Calculation Of Cross-Section’s Capacity To Resist Rotation Using First Moment Of Area And Moment Of Inertia Theorems

Structures are subjected to many forces, some are natural others are non-natural. Some causes the structure to bend, while others causes the structure to rotate, be it angular bending. It is an engineer’s responsibility to determine the deflections of those structures and to also determine the structures capacity to resist bending or rotation, even before the structure is built. it is therefore necessary to understand the theory associated with the deflection of structures that are subjected to bending and rotation, so that we can be able to prevent or reduce the deflection that might lead to structure failure.

Morh discovered the Moment-Area Method. It is through this method that we are now able to determine the deflections of the structure and calculate the cross-section’s capacity to resist rotation. This consists of two theorems, namely: the first moment of area and the second moment of area.

Discussion

A structural analysis research was carried out, about the moment area method and the findings were as follows:

First moment of area

The first moment of area is the measure of the distribution of a beams section area relative to its axis. It is equal to the addition of the areas multiplied by the distance relative to it axis. This method is used to determine the slope rotation and deflections of the beams and frames, and also to determine the angle of rotation at any given point. It is commonly used to find the deflection of the structures that is subjected to bending. it is calculated by summing up all the areas, multiplied by the distance from a particular axis and it is also used to determine the centre of mass of an object (also known as the Centroid) (Mohr’s Theorem).

Moment of inertia

Moment of inertia, also known as the Second Moment of area. The centre of gravity of an object is the point, within the object, in which the force of gravity act. If the object is said to be at rest, it means that it is balanced at any point along the vertical line passing through the centre of gravity. If the object has one line of symmetry, then the centre of gravity lies at any point along that line of symmetry. The moment of inertia is the measure of an objects resistance to change it rotation, it is the capacity of the objects cross section to resist bending. it is measured in m4 or kg. m2. It is calculated using two theorems, namely:

• The perpendicular axis Theorem
• The parallel axis Theorem.

Conclusion

In conclusion, the moment area method enabled me to calculate the centroid of the given shape and to calculate the deflection of the structure. It’s the basic foundation for structural analysis, it assists with the calculation of any structure of any shape made of an material, by using the structures cross-section.