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Circular And Semi Circular Beam Cross Section

Calculate beam cross section properties for circular beams, semi circular beams, circular beam segments, and circular beam sectors: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity.

A semi circular profile is half of a circle, with a flat base which passes through the center of the circle. For hollow sections, the internal and external sections are assumed concentric with constant wall thickness.

A sector is a triangular slice to the center of a circle (like a slice of pie). Theta (θ) is the half angle of the sector or slice. For hollow sections, the internal and external sections are assumed concentric with constant wall thickness.

A segment is a slice perpendicular to the radius of the circle. Theta (θ) is the half angle of the segment. Refer to the figures for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR : Beam Cross Section Properties (Circular Beam) [FREE]   ±

Calculate circular beam cross section properties for solid and hollow beams.

For hollow sections, the internal and external sections are assumed concentric with constant wall thickness. The elastic centroid and the plastic centroid are located at the center of the circle for all axes. The distance Y to the outer fibre equals the circle radius for all cases.

Tool Input

  • modptype : Material Type
    • αu : User Defined Thermal Expansion Coefficient
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • ρpu : User Defined Density
  • axstype : Cross Section Area Type
  • mltype : Unit Mass And Unit Weight Type
  • mmtype : Added Mass Type (Submerged Beams Only)
    • Cmu : User Defined Added Mass Coefficient
    • h : Gap Height
  • OD : Outside Diameter
  • t : Wall Thickness
  • L : Length
  • ρc : Contents Fluid Density
  • ρd : Displaced Fluid Density

Tool Output

  • α : Thermal Expansion Coefficient
  • ρb : Beam Density
  • Ac : Contents Cross Section Area
  • Ad : Displaced Cross Section Area
  • Ax : Beam Cross Section Area
  • Cm : Added Mass Coefficient
  • E : Elastic Modulus
  • EA : E x A
  • EAα : E x A x alpha
  • EI : E x I
  • G : Shear Modulus
  • I : Moment Of Inertia
  • ID : Inside Diameter
  • Ip : Polar Moment Of Inertia
  • J : Mass Moment Of Inertia
  • L/r : Slenderness Ratio
  • M : Total Beam Mass (Including Contents)
  • SF : Shape Factor
  • SG : Specific Gravity (Submerged Beams Only)
  • Ya : Distance From Outer Fibre To Centroid
  • Yp : Distance From Outer Fibre To Plastic Centroid
  • Zp : Plastic Modulus
  • Zs : Section Modulus
  • m : Mass Per Unit Length (Including Contents And Added Mass)
  • ma : Added Unit Mass
  • mb : Beam Unit Mass
  • mc : Contents Fluid Mass
  • md : Displaced Fluid Unit Mass
  • r : Radius Of Gyration
  • w : Unit Weight (Including Contents And Buoyancy)
CALCULATOR : Beam Cross Section Properties (Semi Circular Beam) [FREE]   ±

Calculate semi circular beam cross section properties for solid and hollow beams.

A semi circular profile is half of a circle, with a flat base which passes through the center of the circle. For hollow sections, the internal and external sections are assumed concentric with constant wall thickness.

Axis 1 is parallel to the flat base of the beam. The distance Ya is the distance from the curved top of the beam to the elastic centroid. The distance Yb is the distance from the flat base of the beam to the elastic centroid. The distance Yp is the distance from the flat base of the beam to the plastic centroid.

Axis 2 is perpendicular to the flat base of the beam, and passes through the center of the circle. For axis 2, the elastic centroid and the plastic centroid lie along axis 2. Ya and Yb are equal to the circle radius. Yp equals zero. Refer to the figure for more details.

Tool Input

  • modptype : Material Type
    • αu : User Defined Thermal Expansion Coefficient
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • ρpu : User Defined Density
  • axstype : Cross Section Area Type
  • mltype : Unit Mass And Unit Weight Type
  • mmtype : Added Mass Type (Submerged Beams Only)
    • Cmu : User Defined Added Mass Coefficient
  • axistype : Bending Axis Type
  • OD : Outside Diameter
  • t : Wall Thickness
  • L : Length
  • ρd : Displaced Fluid Density

Tool Output

  • α : Thermal Expansion Coefficient
  • ρb : Beam Density
  • Ad : Displaced Cross Section Area
  • Ax : Beam Cross Section Area
  • Cm : Added Mass Coefficient
  • E : Elastic Modulus
  • EA : E x A
  • EAα : E x A x alpha
  • EI : E x I
  • G : Shear Modulus
  • I : Moment Of Inertia
  • ID : Inside Diameter
  • Ip : Polar Moment Of Inertia
  • J : Mass Moment Of Inertia
  • L/r : Slenderness Ratio
  • M : Total Beam Mass
  • SF : Shape Factor
  • SG : Specific Gravity (Submerged Beams Only)
  • Ya : Distance From Outer Fibre To Centroid
  • Yb : Distance From Outer Fibre To Centroid
  • Yp : Distance From Center To Plastic Centroid
  • Za : Section Modulus
  • Zb : Section Modulus
  • Zp : Plastic Modulus
  • m : Mass Per Unit Length (Including Added Mass)
  • ma : Added Unit Mass
  • mb : Beam Unit Mass
  • md : Displaced Fluid Unit Mass
  • r : Radius Of Gyration
  • w : Unit Weight (Including Buoyancy)
CALCULATOR : Beam Cross Section Properties (Circular Sector Beam) [FREE]   ±

Calculate circular beam sector cross section properties for solid and hollow beams.

A sector is a triangular slice to the center of a circle (like a slice of pie). Theta (θ) is the half angle of the sector or slice. For hollow sections, the internal and external sections are assumed concentric with constant wall thickness.

Axis 1 is perpendicular to the axis of symmetry (axis 2). The distance Ya is the distance from the curved top of the beam to the elastic centroid. For hollow sections, the distance Yb is the distance from the inside of the beam to the elastic centroid. For solid sections, the distance Yb is the distance from the center of the circle to the elastic centroid.

Axis 2 lies along the axis of symmetry of the beam, and passes through the center of the circle. For axis 2, the elastic centroid lies along axis 2. Ya and Yb are equal, and are the distance from the axis of symmetry to the outer edges of the beam. Refer to the figure for more details.

Tool Input

  • modptype : Material Type
    • αu : User Defined Thermal Expansion Coefficient
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • ρpu : User Defined Density
  • axstype : Cross Section Area Type
  • mltype : Unit Mass And Unit Weight Type
  • mmtype : Added Mass Type (Submerged Beams Only)
    • Cmu : User Defined Added Mass Coefficient
  • axistype : Bending Axis Type
  • OD : Outside Diameter
  • t : Wall Thickness
  • L : Length
  • Θ : Sector Half Angle
  • ρd : Displaced Fluid Density

Tool Output

  • α : Thermal Expansion Coefficient
  • ρb : Beam Density
  • Ad : Displaced Cross Section Area
  • Ax : Beam Cross Section Area
  • Cm : Added Mass Coefficient
  • E : Elastic Modulus
  • EA : E x A
  • EAα : E x A x alpha
  • EI : E x I
  • G : Shear Modulus
  • I : Moment Of Inertia
  • ID : Inside Diameter
  • Ip : Polar Moment Of Inertia
  • J : Mass Moment Of Inertia
  • L/r : Slenderness Ratio
  • M : Total Beam Mass
  • SG : Specific Gravity (Submerged Beams Only)
  • Ya : Distance From Outer Fibre To Centroid
  • Yb : Distance From Outer Fibre To Centroid
  • Za : Section Modulus
  • Zb : Section Modulus
  • m : Mass Per Unit Length (Including Added Mass)
  • ma : Added Unit Mass
  • mb : Beam Unit Mass
  • md : Displaced Fluid Unit Mass
  • r : Radius Of Gyration
  • w : Unit Weight (Including Buoyancy)
CALCULATOR : Beam Cross Section Properties (Circular Segment Beam) [FREE]   ±

Calculate circular beam segment cross section properties for solid beams.

A segment is a slice perpendicular to the radius of the circle. Theta (θ) is the half angle of the segment.

Axis 1 is perpendicular to the axis of symmetry (axis 2). The distance Ya is the distance from the curved top of the beam to the elastic centroid. The distance Yb is the distance from the flat base of the segment to the elastic centroid.

Axis 2 lies along the axis of symmetry of the beam, and passes through the center of the circle. For axis 2, the elastic centroid is along axis 2. The distances Ya and Yb are equal, and are the distance from the axis of symmetry to the outer edges of the beam. Refer to the figure for more details.

Tool Input

  • modptype : Material Type
    • αu : User Defined Thermal Expansion Coefficient
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • ρpu : User Defined Density
  • mltype : Unit Mass And Unit Weight Type
  • mmtype : Added Mass Type (Submerged Beams Only)
    • Cmu : User Defined Added Mass Coefficient
  • axistype : Bending Axis Type
  • OD : Outside Diameter
  • L : Length
  • Θ : Segment Half Angle
  • ρd : Displaced Fluid Density

Tool Output

  • α : Thermal Expansion Coefficient
  • ρb : Beam Density
  • Ad : Displaced Cross Section Area
  • Ax : Beam Cross Section Area
  • Cm : Added Mass Coefficient
  • E : Elastic Modulus
  • EA : E x A
  • EAα : E x A x alpha
  • EI : E x I
  • G : Shear Modulus
  • I : Moment Of Inertia
  • Ip : Polar Moment Of Inertia
  • J : Mass Moment Of Inertia
  • L/r : Slenderness Ratio
  • M : Total Beam Mass
  • SG : Specific Gravity (Submerged Beams Only)
  • Ya : Distance From Outer Fibre To Centroid
  • Yb : Distance From Outer Fibre To Centroid
  • Za : Section Modulus
  • Zb : Section Modulus
  • m : Mass Per Unit Length (Including Added Mass)
  • ma : Added Unit Mass
  • mb : Beam Unit Mass
  • md : Displaced Fluid Unit Mass
  • r : Radius Of Gyration
  • w : Unit Weight (Including Buoyancy)
CALCULATOR : Beam Cross Section Line Pipe Schedule [FREE]   ±

Calculate line pipe schedule outside diameter inside diameter and wall thickness.

Select the pipe schedule (NPS or ISO etc), pipe diameter and wall thickness, or use the user defined option. Use the Result Table option to display the pipe schedule for the selected diameter.

Tool Input

  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Wall Thickness Type
    • tnu : User Defined Wall Thickness

Tool Output

  • ID : Nominal Inside Diameter
  • OD : Nominal Outside Diameter
  • OD/tn : Diameter Over Wall Thickness Ratio
  • tn : Nominal Wall Thickness
CALCULATOR : Beam Cross Section Material Property [FREE]   ±

Calculate beam elastic modulus, shear modulus, bulk modulus, density, and thermal expansion coefficient.

The table values of Poisson ratio and bulk modulus are calculated from the elastic modulus and shear modulus. Use the Result Table option to display a table of properties versus material type.

Tool Input

  • modptype : Material Type
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • Ku : User Defined Bulk Modulus
    • νu : User Defined Poisson Ratio
    • ρu : User Defined Density
    • αu : User Defined Thermal Expansion Coefficient

Tool Output

  • α : Thermal Expansion Coefficient
  • ν : Poisson Ratio
  • ρ : Density
  • E : Elastic Modulus
  • G : Shear Modulus
  • K : Bulk Modulus
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