E0044 tire conicity & ply steer 17 – moment of area#5 : principal axes, angle, sense - EulSeoggy Ko

The slope tan𝜃 from the reference axis to the principal axis is the value obtained by dividing the y axis component by the z axis component. Therefore, if the sign of 𝜃 is positive, the positive direction of the main axis must pass through the first quadrant, and the direction of 𝜃 is clockwise. Contrary to that, the 𝑌 component and 𝑍 component of tan𝜃 have different signs, so if the sign of 𝜃 is negative, the positive direction of the principal axis must pass through the fourth quadrant, and the direction of the principal axis 𝜃 is counterclockwise. • Steps to find the principal axes and calculate the second moment of area on the principal axis 1. Get the coordinates 2. Find the second moment of area. 3. Find the product moment of area. 4. Calculate the angles to the principal axis. 5. Calculate the second moment of area about principal axis. • Two angles(𝜃𝑝 , 𝜃𝑝 +90°) are calculated for major and minor axis. • The small absolute angle 𝜃𝑝 represents the nearest principal axis within ±45°. • The principal axis with a large second moment of area is called the major principal axis, and the smaller one is called the minor principal axis. • The major and minor principal axis have the maximum and minimum second moment of area respectively that the cross-section can have and the product moment of area equals zero with respect to major and minor axes.