Total Hoop Stress in Shell Calculator

✖Design Pressure Shell refers to the maximum allowable pressure that the shell can withstand without experiencing permanent deformation or failure.ⓘ Design Pressure Shell [p_shell]			+10% -10%
✖Internal Diameter of Shell is a measurement of the distance of a straight line from one point on the inner wall of the object, through its center, to an opposite point also on the inside.ⓘ Internal Diameter of Shell [D_i]			+10% -10%
✖Shell thickness is the the distance through the shell.ⓘ Shell Thickness [t]			+10% -10%
✖Joint Efficiency for Shell refers to the effectiveness of the joint between two adjacent sections of a cylindrical shell, such as in a pressure vessel or a storage tank.ⓘ Joint Efficiency for Shell [J]			+10% -10%
✖Design Jacket Pressure refers to a type of pressure vessel designed to withstand high pressures and temperatures, typically used for containing gases or liquids under extreme conditions.ⓘ Design Jacket Pressure [p_j]			+10% -10%
✖Internal Diameter of Half Coil is a measurement of the distance of a straight line from one point on the inner wall of the object, through its center, to an opposite point also on the inside.ⓘ Internal Diameter of Half Coil [d_i]			+10% -10%
✖Thickness of Half Coil Jacket can be determined by considering the heat transfer coefficient, the surface area of the coil, and the temperature difference.ⓘ Thickness of Half Coil Jacket [t_coil]			+10% -10%
✖Weld Joint Efficiency Factor for Coil is a measure of the strength of the weld relative to the strength of the base metal.ⓘ Weld Joint Efficiency Factor for Coil [J_coil]			+10% -10%

✖The Total Hoop Stress in the Shell formula is defined as is the stress around the circumference of the shell due to a pressure gradient.ⓘ Total Hoop Stress in Shell [f_cs]

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Formula

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Total Hoop Stress in Shell

Formula

`"f"_{"cs"} = ("p"_{"shell"}*"D"_{"i"})/(2*"t"*"J")+("p"_{"j"}*"d"_{"i"})/((4*"t"_{"coil"}*"J"_{"coil"})+(2.5*"t"*"J"))`

Example

`"2.703724N/mm²"=("0.61N/mm²"*"1500mm")/(2*"200mm"*"0.85")+("0.105N/mm²"*"54mm")/((4*"11.2mm"*"0.6")+(2.5*"200mm"*"0.85"))`

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Total Hoop Stress in Shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
f_cs = (p_shell*D_i)/(2*t*J)+(p_j*d_i)/((4*t_coil*J_coil)+(2.5*t*J))
This formula uses 9 Variables

Variables Used

Total Hoop Stress - (Measured in Newton per Square Millimeter) - The Total Hoop Stress in the Shell formula is defined as is the stress around the circumference of the shell due to a pressure gradient.
Design Pressure Shell - (Measured in Newton per Square Millimeter) - Design Pressure Shell refers to the maximum allowable pressure that the shell can withstand without experiencing permanent deformation or failure.
Internal Diameter of Shell - (Measured in Millimeter) - Internal Diameter of Shell is a measurement of the distance of a straight line from one point on the inner wall of the object, through its center, to an opposite point also on the inside.
Shell Thickness - (Measured in Millimeter) - Shell thickness is the the distance through the shell.
Joint Efficiency for Shell - Joint Efficiency for Shell refers to the effectiveness of the joint between two adjacent sections of a cylindrical shell, such as in a pressure vessel or a storage tank.
Design Jacket Pressure - (Measured in Newton per Square Millimeter) - Design Jacket Pressure refers to a type of pressure vessel designed to withstand high pressures and temperatures, typically used for containing gases or liquids under extreme conditions.
Internal Diameter of Half Coil - (Measured in Millimeter) - Internal Diameter of Half Coil is a measurement of the distance of a straight line from one point on the inner wall of the object, through its center, to an opposite point also on the inside.
Thickness of Half Coil Jacket - (Measured in Millimeter) - Thickness of Half Coil Jacket can be determined by considering the heat transfer coefficient, the surface area of the coil, and the temperature difference.
Weld Joint Efficiency Factor for Coil - Weld Joint Efficiency Factor for Coil is a measure of the strength of the weld relative to the strength of the base metal.

STEP 1: Convert Input(s) to Base Unit

Design Pressure Shell: 0.61 Newton per Square Millimeter --> 0.61 Newton per Square Millimeter No Conversion Required
Internal Diameter of Shell: 1500 Millimeter --> 1500 Millimeter No Conversion Required
Shell Thickness: 200 Millimeter --> 200 Millimeter No Conversion Required
Joint Efficiency for Shell: 0.85 --> No Conversion Required
Design Jacket Pressure: 0.105 Newton per Square Millimeter --> 0.105 Newton per Square Millimeter No Conversion Required
Internal Diameter of Half Coil: 54 Millimeter --> 54 Millimeter No Conversion Required
Thickness of Half Coil Jacket: 11.2 Millimeter --> 11.2 Millimeter No Conversion Required
Weld Joint Efficiency Factor for Coil: 0.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_cs = (p_shell*D_i)/(2*t*J)+(p_j*d_i)/((4*t_coil*J_coil)+(2.5*t*J)) --> (0.61*1500)/(2*200*0.85)+(0.105*54)/((4*11.2*0.6)+(2.5*200*0.85))

Evaluating ... ...

f_cs = 2.70372404959151

STEP 3: Convert Result to Output's Unit

2703724.04959151 Pascal -->2.70372404959151 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

2.70372404959151 ≈ 2.703724 Newton per Square Millimeter <-- Total Hoop Stress

(Calculation completed in 00.011 seconds)

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< 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

Total Hoop Stress in Shell Formula

What id Design Stress?

Stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as force per unit area. When an object is pulled apart by a force it will cause elongation which is also known as deformation, like the stretching of an elastic band, it is called tensile stress. But, when the forces result in the compression of an object, it is called compressive stress.

How to Calculate Total Hoop Stress in Shell?

Total Hoop Stress in Shell calculator uses 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)) to calculate the Total Hoop Stress, The Total Hoop Stress in Shell formula is defined as is the stress around the circumference of the shell due to a pressure gradient. Total Hoop Stress is denoted by f_cs symbol.

How to calculate Total Hoop Stress in Shell using this online calculator? To use this online calculator for Total Hoop Stress in Shell, enter Design Pressure Shell (p_shell), Internal Diameter of Shell (D_i), Shell Thickness (t), Joint Efficiency for Shell (J), Design Jacket Pressure (p_j), Internal Diameter of Half Coil (d_i), Thickness of Half Coil Jacket (t_coil) & Weld Joint Efficiency Factor for Coil (J_coil) and hit the calculate button. Here is how the Total Hoop Stress in Shell calculation can be explained with given input values -> 2.7E-6 = (610000*1.5)/(2*0.2*0.85)+(105000*0.054)/((4*0.0112*0.6)+(2.5*0.2*0.85)).

FAQ

What is Total Hoop Stress in Shell?

The Total Hoop Stress in Shell formula is defined as is the stress around the circumference of the shell due to a pressure gradient and is represented as f_cs = (p_shell*D_i)/(2*t*J)+(p_j*d_i)/((4*t_coil*J_coil)+(2.5*t*J)) or 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)). Design Pressure Shell refers to the maximum allowable pressure that the shell can withstand without experiencing permanent deformation or failure, Internal Diameter of Shell is a measurement of the distance of a straight line from one point on the inner wall of the object, through its center, to an opposite point also on the inside, Shell thickness is the the distance through the shell, Joint Efficiency for Shell refers to the effectiveness of the joint between two adjacent sections of a cylindrical shell, such as in a pressure vessel or a storage tank, Design Jacket Pressure refers to a type of pressure vessel designed to withstand high pressures and temperatures, typically used for containing gases or liquids under extreme conditions, Internal Diameter of Half Coil is a measurement of the distance of a straight line from one point on the inner wall of the object, through its center, to an opposite point also on the inside, Thickness of Half Coil Jacket can be determined by considering the heat transfer coefficient, the surface area of the coil, and the temperature difference & Weld Joint Efficiency Factor for Coil is a measure of the strength of the weld relative to the strength of the base metal.

How to calculate Total Hoop Stress in Shell?

The Total Hoop Stress in Shell formula is defined as is the stress around the circumference of the shell due to a pressure gradient is calculated using 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)). To calculate Total Hoop Stress in Shell, you need Design Pressure Shell (p_shell), Internal Diameter of Shell (D_i), Shell Thickness (t), Joint Efficiency for Shell (J), Design Jacket Pressure (p_j), Internal Diameter of Half Coil (d_i), Thickness of Half Coil Jacket (t_coil) & Weld Joint Efficiency Factor for Coil (J_coil). With our tool, you need to enter the respective value for Design Pressure Shell, Internal Diameter of Shell, Shell Thickness, Joint Efficiency for Shell, Design Jacket Pressure, Internal Diameter of Half Coil, Thickness of Half Coil Jacket & Weld Joint Efficiency Factor for Coil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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