the topmost fibres of the beam are subjected to maximum compression while the bottom most fibres of the beams are subjected to maximum tension.

Types :

The section is broadly classified into elastic and plastic section modulus. These are derived from stress strain curve of a material. Both elastic and pastic section modulus is used as a design criteria in structural design.

Elastic section modulus:

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre

Plastic section modulus:

Plastic section modulus. The plastic section modulus, Z x, is used to determine the limit-state of steel beams, defined as the point when the entire cross section has yielded.

Materials used:

Consider Stainless steel AISI 302 – cold-rolled – y = 520 MPa.

Solution: - Section modulus indicates the strength of the material if larger section modulus the stronger material will be.

I took the section of hood that I design, prepared the sketch for section inertia analysis, sketch exacted outside of outer panel and inside of inner panel,, to do the section modulus analysis it required closed profile, so I joined inner and outer panel profile with curve.

Moment of inertia is given as the "Sum of the product of mass" of Each Particle with "square of its distance from the axis of the rotation.

Minimum value is the point at which the failure begins and then the max value is where the component fails.

To improve the moment of inertia we have to inertia we have to increase the gap between the outer and inner panel.

The below Shown image is a modulus of section that I designed.

Existing hood design:

The existing area moment of the inertia of the hood assembly with both outer and inner panel is given with less number of embosses thus both the maximum and minimum moment of inertia is given above.

Result:

Thus the obtained result is as follows:

I_max= 5.16560875e⁺⁰⁰⁴(mm⁴)

I_min=1.924802279e⁺⁰⁰⁴(mm⁴)

A=74.499460771(mm²)

Y=441mm

From the bending equation ,

S=I/Y

S_max=I_max/Y

=(5.00176583e⁺⁰⁰⁶)/(441).

=10995.05mm³.

After changes hood section:

Result:

Thus the obtained result is as follows

I_max=5.81176583e⁺⁰⁰⁶(mm⁴)

I_min=1.56285093e5e⁺⁰⁰⁴(mm⁴)

A=75.33438333(mm²)

Y=441mm

S_max=I_max/Y

=(5.81176583e⁺⁰⁰⁶)/441

=11721.1mm³.

	AREA	SECTION MODULUS
BEFORE	74.499460771	10995.05mm3.
AFTER	75.33438333	11721.1mm3.
% INCREASE	2.4	6.6

Conclusion:

Thus the increase in stiffness of the component can be increased by changing section modulus using change in section area.