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

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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. Check FAQs

f 1 = \frac{M 1}{k 1 \cdot π \cdot {(R)}^{2} \cdot t}

f₁ - Stress Bending Moment at Topmost of Cross Section?M₁ - Bending Moment at Support?k₁ - Value of k1 depending on Saddle Angle?R - Shell Radius?t - Shell Thickness?π - Archimedes' constant?

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

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Here is how the Stress due to Longitudinal Bending at Top most Fibre of Cross Section equation looks like with Values.

Here is how the Stress due to Longitudinal Bending at Top most Fibre of Cross Section equation looks like with Units.

Here is how the Stress due to Longitudinal Bending at Top most Fibre of Cross Section equation looks like.

0.0078 = \frac{1E+6}{0.107 \cdot 3.1416 \cdot {(1380)}^{2} \cdot 200}

0.0078N/mm² = \frac{1E+6N*mm}{0.107 \cdot 3.1416 \cdot {(1380mm)}^{2} \cdot 200mm}

0.0078 = \frac{1E+6}{0.107 \cdot 3.1416 \cdot {(1380)}^{2} \cdot 200}

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

Follow our step by step solution on how to calculate Stress due to Longitudinal Bending at Top most Fibre of Cross Section?

FIRST Step Consider the formula

f 1 = \frac{M 1}{k 1 \cdot π \cdot {(R)}^{2} \cdot t}

Next Step Substitute values of Variables

∴

f 1 = \frac{1E+6N*mm}{0.107 \cdot π \cdot {(1380mm)}^{2} \cdot 200mm}

Next Step Substitute values of Constants

∴

f 1 = \frac{1E+6N*mm}{0.107 \cdot 3.1416 \cdot {(1380mm)}^{2} \cdot 200mm}

Next Step Convert Units

∴

f 1 = \frac{1000N*m}{0.107 \cdot 3.1416 \cdot {(1.38m)}^{2} \cdot 0.2m}

Next Step Prepare to Evaluate

∴

f 1 = \frac{1000}{0.107 \cdot 3.1416 \cdot {(1.38)}^{2} \cdot 0.2}

Next Step Evaluate

∴

f 1 = 7810.48820988558Pa

Next Step Convert to Output's Unit

∴

f 1 = 0.00781048820988558N/mm²

LAST Step Rounding Answer

∴

f 1 = 0.0078N/mm²

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

Variables

Constants

Stress Bending Moment at Topmost of Cross Section

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.

Symbol: f₁

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Stress Bending Moment at Topmost of Cross Section

Bending Moment at Support

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.

Symbol: M₁

Measurement: Bending MomentUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment at Support

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.

Symbol: k₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of k1 depending on Saddle Angle

Shell Radius

Shell Radius refers to the distance from the center of the vessel to its outermost point on the cylindrical or spherical shell.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Shell Radius

Shell Thickness

Shell thickness is the the distance through the shell.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Shell Thickness

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Saddle Support category

Go Combined Stresses at Mid Span

f cs3 = f cs1 + f 3

Go Bending Moment at Support

M 1 = Q \cdot A \cdot ((1) - (\frac{1 - (\frac{A}{L}) + (\frac{{(R vessel)}^{2} - {(Depth Head)}^{2}}{2 \cdot A \cdot L})}{1 + (\frac{4}{3}) \cdot (\frac{Depth Head}{L})}))

Go Combined Stresses at Bottommost Fibre of Cross Section

f cs2 = f cs1 - f 2

Go Combined Stresses at Topmost Fibre of Cross Section

f 1cs = f cs1 + f 1

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

Stress due to Longitudinal Bending at Top most Fibre of Cross Section evaluator 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 evaluate 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 evaluate Stress due to Longitudinal Bending at Top most Fibre of Cross Section using this online evaluator? To use this online evaluator 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.

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

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

The formula of Stress due to Longitudinal Bending at Top most Fibre of Cross Section is expressed as 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). Here is an example- 7.8E-9 = 1000/(0.107*pi*(1.38)^(2)*0.2).

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

With Bending Moment at Support (M₁), Value of k1 depending on Saddle Angle (k₁), Shell Radius (R) & Shell Thickness (t) we can find Stress due to Longitudinal Bending at Top most Fibre of Cross Section using the 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). This formula also uses Archimedes' constant .

Can the Stress due to Longitudinal Bending at Top most Fibre of Cross Section be negative?

No, the Stress due to Longitudinal Bending at Top most Fibre of Cross Section, measured in Stress cannot be negative.

Which unit is used to measure Stress due to Longitudinal Bending at Top most Fibre of Cross Section?

Stress due to Longitudinal Bending at Top most Fibre of Cross Section is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Stress due to Longitudinal Bending at Top most Fibre of Cross Section can be measured.

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

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

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

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

Other formulas in Saddle Support category

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

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

Variable Name