Maximum Equivalent Stress at Junction with Shell Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))))
fe = (sqrt((fas)^(2)+(fcs)^(2)+(fcc)^(2)-((fas*fcs)+(fas*fcc)+(fcc*fcs))))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Maximum Equivalent Stress at Junction with Shell - (Measured in Newton per Square Millimeter) - Maximum Equivalent Stress at Junction with Shell at stress elements on material or part must be smaller from the yield strength of that used material.
Total Axial Stress - (Measured in Newton per Square Millimeter) - The Total Axial Stress in the Vessel formula is defined as the result of a force acting perpendicular to an area of a vessel, causing the extension or compression of the vessel.
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.
Maximum Hoop Stress in Coil at Junction with Shell - (Measured in Newton per Square Millimeter) - Maximum Hoop Stress in Coil at Junction with Shell is the stress around the circumference of the pipe due to a pressure gradient.
STEP 1: Convert Input(s) to Base Unit
Total Axial Stress: 1.2 Newton per Square Millimeter --> 1.2 Newton per Square Millimeter No Conversion Required
Total Hoop Stress: 2.7 Newton per Square Millimeter --> 2.7 Newton per Square Millimeter No Conversion Required
Maximum Hoop Stress in Coil at Junction with Shell: 0.421875 Newton per Square Millimeter --> 0.421875 Newton per Square Millimeter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fe = (sqrt((fas)^(2)+(fcs)^(2)+(fcc)^(2)-((fas*fcs)+(fas*fcc)+(fcc*fcs)))) --> (sqrt((1.2)^(2)+(2.7)^(2)+(0.421875)^(2)-((1.2*2.7)+(1.2*0.421875)+(0.421875*2.7))))
Evaluating ... ...
fe = 2.0056584992528
STEP 3: Convert Result to Output's Unit
2005658.4992528 Pascal -->2.0056584992528 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
2.0056584992528 2.005658 Newton per Square Millimeter <-- Maximum Equivalent Stress at Junction with Shell
(Calculation completed in 00.004 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

Maximum Equivalent Stress at Junction with Shell Formula

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))))
fe = (sqrt((fas)^(2)+(fcs)^(2)+(fcc)^(2)-((fas*fcs)+(fas*fcc)+(fcc*fcs))))

What is 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 Maximum Equivalent Stress at Junction with Shell?

Maximum Equivalent Stress at Junction with Shell calculator uses 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)))) to calculate the Maximum Equivalent Stress at Junction with Shell, The Maximum Equivalent Stress at Junction with Shell is defined as stress elements on shell or part must be smaller from the yield strength of that used material. Maximum Equivalent Stress at Junction with Shell is denoted by fe symbol.

How to calculate Maximum Equivalent Stress at Junction with Shell using this online calculator? To use this online calculator for Maximum Equivalent Stress at Junction with Shell, enter Total Axial Stress (fas), Total Hoop Stress (fcs) & Maximum Hoop Stress in Coil at Junction with Shell (fcc) and hit the calculate button. Here is how the Maximum Equivalent Stress at Junction with Shell calculation can be explained with given input values -> 2E-6 = (sqrt((1200000)^(2)+(2700000)^(2)+(421875)^(2)-((1200000*2700000)+(1200000*421875)+(421875*2700000)))).

FAQ

What is Maximum Equivalent Stress at Junction with Shell?
The Maximum Equivalent Stress at Junction with Shell is defined as stress elements on shell or part must be smaller from the yield strength of that used material and is represented as fe = (sqrt((fas)^(2)+(fcs)^(2)+(fcc)^(2)-((fas*fcs)+(fas*fcc)+(fcc*fcs)))) or 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)))). The Total Axial Stress in the Vessel formula is defined as the result of a force acting perpendicular to an area of a vessel, causing the extension or compression of the vessel, 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 & Maximum Hoop Stress in Coil at Junction with Shell is the stress around the circumference of the pipe due to a pressure gradient.
How to calculate Maximum Equivalent Stress at Junction with Shell?
The Maximum Equivalent Stress at Junction with Shell is defined as stress elements on shell or part must be smaller from the yield strength of that used material is calculated using 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)))). To calculate Maximum Equivalent Stress at Junction with Shell, you need Total Axial Stress (fas), Total Hoop Stress (fcs) & Maximum Hoop Stress in Coil at Junction with Shell (fcc). With our tool, you need to enter the respective value for Total Axial Stress, Total Hoop Stress & Maximum Hoop Stress in Coil at Junction with Shell 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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