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CALCULATOR MODULE : Beam Torsional Vibration Frequency   ±

Calculate beam torsional natural vibration frequency from for modes 1 to 8.

The torsional natural vibration frequency for a beam can be calculated by

`fn = k / (2 L) √(G / ρ) `

where :

fn = natural frequency [Hz]
k = mode factor
L = beam length
G = beam shear modulus
ρ = beam density

The mode factor k is dependent on the mode number and the beam end type. The torsional natural frequency is independent of the cross section profile. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes.

Use the Result Table and Result Plot options to display tables and plots. Refer to the help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

Change Module :

CALCULATOR MODULE : Beam Torsional Vibration Frequency With End Mass   ±

Calculate beam torsional vibration frequency for a beam with an end mass for modes 1 to 8.

The torsional natural vibration frequency for a beam with an end mass can be calculated by

`fn = β / (2 π L) √(G / ρ) `
`β tan(β) = (Jb)/(Jm) `

where :

fn = natural frequency [Hz]
β = mode factor
L = beam length
G = beam shear modulus
ρ = beam density
Jb = beam mass moment of inertia
Jm = end mass mass moment of inertia

The mode factor (β) can be solved iteratively for each mode (modes 1 to 8). The system is modelled as a beam fixed at one end, with a mass at the other (free) end.

Use the Result Table and Result Plot options to display tables and plots. Refer to the help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

Change Module :

CALCULATOR MODULE : Right Angle Beam Natural Vibration Frequency   ±

Calculate the damped and undamped natural vibration frequency for right angle section 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. 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. The right angle beams are assumed to have equal leg length and leg thickness.

Use the Result Table and Result Plot options to display tables and plots. Refer to the figures and help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Right Angle Beam Cross Section   ±
CALCULATOR MODULE : Right Angle Beam Bending   ±

Calculate beam bending shear force, bending moment, slope and deflection for right angle 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).

Use the Result Plot option to plot the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details.

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

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CALCULATOR MODULE : Right Angle Beam Buckling Load   ±

Calculate beam buckling load for right angle beams.

The right angle beams are assumed to have equal leg length and leg thickness.

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. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed).

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 buckling load is positive. The axial load is negative in compression. Buckling will generally occur about the axis with the lowest EI, depending on constraints.

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 plot the buckling load versus nominal length. Use the Result Table option to plot the buckling load versus end type. Refer to the figures and help pages for more details. Refer to the figures for more details.

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

Change Module :

CALCULATOR MODULE : Hot Pipeline Soil Friction   ±
CALCULATOR MODULE : Dimensionless Wave Number   ±

Calculate common dimensionless and dimensional ocean wave numbers.

Ocean wave numbers include :

`kw = (2 pi) / L = 2 pi(fw) / c `
`fw = 1 / T `
`Ur = h l^2 / d^3 = (h/d)^3 / (l/d)^2 `
`H* = H / (g t^2) `
`d* = d / (g t^2) `

where :

kw = wave number (dimesion 1/length)
fw = wave frequency (dimension 1/time)
Ur = dimensionless Ursell number
H* = dimensionless wave height
d* = dimensionless water depth
L = wave length
f = wave frequency
c = wave celerity or propagation speed

Change Module :

Related Modules :

CALCULATOR MODULE : DNVGL RP O501 Pipeline Reducer Erosion Rate   ±
CALCULATOR MODULE : Maths Trigonometry   ±

Calculate the maths trigonometric functions (sin, cos, tan, cosec, sec and cot), and the inverse trigonometric functions (asin, acos, atan, acosec, asec, and acot).

The trigonometric fuctions are circular functions calculated for a right angle triangle with a hypotenuse equals 1 and angle θ. The base length of the triangle = cos(θ). The height of the triangle equals sin(θ). The slope of the hypotenuse equals tan(θ), equals sin(θ) / cos(θ). From Pythagorus' formula cos(θ)^2 + sin(θ)^2 = 1. The functions cosec (1/sin), sec (1/cos) and cot (1/tan) were mainly used for navigation.

Change Module :

CALCULATOR MODULE : Maths Right Angle Triangle (Pythagorus)   ±

Calculate maths triangle sides, heights and angles for a right angled triangle.

The area is calculated from the base and height. Angles, sides and heights can be calculated using cos, sin, tan, and Pythagorus theorem.

Change Module :

DATA MODULE : Soil Properties : Density Uplift Coefficient Shear Strength And Friction Factor ( Open In Popup Workbook )   ±

Soil properties, soil density, uplift coefficient, shear strength and friction factors.

    Related Modules :

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