Section Modulus calculation and optimization

SECTION MODULUS

Section Modulus is also referred to as the Polar Modulus or the Torsional Sectional Modulus. It is denoted by S.

Section Modulus is the geometric property of the given cross-section of any beam structures. It is the direct measure of the strength of the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus is defined as the ratio of polar moment of inertia to the distance from the neutral axis to the outer fibres.

Were,

S = Section Modulus.

I = Moment of Inertia.

y = Distance Between the Neutral Axis and the Extreme end of the object.

The above formula depicts that – Section Modulus is directly proportional to the Moment of Inertia and Inversely Proportional to the Section Modulus.

• SECTION MODULUS CALCULATION AND OPTIMIZATION OF DESIGNED HOOD

The Section Modulus Calculation and Optimization is done on the Designed Hood.

• The Designed Hood Comprises of Inner Panel and Outer Panel.
• The Outer Panel and Inner Panel forms a closed structure by the process of Hemming, where the Outer Panel having extended Flanges folds over the Inner Panel by the help of Hemming Tool.
• The Section considered for Section Modulus Calculation is shown in below diagram,

The Calculated Moment of Inertia for the selected section in the designed hood are obtained in NX-CAD tool, by using “SECTION INERTIA ANALYSIS” command.

The Results of the Calculated Moment of Inertia for the selected section in designed hood are shown below,

From above Results, the Moment of Inertia Values are,

The Total Value of “Y” at Neutral Axis will be Y/2 = Y_NA

=488.5/2

Y_NA=244.25 mm. (Y_NA – Value of Y at Neutral Axis)

The Section modulus is now calculated for two values: - one with Maximum moment of Inertia and another with Minimum moment of inertia.

• Section Modulus (S) considering Maximum Moment of Inertia,

S₁ = I_MAX/Y_NA

= 8.263191x10⁵ mm⁴ / 244.25 mm

= 3.383 x 10³ mm³

• Section Modulus (S) considering Minimum Moment of Inertia,

S₁ = I_MIN/Y_NA

= 5.998021x10³ mm⁴ / 244.25 mm

= 0.0245 x 10³ mm³

• SECTION-2

The Selection of Section-2 is same as that of Section-1 in the designed car hood, but there is an offset of 1 mm on outward direction provided for the Hood inner panel.

The Results for the Calculated Moment of Inertia for the Section-2 with 1 mm outward offset for hood inner panel is shown below,

From above Results, the Moment of Inertia Values are,

The Total Value of “Y” at Neutral Axis will be Y/2 = Y_NA

=488.5/2

Y_NA=244.25 mm. (Y_NA – Value of Y at Neutral Axis)

The Section modulus for the new section (Section-2) is now calculated for two values: - one with Maximum moment of Inertia and another with Minimum moment of inertia.

• Section Modulus (S) considering Maximum Moment of Inertia,

S₂ = I_MAX/Y_NA

= 8.326561x10⁵ mm⁴ / 244.25 mm

= 3.409 x 10³ mm³

• Section Modulus (S) considering Minimum Moment of Inertia,

S₂ = I_MIN/Y_NA

= 6.074705x10³ mm⁴ / 244.25 mm

= 0.0248 x 10³ mm³

• CONCLUSION

The two Sections (SECTION-1 & SECTION-2) were analysed and the following Results were arrived as shown below,

• The Section-2 has the maximum Section modulus while compared to the section modulus of Section-1.
• The Calculated Section modulus for both – maximum and minimum moment of inertia is more for Section-2 while compared to Section-1.
• The Increase in Section Modulus for Section-2 compared to Section-1, is due to the outward offset of 1 mm provided to the hood inner panel.

Hence, we conclude that with increase in section area, the Section modulus increases and consequently increases the strength of the Hood in terms of providing better resistance to deformation upon acting load.