Section Modulus calculation and optimization

Calculation of section modulus and optimization of the Hood

Section modulus: Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia) and y is the distance from the neutral axis to any given fibre.

Also, yield moment (My) = S × σy, where σy is the yield strength of the material.

Section modulus calculation of Hood cross-section:

• For calculating the section modulus of the hood, cross-section of the hood is taken by cutting along the middle plane and find the section modulus .

We have, S = I / y

where I - second moment of area (or area moment of inertia)

y - the distance from the neutral axis to any given fibre.

Imin – for the above section = 2.263903077mm^4 mm4

y = L/2

=483.4758/2

=241.7379

So, S 1= Imax/Y

= (2.263903077mm^4)/241.7379

= 9.36511x10^-3 mm^3

Section modulus calculation of Improved Hood cross-section:

• To increase the strength of the hood, it is required to increase the bending moment capacity.
• As Bending moment is directly proportional to section modulus, which is directly proportional Moment of Inertia.
• To increase Bending moment capacity, Moment of inertia has to be increased.
• To increase the Moment of inertia area of the cross-section has to be increased.
• To increase the area of cross-section, the gap between the outer panel and inner panel is increased by providing more offset of 0.3mm between the inner and outer panel as shown in the figure below.
  

• For calculating the section modulus of the hood after making changes .

We have, S = I / y

where I - second moment of area (or area moment of inertia)

y - the distance from the neutral axis to any given fibre.

Imin – for the above section = mm4

y = L/2

=483.4758/2

=241.7379mm

So, S 2= Imax/Y

= (8.858046148mm^4)/241.7379

= 36.64x10^-3 mm^3

Observation:

Section modulus of Hood without any modification = 9.36511x10^-3 mm^3

Section modulus of Hood after modification = 36.64x10^-3 mm^3

Result: Hence, hereby we conclude that the hood with increased depth of 0.3mm has good strength.