Section Modulus calculation and optimization

Section Modulus is a geometric property used to calculate the bending stresses in a structural member.

Mathematically,

It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.

It is denoted by Z.

where,

I = Moment of Inertia(m⁴)

y = distance from NA to extreme layer(m)

The unit of section modulus is m³.

Mass moment of inertia also known as rotational inertia is a quantity that is used in measuring a body’s resistance to a change in its rotation direction or the angular momentum. It basically characterizes the acceleration undergone by an object or solid when torque is applied. The mass moment of inertia is usually denoted by the letter I.

If we talk about the relationship, when there is a given moment or torque applied on a body, if the body’s mass moment of inertia is larger its angular acceleration will be lower. Meanwhile, I also affect how a body stores kinetic energy in rotation.

Key Points To Remember

• Mass Moment of Inertia depends on the body’s mass and the location of the mass.
• If the distance of the mass is farther from the rotational axis, the mass moment of inertia will be relatively larger.

Mathematical Equations To Calculate Mass Moment Of Inertia

If we take the point mass the MOI can be represented as;

I = m r²

If we closely analyze this equation, the mass moment of inertia will have units of mass times length squared. However, the mass moment of inertia should not be confused with the area moment of inertia. On the other hand, mass moments of inertia are usually a part of the equations of motion and it relays information on how much inertia there is to rotate the particle around a given axis.

section modulus calculation on the design of the hood

intially created intersection curve using inputs as the inner and outer panel as one input and mid plane as the another input created an intersection curve and closed the intersection curves as the closed curve and applied the fill command and checked the moment of inertia of the hood

.

• calculation of the moment of inertia of design 1

• 

as per the hood design specifications the moment of ineria is

I(min)=8.58*10^4 mm^4

calculation of the distance from the neutral axis

created a point on both the edges of the hood projected a line on both the points and calculated the distance between two lines

overall distance =488.734 mm

as we need the distance from the neutral axis so

y(distance from the neutral axis )=488.734/2=244.367mm

optimization

in order to ckeck the section modulus is good need to verify with the hood by making some optimizations on the inner pannel by adding embosses so created a hood with two additional embosses

calculated the moment of inertia on this surface by appling the fill command

I(min)=8.685*10^4 mm^4

section modulus calculation

Z = I/ymax

section modulus of design 1(z)=8.58*10^4 mm^4/244.367 mm=351.111mm^3

section modulus of design 2(z)=8.685*10^4 mm^4/244.367 mm=355.408mm^3

conclusion

By comparing both the section modulus of the design 2 consits of greater strength 0.89%