Combined Moment of Inertia of Shell and Stiffener per Unit Length Calculator

✖Vessel Shell Outer Diameter refers to the outermost dimension of the cylindrical shell of a vessel, such as a tank or pressure vessel.ⓘ Vessel Shell Outer Diameter [D_o]			+10% -10%
✖Effective Length Between Stiffeners refers to the distance between adjacent stiffeners or bracing elements that help to prevent buckling or lateral deflection of the member.ⓘ Effective Length Between Stiffeners [L_eff]			+10% -10%
✖Shell Thickness for Jackted Reaction Vessel is the distance through the shell.ⓘ Shell Thickness for Jackted Reaction Vessel [t_{jacketedreaction}]			+10% -10%
✖Cross Sectional Area of Stiffening Ring in a vessel is the area of the ring when viewed in cross-section perpendicular to its axis.ⓘ Cross Sectional Area of Stiffening Ring [A_s]			+10% -10%
✖Allowable Stress for Jacket Material at Design Temperature is defined as the material failure stress divided by a factor of safety greater than one.ⓘ Allowable Stress for Jacket Material [f_j]			+10% -10%
✖Modulus of Elasticity Jacketed Reaction Vessel refers to the measure of the vessel's ability to deform elastically under an applied load.ⓘ Modulus of Elasticity Jacketed Reaction Vessel [E]			+10% -10%

✖Combined Moment of Inertia of Shell and Stiffener is a measure of the resistance to bending of a composite beam consisting of a cylindrical shell and a series of stiffeners.ⓘ Combined Moment of Inertia of Shell and Stiffener per Unit Length [I_required]

⎘ Copy

👎

Formula

✖

Combined Moment of Inertia of Shell and Stiffener per Unit Length

Formula

`"I"_{"required"} = ("D"_{"o"}^(2)*"L"_{"eff"}*("t"_{"jacketedreaction"}+"A"_{"s"}/"L"_{"eff"})*"f"_{"j"})/(12*"E")`

Example

`"1.2E^14mm⁴/mm"=(("550mm")^(2)*"330mm"*("15mm"+"1640mm²"/"330mm")*"120N/mm²")/(12*"170000N/mm²")`

Calculator

LaTeX

Reset

👍

Download Jacketed Reaction Vessel Formulas PDF PDF Image

Combined Moment of Inertia of Shell and Stiffener per Unit Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Combined Moment of Inertia of Shell and Stiffener = (Vessel Shell Outer Diameter^(2)*Effective Length Between Stiffeners*(Shell Thickness for Jackted Reaction Vessel+Cross Sectional Area of Stiffening Ring/Effective Length Between Stiffeners)*Allowable Stress for Jacket Material)/(12*Modulus of Elasticity Jacketed Reaction Vessel)
I_required = (D_o^(2)*L_eff*(t_{jacketedreaction}+A_s/L_eff)*f_j)/(12*E)
This formula uses 7 Variables

Variables Used

Combined Moment of Inertia of Shell and Stiffener - (Measured in Meter⁴ per Meter) - Combined Moment of Inertia of Shell and Stiffener is a measure of the resistance to bending of a composite beam consisting of a cylindrical shell and a series of stiffeners.
Vessel Shell Outer Diameter - (Measured in Millimeter) - Vessel Shell Outer Diameter refers to the outermost dimension of the cylindrical shell of a vessel, such as a tank or pressure vessel.
Effective Length Between Stiffeners - (Measured in Millimeter) - Effective Length Between Stiffeners refers to the distance between adjacent stiffeners or bracing elements that help to prevent buckling or lateral deflection of the member.
Shell Thickness for Jackted Reaction Vessel - (Measured in Millimeter) - Shell Thickness for Jackted Reaction Vessel is the distance through the shell.
Cross Sectional Area of Stiffening Ring - (Measured in Square Millimeter) - Cross Sectional Area of Stiffening Ring in a vessel is the area of the ring when viewed in cross-section perpendicular to its axis.
Allowable Stress for Jacket Material - (Measured in Newton per Square Millimeter) - Allowable Stress for Jacket Material at Design Temperature is defined as the material failure stress divided by a factor of safety greater than one.
Modulus of Elasticity Jacketed Reaction Vessel - (Measured in Newton per Square Millimeter) - Modulus of Elasticity Jacketed Reaction Vessel refers to the measure of the vessel's ability to deform elastically under an applied load.

STEP 1: Convert Input(s) to Base Unit

Vessel Shell Outer Diameter: 550 Millimeter --> 550 Millimeter No Conversion Required
Effective Length Between Stiffeners: 330 Millimeter --> 330 Millimeter No Conversion Required
Shell Thickness for Jackted Reaction Vessel: 15 Millimeter --> 15 Millimeter No Conversion Required
Cross Sectional Area of Stiffening Ring: 1640 Square Millimeter --> 1640 Square Millimeter No Conversion Required
Allowable Stress for Jacket Material: 120 Newton per Square Millimeter --> 120 Newton per Square Millimeter No Conversion Required
Modulus of Elasticity Jacketed Reaction Vessel: 170000 Newton per Square Millimeter --> 170000 Newton per Square Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_required = (D_o^(2)*L_eff*(t_{jacketedreaction}+A_s/L_eff)*f_j)/(12*E) --> (550^(2)*330*(15+1640/330)*120)/(12*170000)

Evaluating ... ...

I_required = 117263.235294118

STEP 3: Convert Result to Output's Unit

117263.235294118 Meter⁴ per Meter -->117263235294118 Millimeter⁴ per Millimeter (Check conversion here)

FINAL ANSWER

117263235294118 ≈ 1.2E+14 Millimeter⁴ per Millimeter <-- Combined Moment of Inertia of Shell and Stiffener

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Chemical Engineering » Process Equipment Design » Jacketed Reaction Vessel » Combined Moment of Inertia of Shell and Stiffener per Unit Length

Credits

Created by Heet

Thadomal Shahani Engineering College (Tsec), Mumbai

Heet has created this Calculator and 200+ more calculators!

Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has verified this Calculator and 1600+ more calculators!

< 21 Jacketed Reaction Vessel Calculators

Total Axial Stress in Vessel Shell

Go Total Axial Stress = ((Internal Pressure in Vessel*Internal Diameter of Shell)/(4*Shell Thickness*Joint Efficiency for Shell))+((Design Jacket Pressure*Internal Diameter of Half Coil)/(2*Shell Thickness*Joint Efficiency for Shell))+(2*Maximum difference between Coil and Shell Pressure*(Outer Diameter of Half Coil)^(2))/(3*Shell Thickness^(2))

Maximum Equivalent Stress at Junction with Shell

Go Maximum Equivalent Stress at Junction with Shell = (sqrt((Total Axial Stress)^(2)+(Total Hoop Stress)^(2)+(Maximum Hoop Stress in Coil at Junction with Shell)^(2)-((Total Axial Stress*Total Hoop Stress)+(Total Axial Stress*Maximum Hoop Stress in Coil at Junction with Shell)+(Maximum Hoop Stress in Coil at Junction with Shell*Total Hoop Stress))))

Total Hoop Stress in Shell

Go Total Hoop Stress = (Design Pressure Shell*Internal Diameter of Shell)/(2*Shell Thickness*Joint Efficiency for Shell)+(Design Jacket Pressure*Internal Diameter of Half Coil)/((4*Thickness of Half Coil Jacket*Weld Joint Efficiency Factor for Coil)+(2.5*Shell Thickness*Joint Efficiency for Shell))

Combined Moment of Inertia of Shell and Stiffener per Unit Length

Go Combined Moment of Inertia of Shell and Stiffener = (Vessel Shell Outer Diameter^(2)*Effective Length Between Stiffeners*(Shell Thickness for Jackted Reaction Vessel+Cross Sectional Area of Stiffening Ring/Effective Length Between Stiffeners)*Allowable Stress for Jacket Material)/(12*Modulus of Elasticity Jacketed Reaction Vessel)

Shell Thickness for Critical External Pressure

Go Critical External Pressure = (2.42*Modulus of Elasticity Jacketed Reaction Vessel)/(1-(Poisson Ratio)^(2))^(3/4)*((Vessel Thickness/Vessel Shell Outer Diameter)^(5/2)/((Length of Shell/Vessel Shell Outer Diameter)-0.45*(Vessel Thickness/Vessel Shell Outer Diameter)^(1/2)))

Depth of Torisperical Head

Go Depth of Head = Crown Radius for Jacketed Reaction Vessel-sqrt((Crown Radius for Jacketed Reaction Vessel-Vessel Shell Outer Diameter/2)*(Crown Radius for Jacketed Reaction Vessel+Vessel Shell Outer Diameter/2-2*Knuckle Radius))

Design of Shell Thickness Subjected to Internal Pressure

Go Shell Thickness for Jackted Reaction Vessel = (Internal Pressure in Vessel*Internal Diameter of Shell)/((2*Allowable Stress for Jacket Material*Joint Efficiency for Shell)-(Internal Pressure in Vessel))+Corrosion Allowance

Maximum Axial Stress in Coil at Junction with Shell

Go Maximum Axial Stress in Coil at Junction = (Design Jacket Pressure*Internal Diameter of Half Coil)/((4*Thickness of Half Coil Jacket*Weld Joint Efficiency Factor for Coil)+(2.5*Shell Thickness*Joint Efficiency for Shell))

Dished Head Thickness

Go Dished Head Thickness = ((Internal Pressure in Vessel*Crown Radius for Jacketed Reaction Vessel*Stress Intensification Factor)/(2*Allowable Stress for Jacket Material*Joint Efficiency for Shell))+Corrosion Allowance

Thickness of Bottom Head subjected to Pressure

Go Head Thickness = 4.4*Crown Radius for Jacketed Reaction Vessel*(3*(1-(Poisson Ratio)^(2)))^(1/4)*sqrt(Internal Pressure in Vessel/(2*Modulus of Elasticity Jacketed Reaction Vessel))

Thickness of Half Coil Jacket

Go Thickness of Half Coil Jacket = (Design Jacket Pressure*Internal Diameter of Half Coil)/((2*Allowable Stress for Jacket Material*Joint Efficiency for Shell))+Corrosion Allowance

Thickness of Jacket Shell for Internal Pressure

Go Required Thickness of Jacket = (Design Jacket Pressure*Internal Diameter of Shell)/((2*Allowable Stress for Jacket Material*Joint Efficiency for Shell)-Design Jacket Pressure)

Channel Jacket Thickness

Go Channel Wall Thickness = Design Length of Channel Section*(sqrt((0.12*Design Jacket Pressure)/(Allowable Stress for Jacket Material)))+Corrosion Allowance

Maximum Hoop Stress in Coil at Junction with Shell

Go Maximum Hoop Stress in Coil at Junction with Shell = (Design Jacket Pressure*Internal Diameter of Half Coil)/(2*Thickness of Half Coil Jacket*Weld Joint Efficiency Factor for Coil)

Vessel Wall Thickness for Channel Type Jacket

Go Vessel Thickness = Design Length of Channel Section*sqrt((0.167*Design Jacket Pressure)/(Allowable Stress for Jacket Material))+Corrosion Allowance

Required Plate Thickness for Dimple Jacket

Go Required Thickness of Dimple Jacket = Maximum Pitch between Steam Weld Centre Lines*sqrt(Design Jacket Pressure/(3*Allowable Stress for Jacket Material))

Required Thickness for Jacket Closer Member with Jacket Width

Go Required Thickness for Jacket Closer Member = 0.886*Jacket Width*sqrt(Design Jacket Pressure/Allowable Stress for Jacket Material)

Length of Shell under Combined Moment of Inertia

Go Length of Shell = 1.1*sqrt(Vessel Shell Outer Diameter*Vessel Thickness)

Cross Sectional Area of Stiffening Ring

Go Cross Sectional Area of Stiffening Ring = Width of Stiffener*Thickness of Stiffener

Length of Shell for Jacket

Go Length of Shell for Jacket = Length of Straight Side Jacket+1/3*Depth of Head

Jacket Width

Go Jacket Width = (Inside Diameter of Jacket-Outer Diameter of Vessel)/2

Combined Moment of Inertia of Shell and Stiffener per Unit Length Formula

What is Jacketed Reaction Vessel?

A jacketed reaction vessel is a type of vessel used in the process of chemical reactions or mixing substances together under certain conditions. The vessel is typically made of a durable material such as stainless steel or glass and is designed to withstand high temperatures and pressures. The jacket surrounding the vessel is filled with a heating or cooling medium, such as water or oil, to control the temperature of the contents inside the vessel. The jacketed design allows for precise temperature control and uniform heating or cooling of the contents inside the vessel during the reaction process. These vessels are commonly used in chemical, pharmaceutical, and food processing industries.

What is Moment of Inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotation. It is the sum of the products of each element of mass of the object with the square of its perpendicular distance from the axis of rotation. The moment of inertia is commonly denoted by the symbol "I" and has units of mass times length squared (kg·m² in the SI system). It plays an important role in various physical phenomena, including rotational motion, torque, and angular momentum.

How to Calculate Combined Moment of Inertia of Shell and Stiffener per Unit Length?

Combined Moment of Inertia of Shell and Stiffener per Unit Length calculator uses Combined Moment of Inertia of Shell and Stiffener = (Vessel Shell Outer Diameter^(2)*Effective Length Between Stiffeners*(Shell Thickness for Jackted Reaction Vessel+Cross Sectional Area of Stiffening Ring/Effective Length Between Stiffeners)*Allowable Stress for Jacket Material)/(12*Modulus of Elasticity Jacketed Reaction Vessel) to calculate the Combined Moment of Inertia of Shell and Stiffener, Combined Moment of Inertia of Shell and Stiffener per Unit Length is a property that describes the resistance of the section to bending. It is a measure of the distribution of the area of the section around its centroid. Combined Moment of Inertia of Shell and Stiffener is denoted by I_required symbol.

How to calculate Combined Moment of Inertia of Shell and Stiffener per Unit Length using this online calculator? To use this online calculator for Combined Moment of Inertia of Shell and Stiffener per Unit Length, enter Vessel Shell Outer Diameter (D_o), Effective Length Between Stiffeners (L_eff), Shell Thickness for Jackted Reaction Vessel (t_{jacketedreaction}), Cross Sectional Area of Stiffening Ring (A_s), Allowable Stress for Jacket Material (f_j) & Modulus of Elasticity Jacketed Reaction Vessel (E) and hit the calculate button. Here is how the Combined Moment of Inertia of Shell and Stiffener per Unit Length calculation can be explained with given input values -> 1.2E+23 = (0.55^(2)*0.33*(0.015+0.00164/0.33)*120000000)/(12*170000000000).

FAQ

What is Combined Moment of Inertia of Shell and Stiffener per Unit Length?

Combined Moment of Inertia of Shell and Stiffener per Unit Length is a property that describes the resistance of the section to bending. It is a measure of the distribution of the area of the section around its centroid and is represented as I_required = (D_o^(2)*L_eff*(t_{jacketedreaction}+A_s/L_eff)*f_j)/(12*E) or Combined Moment of Inertia of Shell and Stiffener = (Vessel Shell Outer Diameter^(2)*Effective Length Between Stiffeners*(Shell Thickness for Jackted Reaction Vessel+Cross Sectional Area of Stiffening Ring/Effective Length Between Stiffeners)*Allowable Stress for Jacket Material)/(12*Modulus of Elasticity Jacketed Reaction Vessel). Vessel Shell Outer Diameter refers to the outermost dimension of the cylindrical shell of a vessel, such as a tank or pressure vessel, Effective Length Between Stiffeners refers to the distance between adjacent stiffeners or bracing elements that help to prevent buckling or lateral deflection of the member, Shell Thickness for Jackted Reaction Vessel is the distance through the shell, Cross Sectional Area of Stiffening Ring in a vessel is the area of the ring when viewed in cross-section perpendicular to its axis, Allowable Stress for Jacket Material at Design Temperature is defined as the material failure stress divided by a factor of safety greater than one & Modulus of Elasticity Jacketed Reaction Vessel refers to the measure of the vessel's ability to deform elastically under an applied load.

How to calculate Combined Moment of Inertia of Shell and Stiffener per Unit Length?

Combined Moment of Inertia of Shell and Stiffener per Unit Length is a property that describes the resistance of the section to bending. It is a measure of the distribution of the area of the section around its centroid is calculated using Combined Moment of Inertia of Shell and Stiffener = (Vessel Shell Outer Diameter^(2)*Effective Length Between Stiffeners*(Shell Thickness for Jackted Reaction Vessel+Cross Sectional Area of Stiffening Ring/Effective Length Between Stiffeners)*Allowable Stress for Jacket Material)/(12*Modulus of Elasticity Jacketed Reaction Vessel). To calculate Combined Moment of Inertia of Shell and Stiffener per Unit Length, you need Vessel Shell Outer Diameter (D_o), Effective Length Between Stiffeners (L_eff), Shell Thickness for Jackted Reaction Vessel (t_{jacketedreaction}), Cross Sectional Area of Stiffening Ring (A_s), Allowable Stress for Jacket Material (f_j) & Modulus of Elasticity Jacketed Reaction Vessel (E). With our tool, you need to enter the respective value for Vessel Shell Outer Diameter, Effective Length Between Stiffeners, Shell Thickness for Jackted Reaction Vessel, Cross Sectional Area of Stiffening Ring, Allowable Stress for Jacket Material & Modulus of Elasticity Jacketed Reaction Vessel and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search