Calculate the damped and undamped natural vibration frequency for solid and hollow circular beams (simply supported, fixed, and cantilever beams).
For beams with axial load the axis with minimum stiffness (I1 or I2) should be used unless the beam is constrained to deflect on an alternative axis (buckling normally occurs on the minimum stiffness axis). Use the general beam calculators for cases where vibration and buckling are not parallel (not neccessary for round beams). The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). The buckling load is dependent on the end type, and is used for mode 1 vibration only.
Added mass should be included for submerged or wet beams. The added mass coefficient can be calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. For beams on a soft foundation such as soil, use the effective length factor to allow for movement at the beam ends. For defined beam ends such as structures, the effective length factor should be set to one. The axial load is calculated from temperature.
For longitudinal and torsional vibration, the natural frequency is independent of the cross section, and the general beam calculators can be used.
The mode factor k is dependent on the mode number, and the beam end type. The k factors have been taken from the Shock and Vibration handbook. The damping factor should be set to zero for undamped vibration or set greater than zero and less than or equal to one for damped vibration. For hollow beams the wall thickness is assumed constant.
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CALCULATOR : Beam Longitudinal Natural Vibration Frequency (General Beam) [FREE] ±
Calculate beam damped and undamped longitudinal natural vibration frequency from beam elastic modulus, density and length. The longitudinal natural frequency is independent of the cross section profile. Select the end type, and vibration mode number (modes 1 to 8). The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type. Tool Input- modptype : Material Property Type
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- endtype : End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- L : Length
Tool Output- ρ : Density
- E : Elastic Modulus
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
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CALCULATOR : Beam Torsional Natural Vibration Frequency (General Beam) [FREE] ±
Calculate beam damped and undamped torsional natural vibration frequency from beam shear modulus, density and length. The torsional natural frequency is independent of the cross section profile. Select the end type, and vibration mode number (modes 1 to 8). The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type. Tool Input- modptype : Material Property Type
- Gu : User Defined Shear Modulus
- ρpu : User Defined Density
- endtype : End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- L : Length
Tool Output- ρ : Density
- G : Shear Modulous
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
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CALCULATOR : Beam Added Mass Coefficient (General Beam) [FREE] ±
Calculate general beam added mass coefficient and added mass from gap height and characteristic length. Added mass is included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The added mass coefficient is calculated in accordance with DNVGL RP F105. The equation is suitable for undamped vibration of circular pipes in still fluid. For circular pipes the diameter should be used as the characteristic length. For other profile shapes the width can be used as the characteristic length. The method may not be valid for other profile shapes (engineering judgement is required). Refer to the help pages for more details. Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website) Tool Input- cmtype : Added Mass Coefficient Type
- Cmu : User Defined Added Mass Coefficient
- mb : Beam Mass Per Unit Length
- ρe : External Fluid Density
- W : Beam Characteristic Length
- G : Gap Height
- AX : Beam Cross Section Area
Tool Output- Cm : Added Mass Coefficient
- G/W : Gap Over Characteristic Length Ratio
- m : Total Mass Per Unit Length
- ma : Added Mass Per Unit Length
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CALCULATOR : Beam Lateral Natural Vibration Frequency (General Beam) [FREE] ±
Calculate beam damped and undamped lateral natural vibration frequency for general beams (user defined properties - with axial load or no axial load). Beam unit mass bending stiffness modulus and axial load are user defined. Select the load type, end type, and vibration mode number (modes 1 to 5 for beams with no axial load, or mode 1 for beams with axial load. The end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, also pinned free ends, and free ends (unsupported beams). For beams with axial load the natural frequency equals zero for compressive axial loads greater than or equal to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). Buckling normally occurs on the axis with lowest stiffness modulus. The buckling stiffness modulus and the vibration stiffness modulus can be defined independently for cases where vibration is not parallel to buckling. The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. The natural frequency equals zero for critical damping. Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, beam length and end type, or axial load and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. Refer to the figures and help pages for more details. Tool Input- eitype : Bending Modulus Type
- EIvu : User Defined Vibration Bending Modulus (E x I)
- EIbu : User Defined Buckling Bending Modulus (E x I)
- loadtype : Axial Load Type
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : End Type
- MN : Mode Number
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- AX : Cross Section Area
- m : Unit Mass
- Lo : Nominal Length
- SY : Yield Stress
Tool Output- EIb : Buckling Bending Modulus (E x I)
- EIv : Vibration Bending Modulus (E x I)
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- Le : Effective Length
- Lt : Transition Length (Short to Long Beam)
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
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CALCULATOR : Beam Vibration 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
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CALCULATOR : Beam Vibration Yield Stress [FREE] ±
Calculate beam yield stress (SMYS) and tensile stress (SMTS). Select one of the API, ASME or DNV stress table options. Use the Result Table option to display the stress values for the selected stress table. Tool Input- syutype : Stress Table Type
- mattype : Material Type
- SMYSu : User Defined Specified Minimum Yield Stress
- SMTSu : User Defined Specified Minimum Tensile Stress
Tool Output- SMTS : Specified Minimum Tensile Stress
- SMTS/SMYS : Tensile Stress Over Yield Stress Ratio
- SMYS : Specified Minimum Yield Stress
- SMYS/SMTS : Yield Stress Over Tensile Stress Ratio
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CALCULATOR : Beam Vibration 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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CALCULATOR : Beam Lateral Natural Vibration Frequency (Circular Beam) [PLUS] ±
Calculate circular beam lateral natural vibration frequency for solid and hollow beams, either with axial load (mode 1 only), or with no axial load (modes 1 to 5). For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). For tension loads, the natural frequency increases with increasing tension. The axial load can either be calculated from delta temperature, or user defined. Added mass can be included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. For hollow sections, the internal and external sections are assumed to be concentric with constant wall thickness. The elastic centroid is located at the center of the circle for all axes. The distance Y to the outer fibre equals the circle radius for all cases. Refer to the figures and help pages for more details. Use the Result Table option to table either the natural frequency versus mode number, or the natural frequency versus end type. Use the Result Plot option to plot the natural frequency versus either beam length and mode number, beam length and end type, or axial load and end type. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- axstype : Cross Section Area Type
- mltype : Unit Mass And Unit Weight Type
- mmtype : Added Mass Type (Submerged Beams Only)
- h : Gap Height
- Cmu : User Defined Added Mass Coefficient
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- loadtype : Axial Load Type
- Td : User Defined Operating Temperature
- Tin : User Defined Installation Temperature
- Fin : User Defined Preload
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : Beam End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- OD : Outside Diameter
- t : Wall Thickness
- Lo : Nominal Length
- SY : Yield Stress
- ρc : Contents Fluid Density
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- ρb : Beam Density
- AX : Cross Section Area
- Ac : Contents Cross Section Area
- Ad : Displaced Cross Section Area
- Cm : Added Mass Coefficient
- E : Elastic Modulus
- EAα : E x A x alpha
- EI : E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- I : Moment Of Inertia
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- 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
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CALCULATOR : Beam Lateral Natural Vibration Frequency (Semi Circular Beam) [PLUS] ±
Calculate semi circular beam lateral natural vibration frequency for solid and hollow beams. The lateral natural vibration frequency can be calculated either with axial load (mode 1 only), or with no axial load (modes 1 to 5). For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). For tension loads, the natural frequency increases with increasing tension. The axial load can either be calculated from delta temperature, or user defined. Added mass can be included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The submerged natural frequency is calculated for still water conditions. 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. 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 is on axis 2. Ya and Yb are equal to the circle radius. Yp equals zero. Refer to the figures and help pages for more details. Use the Result Table option to table either the natural frequency versus mode number, or the natural frequency versus end type. Use the Result Plot option to plot the natural frequency versus either beam length and mode number, beam length and end type, or axial load and end type. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic 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
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- loadtype : Axial Load Type
- Td : User Defined Operating Temperature
- Tin : User Defined Installation Temperature
- Fin : User Defined Preload
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : Beam End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- OD : Outside Diameter
- t : Wall Thickness
- Lo : Nominal Length
- SY : Yield Stress
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- ρb : Beam Density
- AX : Cross Section Area
- Ad : Displaced Cross Section Area
- Cm : Added Mass Coefficient
- E : Elastic Modulus
- EAα : E x A x alpha
- EI : E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- I : Moment Of Inertia
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Mass Per Unit Length (Including Added Mass)
- ma : Added Unit Mass
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
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CALCULATOR : Beam Lateral Natural Vibration Frequency (Circular Sector Beam) [PLUS] ±
Calculate circular beam sector lateral natural vibration frequency for solid and hollow beams. The lateral natural vibration frequency can be calculated either with axial load (mode 1 only), or with no axial load (modes 1 to 5). For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). For tension loads, the natural frequency increases with increasing tension. The axial load can either be calculated from delta temperature, or user defined. Added mass can be included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The submerged natural frequency is calculated for still water conditions. 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 figures and help pages for more details. Use the Result Table option to table either the natural frequency versus mode number, or the natural frequency versus end type. Use the Result Plot option to plot the natural frequency versus either beam length and mode number, beam length and end type, or axial load and end type. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic 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
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- loadtype : Axial Load Type
- Td : User Defined Operating Temperature
- Tin : User Defined Installation Temperature
- Fin : User Defined Preload
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : Beam End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- OD : Outside Diameter
- t : Wall Thickness
- Lo : Nominal Length
- SY : Yield Stress
- Θ : Sector Half Angle
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- ρb : Beam Density
- AX : Cross Section Area
- Ad : Displaced Cross Section Area
- Cm : Added Mass Coefficient
- E : Elastic Modulus
- EAα : E x A x alpha
- EI : E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- I : Moment Of Inertia
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Mass Per Unit Length (Including Added Mass)
- ma : Added Unit Mass
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
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CALCULATOR : Beam Lateral Natural Vibration Frequency (Circular Segment Beam) [PLUS] ±
Calculate circular beam segment lateral natural vibration frequency for solid beams. The lateral natural vibration frequency can be calculated either with axial load (mode 1 only), or with no axial load (modes 1 to 5). For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). For tension loads, the natural frequency increases with increasing tension. The axial load can either be calculated from delta temperature, or user defined. Added mass can be included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The submerged natural frequency is calculated for still water conditions. 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 figures and help pages for more details. Use the Result Table option to table either the natural frequency versus mode number, or the natural frequency versus end type. Use the Result Plot option to plot the natural frequency versus either beam length and mode number, beam length and end type, or axial load and end type. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic 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
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- loadtype : Axial Load Type
- Td : User Defined Operating Temperature
- Tin : User Defined Installation Temperature
- Fin : User Defined Preload
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : Beam End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- OD : Outside Diameter
- Lo : Nominal Length
- SY : Yield Stress
- Θ : Segment Half Angle
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- ρb : Beam Density
- AX : Cross Section Area
- Ad : Displaced Cross Section Area
- Cm : Added Mass Coefficient
- E : Elastic Modulus
- EAα : E x A x alpha
- EI : E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- I : Moment Of Inertia
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Mass Per Unit Length (Including Added Mass)
- ma : Added Unit Mass
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
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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)
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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)
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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)
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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)
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