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CALCULATOR MODULE : Beam Cross Section ±
Calculate beam cross section properties for circular pipes: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, section modulus, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. Unit mass can be calculated with or without added mass. 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 can be calculated in accordance with DNVGL RP F105. For multi layer pipes the bending stifness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. Use the Result Table option to display the cross section properties versus wall thickness. Refer to the help pages for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : Related Modules : |
CALCULATOR MODULE : Beam Cross Section Added Mass ±
Calculate beam cross section added mass coefficient and added mass from gap height for circular pipes and beams. 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 can be calculated in accordance with DNVGL RP F105. The equation is suitable for undamped vibration of circular beams 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 : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Beam Cross Section Concrete Stiffness Factor ±
Calculate beam cross section concrete stiffness factor (CSF) and effective EI from the concrete to beam EI ratio. Concrete stiffness can be included in EI by multiplying EI by a factor (1 + CSF). The bending stress should also be multiplied by the factor (1 + CSF) to account for stress localisation at the field joints. The concrete stiffness factor is calculated from the ratio of concrete EI over beam EI. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. The method is suitable for circular beams and pipes. For other profile shapes engineering judgement is required. Use the Result Plot option to plot the concrete stiffness factor (CSF) versus EI ratio and CSF type, or effective EI versus EI ratio and CSF type. Refer to the help pages for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Beam Section Modulus ±
Calculate beam EI and section modulus for a circular pipe. The section modulus is equal to the moment of inertia divided by the length from the centroid to the outer fiber (the outside radius). For combined stress calculations, the section modulus can be calculated using the length from the centroid to the pipe mid wall. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Beam Cross Section Parallel Axis Theorem ±
Calculate beam moment of inertia using the parallel axis theorem. The moment of inertia about an offset can be calculated by `Ix = Il + Y AX^2 `
`Iy = Im + X AX^2 ::Hxy = Hlm + X Y AX^2 ` where : Ix = moment of inertia about X axis
Iy = moment of inertia about Y axis
Il = moment of inertia about L axis
Im = moment of inertia about M axis
Hxy = product of inertia about offset
Hlm = product of inertia about the centroid
X = offset length from Y axis to centroid
Y = offset length from X axis to centroid
AX = cross section area X and Y are perpendicular axes passing through the offset. L and M are perpendicular axes passing through the centroid and parallel to X and Y. The X and Y axes pass through the offset point. For principal axes the product of inertia equals zero. Axes which are an axis of symmetry are principal axes. If the moment of inertia for a principal axis is equal to the moment of inertia of any other axis, all moments of inertia through that point are equal. For rotated axes, the rotation is calculated relative to either the X axis or the L axis (anti clockwise is positive). Use the Result Plot option to plot the rotated moments of inertia and product of inertia versus the rotation angle. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Circular And Semi Circular Beam Cross Section ±
Calculate beam cross section properties for circular beams, semi circular beams, circular beam segments, and circular beam sectors: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. A semi circular profile is half of a circle, with a flat base which passes through the center of the circle. For hollow sections, the internal and external sections are assumed concentric with constant wall thickness. A sector is a triangular slice to the center of a circle (like a slice of pie). Theta (θ) is the half angle of the sector or slice. For hollow sections, the internal and external sections are assumed concentric with constant wall thickness. A segment is a slice perpendicular to the radius of the circle. Theta (θ) is the half angle of the segment. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Elliptical And Semi Elliptical Beam Cross Section ±
Calculate beam cross section properties for elliptical and semi elliptical beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. For hollow ellipse and semi ellipse sections the internal and external sections can be assumed elliptical (the wall thickness is not constant), or the wall thickness can be assumed constant (the mid wall is assumed elliptical but the internal and external surfaces are not elliptical). Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Square Beam Cross Section ±
Calculate beam cross section properties for solid and hollow square beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. For hollow sections the wall thickness is assumed constant for all four sides. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Rectangular Beam Cross Section ±
Calculate beam cross section properties for solid and hollow rectangular beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. For hollow sections the wall thickness on opposite sides are assumed equal. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Parallelogram Beam Cross Section ±
Calculate beam cross section properties for solid and hollow parallelogram beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. For hollow sections the wall thickness on opposite sides are assumed equal. Axis L is parallel to the base. Axis M is perpendicular to the base. Axis 1 and 2 are the principal axes. The geometry should be arranged so that the offset is positive. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Trapezoid Beam Cross Section ±
Calculate beam cross section properties for solid trapezoid beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, section modulus, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. Axis L is parallel to the base. Axis M is perpendicular to the base. Axis 1 and 2 are the principal axes. The geometry should be arranged so that the offset is positive. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Diamond Beam Cross Section ±
Calculate beam cross section properties for solid and hollow diamond beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. For hollow sections the wall thickness is assumed constant for all four sides. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Rectangular Channel Beam Cross Section ±
Calculate beam cross section properties for rectangular channel section beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. The wall thickness on both sides are assumed equal. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Triangular Beam Cross Section ±
Calculate beam cross section properties for triangle beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. Equilateral triangles have three equal sides, and three equal angles. Isoceles triangles have two equal sides, and two equal angles. Scalene triangles have three unequal sides and three unequal angles. For hollow sections, the wall thickness is assumed constant on all sides. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Right Angle Beam Cross Section ±
Calculate beam cross section properties for right angle beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. The right angle beams are assumed to have equal leg length and leg thickness. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : T Beam Cross Section ±
Calculate beam cross section properties for T section beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, section modulus, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. The Tee section is assumed to be symmetrical along axis 2, and the flanges are assumed to be equal length and thickness. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : I Beam Cross Section ±
Calculate beam cross section properties for I section beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. The I section is assumed to be symmetrical along axis 1 and 2, and the flanges are equal length and thickness. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Polygon Beam Cross Section ±
Calculate beam cross section properties for regular polygon beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. The polygon section is assumed to be symmetric along axis 1 and 2, and all sides and wall thickness are assumed to be equal. The minimum number of sides is 3. A regular polygon with 3 sides is equivalent to an equilateral triangle. A regular polygon with 4 sides is equivalent to a square. Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Beam Bending ±
Calculate beam bending shear force, bending moment, slope and deflection for general beams using the Euler Bernoulli beam equation. 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. Refer to the links below for other beam options. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |