Stress due to Longitudinal Bending at Mid-Span Calculator

✖Bending Moment at Centre of Vessel Span refers to the maximum bending moment that occurs at the midpoint of a vessel's span, which is the distance between the supports that hold up the vessel.ⓘ Bending Moment at Centre of Vessel Span [M₂]			+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%

✖Stress due to Longitudinal Bending at Mid-Spann refers to the amount of stress that develops at the extreme fibre located at the bottom of a cross section.ⓘ Stress due to Longitudinal Bending at Mid-Span [f₃]

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Stress due to Longitudinal Bending at Mid-Span

Formula

`"f"_{"3"} = "M"_{"2"}/(pi*("R")^(2)*"t")`

Example

`"26.12199N/mm²"="31256789045N*mm"/(pi*("1380mm")^(2)*"200mm")`

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Stress due to Longitudinal Bending at Mid-Span Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness)
f₃ = M₂/(pi*(R)^(2)*t)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Stress due to Longitudinal Bending at Mid-Span - (Measured in Pascal) - Stress due to Longitudinal Bending at Mid-Spann refers to the amount of stress that develops at the extreme fibre located at the bottom of a cross section.
Bending Moment at Centre of Vessel Span - (Measured in Newton Meter) - Bending Moment at Centre of Vessel Span refers to the maximum bending moment that occurs at the midpoint of a vessel's span, which is the distance between the supports that hold up 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 Centre of Vessel Span: 31256789045 Newton Millimeter --> 31256789.045 Newton Meter (Check conversion here)
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

f₃ = M₂/(pi*(R)^(2)*t) --> 31256789.045/(pi*(1.38)^(2)*0.2)

Evaluating ... ...

f₃ = 26121993.7076893

STEP 3: Convert Result to Output's Unit

26121993.7076893 Pascal -->26.1219937076893 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

26.1219937076893 ≈ 26.12199 Newton per Square Millimeter <-- Stress due to Longitudinal Bending at Mid-Span

(Calculation completed in 00.021 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 Mid-Span Formula

Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness)
f₃ = M₂/(pi*(R)^(2)*t)

What is Design Stress?

Design stress refers to the maximum allowable stress that a material or structure can withstand under certain design conditions without experiencing deformation or failure. It is a key factor in engineering design, as it ensures that a structure or component will be able to function safely and effectively under anticipated loading conditions. Design stress is typically determined through various types of analysis, including theoretical calculations, computer simulations, and physical testing. The specific factors that are taken into account when determining design stress include the type of material used, the geometry and shape of the structure, the anticipated loads and forces that will be applied, and the operating environment in which the structure will be used.

How to Calculate Stress due to Longitudinal Bending at Mid-Span?

Stress due to Longitudinal Bending at Mid-Span calculator uses Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness) to calculate the Stress due to Longitudinal Bending at Mid-Span, Stress due to Longitudinal Bending at Mid-Span refers to the maximum tensile and compressive stresses experienced by a structural member at the point of maximum bending moment, which is typically located at the center of the span. Stress due to Longitudinal Bending at Mid-Span is denoted by f₃ symbol.

How to calculate Stress due to Longitudinal Bending at Mid-Span using this online calculator? To use this online calculator for Stress due to Longitudinal Bending at Mid-Span, enter Bending Moment at Centre of Vessel Span (M₂), Shell Radius (R) & Shell Thickness (t) and hit the calculate button. Here is how the Stress due to Longitudinal Bending at Mid-Span calculation can be explained with given input values -> 2.6E-5 = 31256789.045/(pi*(1.38)^(2)*0.2).

FAQ

What is Stress due to Longitudinal Bending at Mid-Span?

Stress due to Longitudinal Bending at Mid-Span refers to the maximum tensile and compressive stresses experienced by a structural member at the point of maximum bending moment, which is typically located at the center of the span and is represented as f₃ = M₂/(pi*(R)^(2)*t) or Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness). Bending Moment at Centre of Vessel Span refers to the maximum bending moment that occurs at the midpoint of a vessel's span, which is the distance between the supports that hold up 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 Mid-Span?

Stress due to Longitudinal Bending at Mid-Span refers to the maximum tensile and compressive stresses experienced by a structural member at the point of maximum bending moment, which is typically located at the center of the span is calculated using Stress due to Longitudinal Bending at Mid-Span = Bending Moment at Centre of Vessel Span/(pi*(Shell Radius)^(2)*Shell Thickness). To calculate Stress due to Longitudinal Bending at Mid-Span, you need Bending Moment at Centre of Vessel Span (M₂), Shell Radius (R) & Shell Thickness (t). With our tool, you need to enter the respective value for Bending Moment at Centre of Vessel Span, 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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