8/17/2019 formulas of Area Moment of Inertia

1/12

http://www.efunda.com/formulae/formula_index.cfm

Square I-Beam

Cx Cy Area

Moment of Inertia

about the  x c axis

Ixc

Moment of Inertia

about the y c axis

Iyc

Polar Moment of Inertia

about the  z c axis

= Ixc + Iyc

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the y c axis

kyc

Radius of Gyration

about the  z c axis

rc

rc2  = kxc

2 +ky2

!apered I-Beam

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfm

8/17/2019 formulas of Area Moment of Inertia

2/12

Cx Cy Area

Moment of Inertia

about the  x c axis

Ixc

Moment of Inertia

about the y c axis

Iyc

Polar Moment of Inertia

about the  z c axis

"c

= Ixc + Iyc

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the y c axis

kyc

Radius of Gyration

about the  z c axis

rc

rc2

  = kxc2

 +kyc2

#ne$en I Beam

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=z

8/17/2019 formulas of Area Moment of Inertia

3/12

Cy Area

Moment of Inertia

about the  x c axis

Ixc

Polar Moment of Inertia

about the  z c axis

"c

= Ixc+Iyc

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the  z c axis

rc

r2  = kx

2 +ky2

%ectan&ular S Beam

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=z

8/17/2019 formulas of Area Moment of Inertia

4/12

Cx Cy Area

Moment of Inertia

about the  x c axis

Ixc

Moment of Inertia

about the y c axis

Iyc

Polar Moment of Inertia

about the  z c axis

"c

= Ixc+Iyc

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the y c axis

kyc

Radius of Gyration

about the  z c axis

rc

rc2  = kxc

2 +kyc2

Square Channel

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=z

8/17/2019 formulas of Area Moment of Inertia

5/12

Cx Cy Area

Moment of Inertia

about the xc axis

Ixc

Moment of Inertia

about the yc axis

Iyc

Polar Moment of Inertia

about the zc axis

"c

= Ixc + Iyc

Radius of Gyration

about

the  x c axis

8/17/2019 formulas of Area Moment of Inertia

6/12

Cx Cy Area

Moment of Inertia

about the  x c axis

Ixc

Moment of Inertia

about the y c axis

Iyc

Polar Moment of 

Inertia

about the  z c axis

"c

= Ixc + Iyc

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=z

8/17/2019 formulas of Area Moment of Inertia

7/12

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the y c axis

kyc

Radius of Gyration

about the  z c axis

rc

rc2 = kxc

2+kyc2

http://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=z

8/17/2019 formulas of Area Moment of Inertia

8/12

Square * Beam

Cx Cy Area

Moment of Inertia

about the  x c axis

Ixc

Moment of Inertia

about the y c axis

Iyc

Polar Moment of 

Inertia

about the  z c axis

"c

$iew = Ixc = Ixc + Iyc

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/BasicLBeamIxc.cfmhttp://www.efunda.com/designstandards/beams/BasicLBeamIxc.cfmhttp://www.efunda.com/designstandards/beams/BasicLBeamIxc.cfmhttp://www.efunda.com/designstandards/beams/BasicLBeamIxc.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/BasicLBeamIxc.cfmhttp://www.efunda.com/designstandards/beams/BasicLBeamIxc.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=z

8/17/2019 formulas of Area Moment of Inertia

9/12

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the y c axis

kyc

Radius of Gyration

about the  z c axis

rc

rc2 = kxc

2+kyc2

Distance to

the Principal axis

d 

Moment of Inertia

about the Principal

axis

Ip

Polar Moment of 

Inertia

about the Principal

axis

"p

$iew = "c

%ectan&ular * Beam

Cx Cy Area

http://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/BasicLBeamIxp.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/BasicLBeamIxp.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfm

8/17/2019 formulas of Area Moment of Inertia

10/12

Moment of Inertia

about the  x c axis

Ixc

Moment of Inertia

about the y c axis

Iyc

Polar Moment of 

Inertia

about the  z c axis

"c

= Ixc + Iyc

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the y c axis

kyc

Radius of Gyration

about the  z c axis

rc

rc2 = kxc

2+kyc2

http://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=ychttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=ychttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=z

8/17/2019 formulas of Area Moment of Inertia

11/12

Square !-Beam

Cy Area

Moment of Inertia

about the  x c axis

Ixc

Polar Moment of Inertia

about the  z c axis

"c

= Ixc + Iyc

http://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zhttp://www.efunda.com/designstandards/beams/Centroid.cfmhttp://www.efunda.com/designstandards/beams/Area.cfmhttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=xchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=zchttp://www.efunda.com/designstandards/beams/MomentOfInertia.cfm?Moment=z

8/17/2019 formulas of Area Moment of Inertia

12/12

Radius of Gyration

about the  x c axis

kxc

Radius of Gyration

about the  z c axis

rc

rc2 = kxc

2+kyc2

http://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zhttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=xchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=zchttp://www.efunda.com/designstandards/beams/RadiusOfGyration.cfm?RadiusOfGyration=z