Section Modulus calculation and optimization

BRIEF EXPLANATION ABOUT SECTION MODULUS, ALSO CALCULATE AND STUDY USING THE HOOD DESIGN AS An INPUT

Before we studied about the section modulus first, we known about bending stress

BENDING STRESS

Bending stress is the normal stress that an object withstands when it is subjected to external load at any cross-section.

The bending stress is also defined as the ratio between the bending moment and the section modulus of the section.

σ = M/S

where M is a bending moment of the section

S is a section modulus of section

Based on the above relation the section modulus and bending stress are inversely proportional

σ ∝ 1/S

Based on the condition section modulus increases the bending stress decreases so bending stress decreases Strength increases

For our study first we know section modulus

SECTION MODULUS

Section Modulus is a geometric property used to calculate the bending stresses in a structural member. 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.

Z = I/ymax

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 behaviour till the yield point.

Plastic Section Modulus

The plastic section modulus is used for materials where the elastic yield is acceptable and the plastic behaviour is considered to be an acceptable range.

It depends on the location of the plastic neutral axis. The PNA is the axis that bisects the cross-section such that the compressive force from the region in compression is equal to the tension force from the region under tension

So now we calculate a section modulus using a hood design

Procedure

• Initially we take previous hood as a reference, did not change any data, directly proceed to calculate moment of inertia using Siemens NX cad and also calculate the initial Section modulus

To calculate the section modulus

Moment of inertia is 1.640299574*10^4

Distance from neutral axis is 905.1/2

For MOI is minimum, section modulus is

Z = I/ymax

=Moment of inertia * distance of extreme layer to neutral axis

= (1.640299574*10^4) mm⁴ /452.55mm

= (0.03627*10^3) mm³

• For the next step we do offset to 0.5 mm from the inner panel sketch taken as the reference sketch then do section inertia analysis

For minimum MOI

Z = I/ymax

=Moment of inertia * distance of extreme layer to neutral axis

= (1.65849296*E^4) mm⁴ /452.55mm

= (0.036656*10^3) mm³

Conclusion

So finally concluded the strength of the material is based on the bending stress, the bending stress is inversely proportional to the moment of inertia. Based on study the Sectional area increases the Moment of inertia increases, bending stress decreases and finally Strength increases

PARAMETER	INCREASE OR DECREASE
SECTION AREA↑,	INCREASES
MOI ↑	INCREASES
BENDING STRESS↓	DECREASES
STRENGTH ↑	INCREASES