Calculate beam bending shear force, bending moment, slope and deflection for circular beams, semi circular beams, circular beam segments, and circular beam sectors.
The Euler Bernoulli beam equation is suitable for slender beams (it does not include the effect of shear), and for small angles (θ < 0.5 rad). The calculations are not valid past the beam end points. For combined loads, the shear force, bending moment, slope and deflection are assumed to be additive. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed). All distances are measured from the left end of the beam.
Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends.
Combined loads include axial loads, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature gradient.
For beams with compressive axial loads the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length.
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).
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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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CALCULATOR : Beam Bending Combined Load (General Beam - Matrix Data) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check from combined loads for general beams (user defined properties - matrix data). Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load (load controlled conditions). For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The axial load can either be calculated from temperature and pressure or user defined. The stress can be calculated at either the top of the beam, or the base of the beam. The beam orientation can be flipped (Ya at the top or Yb at the top). 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). Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. Tool Input- modptype : Material Property Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- eitype : E x I Type
- Iu : User Defined Section Modulus
- ru : User Defined Radius Of Gyration
- EIu : User Defined E x I
- eaatype : E x A x alpha Type
- EAαu : User Defined E x A x alpha
- 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
- Fbu : User Defined Buckling Load
- endtype : End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- yytype : Beam Orientation Type
- chktype : Check Stress Type
- btype : Location On Beam
- Data : Combined Loads
- AX : Cross Section Area
- w : Weight Per Unit Length
- Lo : Nominal Length
- x : Length From End
- Ya : Distance To Outer Fiber
- Yb : Distance To Outer Fiber
- Sy : Yield Stress
Tool Output- α : Thermal Expansion Coefficient
- θ : Slope Or Angle
- E : Elastic Modulus
- EAα : E x A x alpha (E x AX x α)
- 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)
- M : Maximum Bending Moment
- R : Reaction Or Shear Load
- Schk : Check Stress
- Schk/Sd : Check Stress Over Yield Stress Ratio
- Sx : Axial Stress
- h : Beam Height In Plane Of Bending
- r : Radius Of Gyration
- y : Deflection
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CALCULATOR : Beam Bending Combined Load (General Beam - File Data - Modern Browser Required) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check from combined loads for general beams (user defined properties - file data - a modern browser is required). Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load (load controlled conditions). For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The axial load can either be calculated from temperature and pressure or user defined. The stress can be calculated at either the top of the beam, or the base of the beam. The beam orientation can be flipped (Ya at the top or Yb at the top). 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). Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. Refer to the example text file in resources. Tool Input- modptype : Material Property Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- eitype : E x I Type
- Iu : User Defined Section Modulus
- ru : User Defined Radius Of Gyration
- EIu : User Defined E x I
- eaatype : E x A x alpha Type
- EAαu : User Defined E x A x alpha
- 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
- Fbu : User Defined Buckling Load
- endtype : End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- yytype : Beam Orientation Type
- chktype : Check Stress Type
- btype : Location On Beam
- AX : Cross Section Area
- w : Weight Per Unit Length
- Lo : Nominal Length
- x : Length From End
- Ya : Distance To Outer Fiber
- Yb : Distance To Outer Fiber
- Sy : Yield Stress
Tool Output- α : Thermal Expansion Coefficient
- θ : Slope Or Angle
- E : Elastic Modulus
- EAα : E x A x alpha (E x AX x α)
- 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)
- M : Maximum Bending Moment
- R : Reaction Or Shear Load
- Schk : Check Stress
- Schk/Sd : Check Stress Over Yield Stress Ratio
- Sx : Axial Stress
- h : Beam Height In Plane Of Bending
- r : Radius Of Gyration
- y : Deflection
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CALCULATOR : Beam Bending Combined Load (General Beam) [FREE] ±
Calculate beam bending shear force, bending moment, slope, and deflection from combined loads for general beams (user defined properties - matrix data). Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load (load controlled conditions). For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load is calculated using the Euler equation (suitable for long beams). The effective length is greater than the nominal length 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 equals the nominal length. Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. Tool Input- endtype : End Type
- btype : Location On Beam
- Data : Combined Loads
- w : Weight Per Unit Length
- h : Beam Height In Plane Of Bending
- Le : Effective Length
- x : Length From End
- α : Thermal Expansion Coefficient
- EI : Beam Bending Modulus
- Fa : Axial Load (-ve Compression)
Tool Output- θ : Slope Or Angle
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- M : Maximum Bending Moment
- R : Reaction Or Shear Load
- y : Deflection
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CALCULATOR : Beam Bending 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 Bending 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 Bending 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 Bending Combined Load (Circular Beam) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check from combined loads for solid and hollow circular beams. Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The axial load can either be calculated from temperature or user defined. 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 stress can be calculated at either the top of the beam, or the base of the beam. For hollow sections, the internal and external sections are assumed 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. Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. 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
- wltype : Unit Weight Type
- wu : User Defined Unit Weight
- 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
- Fbu : User Defined Buckling Load
- endtype : Beam End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- chktype : Stress Check Type
- btype : Beam Orientation Type
- Data : Beam Load Data
- OD : Outside Diameter
- t : Wall Thickness
- Lo : Nominal Length
- x : Position From Left End
- Sy : Yield Stress
- ρc : Contents Fluid Density
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- θ : Angle Or Slope
- ρb : Beam Density
- AX : Cross Section Area
- Ac : Contents Cross Section Area
- Ad : Displaced Cross Section Area
- 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
- ID : Internal Diameter
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- M : Bending Moment
- R : Shear Force
- SG : Specific Gravity
- Schk : Check Stress
- Schk/Sd : Check Stress Over Yield Stress Ratio
- Sx : Axial Stress
- Ya : Distance To Outer Fiber
- Yb : Distance To Outer Fiber
- h : Beam Height In Plane Of Bending
- mb : Beam Unit Mass
- mc : Contents Fluid Mass
- md : Displaced Fluid Unit Mass
- r : Radius Of Gyration
- wl : Unit Weight
- y : Deflection
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CALCULATOR : Beam Bending Combined Load (Semi Circular Beam) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check for solid and hollow semi circular beams. Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The axial load can either be calculated from temperature or user defined. 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 stress can be calculated at either the top of the beam, or the base of the beam. 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 beam orientation can be flipped (Ya at the top or Yb at the top). Axis 2 is perpendicular to the flat base of the beam, and passes through the center of the circle. Ya and Yb are equal to the circle radius. Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- wltype : Unit Weight Type
- wu : User Defined Unit Weight
- axstype : Cross Section Area Type
- axistype : Bending Axis Type
- 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
- Fbu : User Defined Buckling Load
- endtype : Beam End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- yytype : Beam Orientation Type
- chktype : Stress Check Type
- btype : Beam Orientation Type
- Data : Beam Load Data
- OD : Outside Diameter
- t : Wall Thickness
- Lo : Nominal Length
- x : Position From Left End
- Sy : Yield Stress
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- θ : Angle Or Slope
- ρb : Beam Density
- AX : Cross Section Area
- Ad : Displaced Cross Section Area
- 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
- ID : Internal Diameter
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- M : Bending Moment
- R : Shear Force
- SG : Specific Gravity
- Schk : Check Stress
- Schk/Sd : Check Stress Over Yield Stress Ratio
- Sx : Axial Stress
- Ya : Distance To Outer Fiber
- Yb : Distance To Outer Fiber
- h : Beam Height In Plane Of Bending
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
- r : Radius Of Gyration
- wl : Unit Weight
- y : Deflection
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CALCULATOR : Beam Bending Combined Load (Circular Sector Beam) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check for solid and hollow circular sector beams. Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The axial load can either be calculated from temperature or user defined. 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 stress can be calculated at either the top of the beam, or the base of the beam. 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. The beam orientation can be flipped (Ya at the top or Yb at the top). Axis 2 lies along the axis of symmetry of the beam, and passes through the center of the circle. Ya and Yb are the distance from the axis of symmetry to the outer edges of the beam. Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- wltype : Unit Weight Type
- wu : User Defined Unit Weight
- axstype : Cross Section Area Type
- axistype : Bending Axis Type
- 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
- Fbu : User Defined Buckling Load
- endtype : Beam End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- yytype : Beam Orientation Type
- chktype : Stress Check Type
- btype : Beam Orientation Type
- Data : Beam Load Data
- OD : Outside Diameter
- t : Wall Thickness
- Lo : Nominal Length
- x : Position From Left End
- Sy : Yield Stress
- Θ : Sector Half Angle
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- θ : Angle Or Slope
- ρb : Beam Density
- AX : Cross Section Area
- Ad : Displaced Cross Section Area
- 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
- ID : Internal Diameter
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- M : Bending Moment
- R : Shear Force
- SG : Specific Gravity
- Schk : Check Stress
- Schk/Sd : Check Stress Over Yield Stress Ratio
- Sx : Axial Stress
- Ya : Distance To Outer Fiber
- Yb : Distance To Outer Fiber
- h : Beam Height In Plane Of Bending
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
- r : Radius Of Gyration
- wl : Unit Weight
- y : Deflection
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CALCULATOR : Beam Bending Combined Load (Circular Segment Beam) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check for solid circular segment beams. Beam end types include free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. Combined loads can include axial load, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature differential. For compressive axial loads, the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The axial load can either be calculated from temperature or user defined. 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 stress can be calculated at either the top of the beam, or the base of the beam. 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. The beam orientation can be flipped (Ya at the top or Yb at the top). Axis 2 lies along the axis of symmetry of the beam, and passes through the center of the circle. Ya and Yb are equal, and are the distance from the axis of symmetry to the outer edges of the beam. Use the Result Plot option to display the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details. Tool Input- modptype : Material Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- wltype : Unit Weight Type
- wu : User Defined Unit Weight
- axistype : Bending Axis Type
- 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
- Fbu : User Defined Buckling Load
- endtype : Beam End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- yytype : Beam Orientation Type
- chktype : Stress Check Type
- btype : Beam Orientation Type
- Data : Beam Load Data
- OD : Outside Diameter
- Lo : Nominal Length
- x : Position From Left End
- Sy : Yield Stress
- Θ : Segment Half Angle
- ρd : Displaced Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- θ : Angle Or Slope
- ρb : Beam Density
- AX : Cross Section Area
- Ad : Displaced Cross Section Area
- 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)
- M : Bending Moment
- R : Shear Force
- SG : Specific Gravity
- Schk : Check Stress
- Schk/Sd : Check Stress Over Yield Stress Ratio
- Sx : Axial Stress
- Ya : Distance To Outer Fiber
- Yb : Distance To Outer Fiber
- h : Beam Height In Plane Of Bending
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
- r : Radius Of Gyration
- wl : Unit Weight
- y : Deflection
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