Section Modulus calculation and optimization

section modulus calculation and optimization:

Aim:

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus.

S=I/Y

Here,

S = Section modulus

I= Moment of Inertia (Unit mm 4)

Y= Distance from Neutral axis to the extreme end (unit mm)

The Unit of a “section modulus” is (mm3)

study of deigned section:

The Intersection of the design was taken and then section Inertia Analysis was done.

I_MAX: 2.384923546X10⁷mm⁴

I_min: 1.682229467x10⁵mm⁴

Total length of 'Y' value was 488.8252mm

So,at neutral axis we need 'Y' value:-Y/2=Y=484.4722/2=242.2361 mm

1)Section modulus(S):-I/Y=2.384923546X10⁷mm⁴/244.412mm

=9.7578X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=1.682229467x10⁵mm⁴/244.412mm

=0.0688x10³mm³(minimum strength).

So the strength of an hood varies from 0.688x10³mm³to 9.7578X10³mm³

Now, one more trail is that, here the inner panel curve offsetting outside by 2mm i.e increasing in cross sectional area,the results shown below.

I obtained the values of

I_MAX: 1.57163545X10⁷mm⁴

I_min: 1.51118420x10⁵mm⁴

Total length of 'Y' value was 488.8252mm

So,at neutral axis we need 'Y' value:-Y/2=488.8252/2=244.412mm

1)Section modulus(S):-I/Y=1.57163545X10⁷mm⁴/244.412mm

=6.4302X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=1.51118420x10⁵mm⁴/244.412mm

=0.0618x10³mm³(minimum strength).

So the strength of an hood varies from 0.0618x10³mm³to 6.4302X10³mm³.

• So, here when comparing both the hoods there is changes in both MAX and MIN strength values,what i came to know that when i increased sectional area by 2mm the value of minimum strength was increased from 0.0618x10³mm³ to 0.0688x10³mm³,Hence with increase in cross sectional area results in increase in strength.
• But, when we seen the value of maximum strength its slightly decreases from 9.7578X10³mm³ to 6.4302X10³mm³,i think this due to design of hood, here what we want to know that when increase in cross sectional area there will be increase in minimum strength or maximum strength or increase in both.
• So Newton's first law also explains that ,if higher the mass , the force required to move the object is also high due to offering more resistance in order to move the object, This resistance we called it as a MOMENT OF INERTIA.
• In case of hood also same principle will work, i.e when increase in cross sectional area by 1mm the minimum load carrying capacity or strength was increased by approximately 8% percentage what we observed from the above discussion.
• The strength of the material also depends upon the composition of material ,thickness and cross sectional area of an object.