Section Modulus calculation and optimization
AIM:
To calculate the Section Modulus of the Hood model by uisng Sectioning in it.
Procedure:
Taking out the intersection of the inner panel and outer panel of the model of Hood which is created already and it is shown below.
Section Modulus:
Section modulus is the direction measurement of the strength of the steel. Bending a steel section that has large 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.
The more section modulus, the more member is resistant to bending of the beam. If two beams are made of the same materials and comparing the "section modulus" of two beams, the beam with bigger section modulus will be tougher and more capable to withstand larger loads.
The section modulus(S) is a geometry property of the cross section for desiging beams and flexural members. It does represent anything physically.
Objectives:
Use the section from your Hood design and calculate the section modulus using the formula S=I/Y.
Formola of section modulus:
It may be defined as the ratio of total moment resisted by the section to the strees in the extreme fibre which is equal to yield strees.
Which is equal to yield strees.
Therefore,
S=I/y, where
S= Section modulus (mm^3)
I= Moment of inertia of the section to the strees in the extreme end of the object (mm^4)
y= Distance between the neutral axis and extreme end of the object (mm).
Moment of inertia:
It is defined as the qualntity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. Moment of inertia is known as the angular mass or rotational inertia. The SI unit of moment of inertia is kg m^2.
Moment of inertiaq is usually specified with respect to a choosen axis of rotation. It mainly depends on the distribution of mass around an axis of rotational. MOI various depending on the axis that is choosen.
In General form,
Moment of inertia is expressed as I = m*r^2
where,
m= Sum of the product of the mass.
r= Distance from the axis of the rotation.
Area Moment of Inertia:
The area amount of inertia of a beam cross section area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.
Where,
M= Bending moment
I= Area moment of inertia
E= Young modulus
R= Radius of gyration
Neutral Axis:
When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibre of the beams are subjected to maximum tension.
This picture contains the following scene, Diagram pf a beam on its narrow edge support at both ends. A man is walking on a straight beam. Diagram of a beam resisting on its flat side support at both ends. A man is working on the straight beam and its bending in the middle.
Calculation:
Case 1:
As per the section modulus equation,
S1=I/y
I = Momenet of inertia (value is considered)
I= 73175 mm^4
y = Total distance / 2
= 873.74/2
= 436.87 mm.
S1 = 73175 / 436.87
S1 = 167.12 mm^3
Case 2:
As per the section modulus equation,
S2=I/y
I = Moment of inertia
= 77450 mm^4
y= Total distance / 2
= 874/2
=437 mm.
S2 = 77450/437
= 177.23 mm^3.
Conclusion:
After the calculation of the above 2 cases the section modulus of an S1 and S2 the different is 10.11mm^3.
Then section modulus value of case 2 is higher than case 1.
So, here the difference can be in the moment of inertia and the change in the section modulus can be seen by the change in the design(deoth).