Section Modulus calculation and optimization

Section Modulus

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.

Z = I/ymax

Mathematically By bending stress equation,

M/I = σmax/ymax

M = σmax × (I/ymax)

M = σmax × Z

Where,

I = Moment of Inertia(m⁴)

y = distance from NA to extreme layer(m)

The unit of section modulus is m³.

 

Types of Section Modulus

There are two types of section modulus:

• Elastic Section Modulus
• Plastic Section Modulus

Elastic Section Modulus

Elastic section modulus is calculated when we are to use the material behavior till the yield point. 

For general design purposes, we use elastic section modulus.

Section modulus - Hood:

 This curve is a result of the intersection of the hood design and a plane. The curves are closed using studio spline. 

Section inertia analysis:

MOI(min), I = 2.7638 e+05 mm4

y = 879.37/2 = 439.685 mm

Section modulus, Z1 = I/y = 2.7638 e+05/439.685 = 628.58 mm3

Design optimization:

The bottom curve is offset by 0.5mm and joined to form a closed curve. Then, section inertia analysis was performed. 

I = 2.8 e+05 mm4

y = 439.685 mm

Section modulus, Z2 = I/y = 2.8 e+05/439.685 = 636.81 mm3

Z1>Z2

Therefore, by optimizing the design the section modulus has been increased.