Stress due to Longitudinal Bending at Top most Fibre of Cross Section Calculator

✖Bending Moment at Support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported.ⓘ Bending Moment at Support [M₁]			+10% -10%
✖Value of k1 depending on Saddle Angle is used in the calculation of the bending moment due to the weight of the vessel.ⓘ Value of k1 depending on Saddle Angle [k₁]			+10% -10%
✖Shell Radius refers to the distance from the center of the vessel to its outermost point on the cylindrical or spherical shell.ⓘ Shell Radius [R]			+10% -10%
✖Shell thickness is the the distance through the shell.ⓘ Shell Thickness [t]			+10% -10%

✖The Stress Bending Moment at Topmost of Cross Section refers to the amount of stress that develops at the outermost or topmost layer of a vessel.ⓘ Stress due to Longitudinal Bending at Top most Fibre of Cross Section [f₁]

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Formula

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Stress due to Longitudinal Bending at Top most Fibre of Cross Section

Formula

`"f"_{"1"} = "M"_{"1"}/("k"_{"1"}*pi*("R")^(2)*"t")`

Example

`"0.00781N/mm²"="1000000N*mm"/("0.107"*pi*("1380mm")^(2)*"200mm")`

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Stress due to Longitudinal Bending at Top most Fibre of Cross Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness)
f₁ = M₁/(k₁*pi*(R)^(2)*t)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Stress Bending Moment at Topmost of Cross Section - (Measured in Pascal) - The Stress Bending Moment at Topmost of Cross Section refers to the amount of stress that develops at the outermost or topmost layer of a vessel.
Bending Moment at Support - (Measured in Newton Meter) - Bending Moment at Support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported.
Value of k1 depending on Saddle Angle - Value of k1 depending on Saddle Angle is used in the calculation of the bending moment due to the weight of the vessel.
Shell Radius - (Measured in Meter) - Shell Radius refers to the distance from the center of the vessel to its outermost point on the cylindrical or spherical shell.
Shell Thickness - (Measured in Meter) - Shell thickness is the the distance through the shell.

STEP 1: Convert Input(s) to Base Unit

Bending Moment at Support: 1000000 Newton Millimeter --> 1000 Newton Meter (Check conversion here)
Value of k1 depending on Saddle Angle: 0.107 --> No Conversion Required
Shell Radius: 1380 Millimeter --> 1.38 Meter (Check conversion here)
Shell Thickness: 200 Millimeter --> 0.2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f₁ = M₁/(k₁*pi*(R)^(2)*t) --> 1000/(0.107*pi*(1.38)^(2)*0.2)

Evaluating ... ...

f₁ = 7810.48820988558

STEP 3: Convert Result to Output's Unit

7810.48820988558 Pascal -->0.00781048820988558 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

0.00781048820988558 ≈ 0.00781 Newton per Square Millimeter <-- Stress Bending Moment at Topmost of Cross Section

(Calculation completed in 00.020 seconds)

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< 12 Saddle Support Calculators

Bending Moment at Support

Go Bending Moment at Support = Total Load per Saddle*Distance from Tangent Line to Saddle Centre*((1)-((1-(Distance from Tangent Line to Saddle Centre/Tangent to Tangent Length of Vessel)+(((Vessel Radius)^(2)-(Depth of Head)^(2))/(2*Distance from Tangent Line to Saddle Centre*Tangent to Tangent Length of Vessel)))/(1+(4/3)*(Depth of Head/Tangent to Tangent Length of Vessel))))

Bending Moment at Centre of Vessel Span

Go Bending Moment at Centre of Vessel Span = (Total Load per Saddle*Tangent to Tangent Length of Vessel)/(4)*(((1+2*(((Vessel Radius)^(2)-(Depth of Head)^(2))/(Tangent to Tangent Length of Vessel^(2))))/(1+(4/3)*(Depth of Head/Tangent to Tangent Length of Vessel)))-(4*Distance from Tangent Line to Saddle Centre)/Tangent to Tangent Length of Vessel)

Period of Vibration at Dead Weight

Go Period of Vibration at Dead Weight = 6.35*10^(-5)*(Overall Height of Vessel/Diameter of Shell Vessel Support)^(3/2)*(Weight of Vessel with Attachments and Contents/Corroded Vessel Wall Thickness)^(1/2)

Stress due to Longitudinal Bending at Top most Fibre of Cross Section

Go Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness)

Stress due to Longitudinal Bending at Bottom most Fibre of Cross Section

Go Stress at Bottom most Fibre of Cross Section = Bending Moment at Support/(Value of k2 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness)

Stress due to Longitudinal Bending at Mid-Span

Go Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness)

Stress due to Seismic Bending Moment

Go Stress due to Seismic Bending Moment = (4*Maximum Seismic Moment)/(pi*(Mean Diameter of Skirt^(2))*Thickness of Skirt)

Combined Stresses at Topmost Fibre of Cross Section

Go Combined Stresses Topmost Fibre Cross Section = Stress due to Internal Pressure+Stress Bending Moment at Topmost of Cross Section

Combined Stresses at Bottommost Fibre of Cross Section

Go Combined Stresses Bottommost Fibre Cross Section = Stress due to Internal Pressure-Stress at Bottom most Fibre of Cross Section

Combined Stresses at Mid Span

Go Combined Stresses at Mid Span = Stress due to Internal Pressure+Stress due to Longitudinal Bending at Mid-Span

Stability Coefficient of Vessel

Go Stability Coefficient of Vessel = (Bending Moment due to Minimum Weight of Vessel)/Maximum Wind Moment

Corresponding Bending Stress with Section Modulus

Go Axial Bending Stress at Base of Vessel = Maximum Wind Moment/Section Modulus of Skirt Cross Section

Stress due to Longitudinal Bending at Top most Fibre of Cross Section Formula

Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness)
f₁ = M₁/(k₁*pi*(R)^(2)*t)

What is Cross Section?

Cross section refers to a two-dimensional view of an object or structure that has been sliced perpendicular to its axis or central line. The resulting view reveals the internal structure of the object or structure and shows its shape and dimensions. Cross sections are commonly used in engineering and science to study the internal structure of materials, components, and structures. For example, a cross section of a tree trunk can reveal its growth rings and internal structure, while a cross section of a bridge beam can show its internal reinforcing bars and other features.

How to Calculate Stress due to Longitudinal Bending at Top most Fibre of Cross Section?

Stress due to Longitudinal Bending at Top most Fibre of Cross Section calculator uses Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness) to calculate the Stress Bending Moment at Topmost of Cross Section, Stress due to Longitudinal Bending at Top most Fibre of Cross Section refers to the amount of stress that develops at the outermost or topmost layer of a beam or structural element when a bending moment is applied. Stress Bending Moment at Topmost of Cross Section is denoted by f₁ symbol.

How to calculate Stress due to Longitudinal Bending at Top most Fibre of Cross Section using this online calculator? To use this online calculator for Stress due to Longitudinal Bending at Top most Fibre of Cross Section, enter Bending Moment at Support (M₁), Value of k1 depending on Saddle Angle (k₁), Shell Radius (R) & Shell Thickness (t) and hit the calculate button. Here is how the Stress due to Longitudinal Bending at Top most Fibre of Cross Section calculation can be explained with given input values -> 7.8E-9 = 1000/(0.107*pi*(1.38)^(2)*0.2).

FAQ

What is Stress due to Longitudinal Bending at Top most Fibre of Cross Section?

Stress due to Longitudinal Bending at Top most Fibre of Cross Section refers to the amount of stress that develops at the outermost or topmost layer of a beam or structural element when a bending moment is applied and is represented as f₁ = M₁/(k₁*pi*(R)^(2)*t) or Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness). Bending Moment at Support refers to the maximum moment or torque that is experienced by a structural member, such as a beam or column, at the point where it is supported, Value of k1 depending on Saddle Angle is used in the calculation of the bending moment due to the weight of the vessel, Shell Radius refers to the distance from the center of the vessel to its outermost point on the cylindrical or spherical shell & Shell thickness is the the distance through the shell.

How to calculate Stress due to Longitudinal Bending at Top most Fibre of Cross Section?

Stress due to Longitudinal Bending at Top most Fibre of Cross Section refers to the amount of stress that develops at the outermost or topmost layer of a beam or structural element when a bending moment is applied is calculated using Stress Bending Moment at Topmost of Cross Section = Bending Moment at Support/(Value of k1 depending on Saddle Angle*pi*(Shell Radius)^(2)*Shell Thickness). To calculate Stress due to Longitudinal Bending at Top most Fibre of Cross Section, you need Bending Moment at Support (M₁), Value of k1 depending on Saddle Angle (k₁), Shell Radius (R) & Shell Thickness (t). With our tool, you need to enter the respective value for Bending Moment at Support, Value of k1 depending on Saddle Angle, Shell Radius & Shell Thickness 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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