Triangular Beam Natural Vibration Frequency

Calculate the damped and undamped natural vibration frequency for solid and hollow triangle 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 required for equilateral triangles). 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. 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 for all three sides.

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

Change Module :

Beam Lateral Vibration Frequency Calculation Module
Beam Lateral Vibration Frequency With Axial Load Calculation Module
Beam Longitudinal Vibration Frequency Calculation Module
Beam Torsional Vibration Frequency Calculation Module
Beam Torsional Vibration Frequency With End Mass Calculation Module
Beam Vibration Added Mass Calculation Module
Beam Vibration Concrete Stiffness Factor CSF Calculation Module
Circular And Semi Circular Beam Natural Vibration Frequency Calculation Module
Circular Pipe Natural Vibration Frequency Calculators
Diamond Beam Natural Vibration Frequency Calculation Module
Elliptical And Semi Elliptical Beam Natural Vibration Frequency Calculation Module
I Section Beam Natural Vibration Frequency Calculation Module
Parallelogram Beam Natural Vibration Frequency Calculation Module
Pipe Beam Natural Vibration Frequency Calculation Module
Polygon Beam Natural Vibration Frequency Calculation Module
Rectangular Beam Natural Vibration Frequency Calculation Module
Rectangular Channel Beam Natural Vibration Frequency Calculation Module
Right Angle Beam Natural Vibration Frequency Calculation Module
Rotated Beam Natural Vibration Frequency Calculation Module
Square Beam Natural Vibration Frequency Calculation Module
T Section Beam Natural Vibration Frequency Calculation Module
Trapezoid Beam Natural Vibration Frequency Calculation Module
Wire Natural Vibration Frequency Calculation Module
All
More Triangular Section Beam Modules

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Links : ±

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.

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

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.

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

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

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

CALCULATOR : Beam Vibration Right Angle Triangle Base And Height [FREE] ±

Calculate right angle triangle base and height from pythagoras theorem.

For a right angle triangle, one of the internal angles equals 90 degrees. The base and height can be calculated from the known lengths and angles using cos, sin, tan, and Pythagorus theorem.

Tool Input

trtype : Triangle Geometry Type
- au : User Defined Length Base Side a
- bu : User Defined Length Right Side b
- cu : User Defined Length Left Side c (Hypotenuse)
- Au : User Defined Angle Opposite Side a
- Bu : User Defined Angle Opposite Side b
- hcu : User Defined Height From Side c (Hypotenuse)

Tool Output

A : Angle Opposite Side a
B : Angle Opposite Side b
C : Angle Opposite Side c
X : Cross Section Area
XA : External Angle A
XB : External Angle B
XC : External Angle C
a : Length Side a
b : Length Side b
c : Length Side c (Hypotenuse)
ha : Height From Side a
hb : Height From Side b
hc : Height From Side c

CALCULATOR : Beam Vibration Scalene Triangle Base Height And Offset [FREE] ±

Calculate scalene triangle base, height and offset from the sin rule and cosine rule.

Scalene triangles have three unequal sides, and three unequal angles. The base, height and offset can be calculated from the known lengths and angles using either the sin rule or the cosine rule. The triangle geometry should be arranged so that the offset is positive.

Tool Input

trtype : Triangle Geometry Type
- au : User Defined Length Base Side a
- bu : User Defined Length Right Side b
- cu : User Defined Length Left Side c
- obu : User Defined Right Side Offset (Top From Side b)
- Au : User Defined Angle Opposite Side a
- Bu : User Defined Angle Opposite Side b
- Cu : User Defined Angle Opposite Side c
- hau : User Defined Height From Base Side a
offtype : Offset Type

Tool Output

A : Angle Opposite Side a
B : Angle Opposite Side b
C : Angle Opposite Side c
X : Cross Section Area
XA : External Angle A
XB : External Angle B
XC : External Angle C
a : Length Side a
b : Length Side b
c : Length Side c
cvg : Convergence Check
ha : Height From Side a
hb : Height From Side b
hc : Height From Side c
ol : Left Side Offset
or : Right Side Offset

CALCULATOR : Beam Vibration Equilateral Triangle Base And Height [FREE] ±

Calculate equilateral triangle height

For an equilateral triangle all three sides and all three angles are equal (the internal angles = 60 degrees). The base and height can be calculated from either the known height, or the known base length.

Tool Input

trtype : Triangle Geometry Type
- au : User Defined Length Side
- hau : User Defined Height From Side

Tool Output

A : Angle A
X : Area A
XA : Angle B
a : Length A
ha : Height

CALCULATOR : Beam Vibration Isoceles Triangle Base And Height [FREE] ±

Calculate isoceles triangle base and height from the sin rule and cosine rule.

Isoceles triangles have two equal sides and two equal angles. The base and height can be calculated from the known lengths and angles using either cos, sin and tan, or the sin rule and the cosine rule.

Tool Input

trtype : Triangle Geometry Type
- au : User Defined Length Base Side
- bu : User Defined Length Equal Side
- Au : User Defined Angle Opposite Base Side
- Bu : User Defined Angle Opposite Equal Side
- hau : User Defined Height From Base Side
- hbu : User Defined Height From Equal Side

Tool Output

A : Angle Opposite Side a
B : Angle Opposite Side b
C : Angle Opposite Side c
X : Cross Section Area
XA : External Angle A
XB : External Angle B
XC : External Angle C
a : Length Side a
b : Length Side b
c : Length Side c
ha : Height From Side a
hb : Height From Side b
hc : Height From Side c

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

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

CALCULATOR : Beam Lateral Natural Vibration Frequency (Equilateral Triangle Beam) [PLUS] ±

Calculate equilateral triangle 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.

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.

Equilateral triangles have three equal sides, and three equal angles (60 degrees). For hollow triangles, the wall thickness is assumed to be equal on all three sides. 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
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)
a : Beam Width
ta : 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)
d : Beam Height
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

CALCULATOR : Beam Lateral Natural Vibration Frequency (Isoceles Triangle Beam) [PLUS] ±

Calculate isoceles triangle beam lateral natural vibration frequency for solid and hollow beams.

Isoceles triangles have two equal sides, and two equal angles. For hollow triangles, the wall thickness is assumed to be equal on all three sides. The isoceles triangle calculator can also be used for equilateral triangle beams. 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
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)
b : Beam Base Width
d : Beam Height
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

CALCULATOR : Beam Lateral Natural Vibration Frequency (Scalene Triangle Beam) [PLUS] ±

Calculate scalene triangle beam lateral natural vibration frequency.

Scalene triangles have three unequal sides and three unequal angles. For triangles with an obtuse angle greater than 90 degrees, the longest side should be used as the base so that the offset is positive. The scalene triangle calculator can also be used for isoceles triangles and equilateral triangles.

Axis L is parallel to the base. Axis M is perpendicular to the base. Axis 1 and 2 are the pricipal axes. Frequency properties can also be calculated for an axis parallel to either side, perpendicular to either side, or at a user defined angle relative to the L axis. 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
mltype : Unit Mass And Unit Weight Type
mmtype : Added Mass Type (Submerged Beams Only)
- Cmu : User Defined Added Mass Coefficient
axistype : Bending Axis Type
- θu : User Defined Axis Angle Relative To L Axis (Positive Anti Clockwise)
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)
d : Beam Height
b : Beam Bottom Width
a : Beam Offset
Lo : Nominal Length
SY : Yield Stress
ρd : Displaced Fluid Density

Tool Output

α : Thermal Expansion Coefficient
θ : Axis Angle Relative To L Axis (Positive Anti Clockwise)
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
H : Product Of Inertia
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
md : Displaced Fluid Unit Mass

CALCULATOR : Beam Cross Section Properties (Equilateral Triangle Beam) [FREE] ±

Calculate equilateral triangle beam cross section properties for solid and hollow beams.

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
a : Beam Width
ta : 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
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
Yb : Distance From Outer Fibre To Centroid
Yp : Distance From Base Of Triangle To Plastic Centroid
Za : Section Modulus (I / Ya)
Zb : Section Modulus (I / Yb)
Zp : Plastic Modulus
ai : Inside Width
d : Beam Height
di : Inside Height
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)

CALCULATOR : Beam Cross Section Properties (Isoceles Triangle Beam) [FREE] ±

Calculate isoceles triangle beam cross section properties for solid and hollow beams.

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
b : Beam Base Width
d : Beam Height
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
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
Yb : Distance From Outer Fibre To Centroid
Yp : Distance From Base Of Triangle To Plastic Centroid
Za : Section Modulus (I / Ya)
Zb : Section Modulus (I / Yb)
Zp : Plastic Modulus
bi : Inside Width
di : Inside Height
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)

CALCULATOR : Beam Cross Section Properties (Scalene Triangle Beam) [FREE] ±

Calculate scalene triangle beam cross section properties.

Axis L is parallel to the base. Axis M is perpendicular to the base. Axis 1 and 2 are the pricipal axes. Section properties can also be calculated for an axis parallel to either side, perpendicular to either side, or at a user defined angle relative to the L axis. 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
- θu : User Defined Axis Angle Relative To L Axis (Positive Anti Clockwise)
d : Beam Height
b : Beam Bottom Width
a : Beam Offset
L : Length
ρd : Displaced Fluid Density

Tool Output

α : Thermal Expansion Coefficient
θ : Axis Angle Relative To L Axis (Positive Anti Clockwise)
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
H : Product Of Inertia
I : Moment Of Inertia
Ip : Polar Moment Of Inertia
J : Mass Moment Of Inertia
L/r : Slenderness Ratio
M : Total Beam Mass (Without Contents)
SG : Specific Gravity (Submerged Beams Only)
Ya : Distance From Outer Fibre To Centroid a
Yb : Distance From Outer Fibre To Centroid b
Za : Section Modulus a
Zb : Section Modulus b
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)