- #1
gladius999
- 60
- 0
Hi guys,
I know the 2nd moment of area about the z axis is defined as the integral of y^2dA, where y is the distance from the centroidal axis and dA is the elemental area.
There is also derived formulas for working out the 2nd moment of area derived from this such as for a rectangle is bd^3/12. When I compare this to calculating the first moment of area which is the integral of ydA, the first moment of area can be caluculated by taking apart the the shape into rectangles and then adding up the moment of areas of each part i.e. a T section can be split into the top rectangle and a bottom rectangle and the respective moment of areas calculated (by their area dA, multiplied by the distance of the shape y, from the centroidal axis), finally sum up to give u the final first moment of area of the whole T section.
I am confused to why when I try to work out the 2nd moment of area by splitting a shape into parts instead of using integration (i.e. bd^3/12) except by squaring the distance y and then multiplying by its respective area, as 2nd moment of area is the integral of y^2dA instead of ydA, why my calculation for the 2nd moment of area is incorrect.
Can someone point to me why this method is incorrect? Thanks
I know the 2nd moment of area about the z axis is defined as the integral of y^2dA, where y is the distance from the centroidal axis and dA is the elemental area.
There is also derived formulas for working out the 2nd moment of area derived from this such as for a rectangle is bd^3/12. When I compare this to calculating the first moment of area which is the integral of ydA, the first moment of area can be caluculated by taking apart the the shape into rectangles and then adding up the moment of areas of each part i.e. a T section can be split into the top rectangle and a bottom rectangle and the respective moment of areas calculated (by their area dA, multiplied by the distance of the shape y, from the centroidal axis), finally sum up to give u the final first moment of area of the whole T section.
I am confused to why when I try to work out the 2nd moment of area by splitting a shape into parts instead of using integration (i.e. bd^3/12) except by squaring the distance y and then multiplying by its respective area, as 2nd moment of area is the integral of y^2dA instead of ydA, why my calculation for the 2nd moment of area is incorrect.
Can someone point to me why this method is incorrect? Thanks