Answer to Question #118785 in Civil and Environmental Engineering for Mikan

Question #118785
How do you calculate the 2nd area movement (Iy,Iz) for a segment of a circle with a freely chosen angle? (z-axis is a symmetry axis)
Expert's answer

formula for calculating the area of a segment is as follows;

A = ½ x r^2(ϴ - sin(ϴ)

where r is the radius of the circle and ,ϴ, is the angle in degrees of the sector that contains a segment.

If it's only the A of a segment it's calculated as follows

A = ½ × r^2 × ((π/180) ϴ - sin ϴ)

  • for example if the radius of the segment is 5" and a sector  of pie with a central angle of 60° or π/3 radians we would plug a formula like this : A = ½ x r^2(ϴ - sinϴ)
  • A = ½ x 5^2(π/3 - sin(π/3)
  • A = 0.5 x 25 x 0.18117214
  • A = 2.26465175 square inches

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