Section Modulus calculation and optimization

Report on Section Modulus Calculation and Optimization

Objective:

• To calculate value of section modulus for Hood assembly
• To improvise section modulus of car hood by modification of its dimensions

What is Section Modulus?

• Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.
• For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.
• The elastic section modulus is defined as

S = I / y

Where,

• I = second moment of area (or area moment of inertia - MOI) in mm⁴

and

• y = distance from the neutral axis to the most extreme fibre = Y/2
  • where Y = Total length from one extreme fibre to other extreme fibre in mm

Different formulas for section modulus is here:

Modification in Hood assembly:

• In Section 2, I have change depth of bottom part from 25 to 50 mm in inner panel.
• Also I have done modifications in values of offset by changing it to 10 mm and 25 mm respectively for outside flanges.

Section Inertia Analysis:

Section: 1

MOMENT OF INERTIA (Maximum): 9.114042471 x 10⁷ mm⁴

MOMENT OF INERTIA (Minimum): 2.686443927 x 10⁵ mm⁴

Length Y = 878.2629 mm

At neutral axis, y = Y/2 = 878.2629/2 = 439.131 mm

Section modulus for Maximum MOI :-

S = 9.114042471 x 10⁷ mm⁴ / 439.131 mm = 207.55 x 10³ mm³

Section modulus for Minimum MOI :-

S = 2.686443927 x 10⁵ mm⁴ / 439.131 mm = 0.612 x 10³ mm³

Section: 2

MOMENT OF INERTIA (Maximum): 9.510732177 x 10⁷ mm⁴

MOMENT OF INERTIA (Minimum): 6.295325861 x 10⁵ mm⁴

Length Y = 878.3375 mm

At neutral axis, y = Y/2 = 878.3375/2 = 439.17 mm

Section modulus for Maximum MOI :-

S = 9.510732177 x 10⁷ mm⁴ / 439.17 mm = 216.56 x 10³ mm³

Section modulus for Maximum MOI :-

S = 6.295325861 x 10⁵ mm⁴ / 439.17 mm = 1.433 x 10³ mm³

Observations:

By comparing both Section 1 and Section 2, we can observe below points:

• For Maximum Moment of Inertia, Section modulus value increases from 207.55 x 10³ mm³ to 216.56 x 10³ mm³
• For Minimum Moment of Inertia, Section modulus value increases from 0.612 x 10³ mm³ to 1.433 x 10³ mm³

The reason behind increment in value of section modulus for maximum as well as minimum moment of inertia are changes made in dimensions of Hood Inner Panel and thus, it increases its cross-sectional area.

So, from above results, one can see that there is improvement in section modulus of Car Hood.

Conclusion:

Section Modulus gives value for strength of material, which is directly proportional to the moment of inertia.

So, when there is increase or decrease in sectional area of a part, it changes overall mass of part. As a result, it will increase or decrease in strength.