Calculate beam bending shear force, bending moment, slope and deflection for I section beams.
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 (I Section Beam) [FREE] ±
Calculate I section beam cross section properties for straight sided I beams, and tapered I beams. The I section is assumed to be symmetrical along axis 1 and 2. The webs or legs are assumed to be equal length and thickness. Tapered I beams have tapered webs. 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
- axstype : Cross Section Area Type
- axistype : Bending Axis Type
- d : Beam Outside Height
- b : Beam Outside Width
- tw : Web Wall Thickness
- tf : Flange Wall Thickness
- tc : Flange Crotch 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
- 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
- Zp : Plastic Modulus
- Zs : Section Modulus (I / Ya)
- m : Mass Per Unit Length (Including Contents And Added Mass)
- ma : Added Unit Mass
- mb : Beam Unit Mass
- md : Displaced Fluid Unit Mass
- r : Radius Of Gyration
- w : Unit Weight (Including Contents And 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 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 (I Section Beam) [PLUS] ±
Calculate beam bending shear force, bending moment, slope, deflection and stress check for straight sided I beams, and tapered I 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. The I section is assumed to be symmetrical along axis 1 and 2. The webs or legs are assumed to be equal length and thickness. Tapered I beams have tapered webs. 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
- chktype : Stress Check Type
- btype : Beam Orientation Type
- Data : Beam Load Data
- d : Beam Outside Height
- b : Beam Outside Width
- tw : Web Wall Thickness
- tf : Flange Wall Thickness
- tc : Flange Crotch 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
- 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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