Section Modulus calculation and optimization

Calculating section modulus and yield moment of designed hood section:

Section modulus is the direct measure of the strength of the steel. Bending a steel section that has a larger section modulus than another will be stronger and harder to bend. Section modulus is a geometric property for a given cross-section used in the design of flexural members. In simple terms, the section modulus is the ratio of bending moment to bending stress for steel. If your steel has a high section modulus it will be harder to bend and can withstand a high moment without having high bending stress.

Yield moment defined as the moment at which the entire cross section has reached its yield stress. This is theoretically the maximum bending moment that the section can resist - when this point is reached a plastic hinge is formed and any load beyond this point will result in theoretically infinite plastic deformation

Section modulus, S = I/y

Where,

                S - Section modulus

 I - Area moment of inertia

 y - Distance between neutral axis and extreme end of the fibre

Yield moment, My = S × σy

where,

σy - Yield strength of material

Case I: Calculating the values for designed section:

Therefore,

 (MOI) I  = 2.764 X 106 mm⁴

                                        (distance)y  = 878.46 /2

                                                          = 439.23 mm

So,

Section modulus,                       S= (2.764 X 10⁶ mm⁴  ) ÷ 439.23 mm

                                                   S= 6292.830 mm³

Yield moment, My = S × σy

where,

                σy - Yield strength of material – i) considering medium carbon Steel AISI 1045
                                                                            i.e. σy= 505 N/ mm²

1. ii) Considering Aluminium Al 6061

                  i.e. σy= 275 N/ mm²

So, yield moment,  

                                     My = 6292.830 x 505 = 3.177 x 10⁶ N-mm ( Steel AISI 1045)

                                     My = 6292.830 x 275 = 1.730 x 10⁶ N-mm ( Al 6061)

Case II : When the distance between outer panel and inner panel is increase by 5mm:

Therefore,

 (MOI) I  = 3.228 X 10⁶ mm⁴

                                        (distance) y = 878.46 /2

                                                          = 439.23 mm

So, Section modulus,                  S= (3.228 X 10⁶ mm⁴  ) ÷ 439.23 mm

                                                    S= 7349.224 mm³

Yield moment, My = S × σy

where,

                σy - Yield strength of material – i) considering medium carbon Steel AISI 1045
                                                                            i.e. σy= 505 N/ mm²

1. ii) Considering Aluminium Al 6061

                  i.e. σy= 275 N/ mm²

So, yield moment, 

                                     My =7349.224  x 505 = 3.711 x 10⁶ N-mm ( Steel AISI 1045)

                                     My = 7349.224 x 275 = 2.021 x 10⁶ N-mm ( Al 6061)

Comparing the values of section modulus of case I and case II it is clear that increasing the distance between the outer panel and inner panel by 5mm, increase the section modulus by 14%, thus increased the strength.

In Case II yield moment of aluminium AL 6061is reduced by 45% compare to steel AISI1045, hence using aluminium as base material for manufacturing of hood panel reduce the overall weight hood and early deformation of section during frontal crash of car.

Conclusion:

• Section modulus for different case is calculated and its found that increase 5mm gap between panel increase the section modulus by 14%.
• CAD design will be passed to CAE team for further kinematic analysis under various condition mimicking the actual crash impact tests.