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Normal Stress Component given Submerged Unit Weight and Depth of Prism Formula

GoNormal Stress Component given Saturated Unit Weight Formula

GoNormal Stress Component given Effective Normal Stress Formula

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Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force. Check FAQs

σ n = F u + (y S \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

σ_n - Normal Stress in Soil Mechanics?F_u - Upward Force in Seepage Analysis?y_S - Submerged Unit Weight in KN per Cubic Meter?z - Depth of Prism?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Normal Stress Component given Submerged Unit Weight and Depth of Prism Example

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Here is how the Normal Stress Component given Submerged Unit Weight and Depth of Prism equation looks like with Values.

Here is how the Normal Stress Component given Submerged Unit Weight and Depth of Prism equation looks like with Units.

Here is how the Normal Stress Component given Submerged Unit Weight and Depth of Prism equation looks like.

67.8843 = 52.89 + (5 \cdot 3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})

67.8843kN/m² = 52.89kN/m² + (5kN/m³ \cdot 3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})

67.8843 = 52.89 + (5 \cdot 3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})

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Normal Stress Component given Submerged Unit Weight and Depth of Prism Solution

Follow our step by step solution on how to calculate Normal Stress Component given Submerged Unit Weight and Depth of Prism?

FIRST Step Consider the formula

σ n = F u + (y S \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

Next Step Substitute values of Variables

∴

σ n = 52.89kN/m² + (5kN/m³ \cdot 3m \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2})

Next Step Substitute values of Constants

∴

σ n = 52.89kN/m² + (5kN/m³ \cdot 3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})

Next Step Convert Units

∴

σ n = 52890Pa + (5000N/m³ \cdot 3m \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2})

Next Step Prepare to Evaluate

∴

σ n = 52890 + (5000 \cdot 3 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2})

Next Step Evaluate

∴

σ n = 67884.2995957502Pa

Next Step Convert to Output's Unit

∴

σ n = 67.8842995957502kN/m²

LAST Step Rounding Answer

∴

σ n = 67.8843kN/m²

Normal Stress Component given Submerged Unit Weight and Depth of Prism Formula Elements

Variables

Constants

Functions

Normal Stress in Soil Mechanics

Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.

Symbol: σ_n

Measurement: StressUnit: kN/m²

Note: Value can be positive or negative.

Formulas to find Normal Stress in Soil Mechanics

Upward Force in Seepage Analysis

Upward Force in Seepage Analysis is due to seepage water.

Symbol: F_u

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Upward Force in Seepage Analysis

Submerged Unit Weight in KN per Cubic Meter

Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.

Symbol: y_S

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight in KN per Cubic Meter

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

Angle of Inclination to Horizontal in Soil

Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination to Horizontal in Soil

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Normal Stress in Soil Mechanics

Go Normal Stress Component given Saturated Unit Weight

σ n = (γ saturated \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

Go Normal Stress Component given Effective Normal Stress

σ n = σ' + F u

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

W prism = (γ saturated \cdot z \cdot b \cdot \cos (\frac{i \cdot π}{180}))

Go Inclined Length of Prism given Saturated Unit Weight

b = \frac{W prism}{γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180})}

Go Vertical Stress on Prism given Saturated Unit Weight

σ zkp = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}))

Go Shear Stress Component given Saturated Unit Weight

ζ soil = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180}))

How to Evaluate Normal Stress Component given Submerged Unit Weight and Depth of Prism?

Normal Stress Component given Submerged Unit Weight and Depth of Prism evaluator uses Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Normal Stress in Soil Mechanics, The Normal Stress Component given Submerged Unit Weight and Depth of Prism is defined as the value of normal stress acting on soil when we have prior information of other parameters used. Normal Stress in Soil Mechanics is denoted by σ_n symbol.

How to evaluate Normal Stress Component given Submerged Unit Weight and Depth of Prism using this online evaluator? To use this online evaluator for Normal Stress Component given Submerged Unit Weight and Depth of Prism, enter Upward Force in Seepage Analysis (F_u), Submerged Unit Weight in KN per Cubic Meter (y_S), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Normal Stress Component given Submerged Unit Weight and Depth of Prism

What is the formula to find Normal Stress Component given Submerged Unit Weight and Depth of Prism?

The formula of Normal Stress Component given Submerged Unit Weight and Depth of Prism is expressed as Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.067884 = 52890+(5000*3*(cos((1.11701072127616*pi)/180))^2).

How to calculate Normal Stress Component given Submerged Unit Weight and Depth of Prism?

With Upward Force in Seepage Analysis (F_u), Submerged Unit Weight in KN per Cubic Meter (y_S), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) we can find Normal Stress Component given Submerged Unit Weight and Depth of Prism using the formula - Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Normal Stress in Soil Mechanics?

Here are the different ways to Calculate Normal Stress in Soil Mechanics-

Normal Stress in Soil Mechanics=(Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Normal Stress in Soil Mechanics=Effective Normal Stress in Soil Mechanics+Upward Force in Seepage Analysis

Can the Normal Stress Component given Submerged Unit Weight and Depth of Prism be negative?

Yes, the Normal Stress Component given Submerged Unit Weight and Depth of Prism, measured in Stress can be negative.

Which unit is used to measure Normal Stress Component given Submerged Unit Weight and Depth of Prism?

Normal Stress Component given Submerged Unit Weight and Depth of Prism is usually measured using the Kilonewton per Square Meter[kN/m²] for Stress. Pascal[kN/m²], Newton per Square Meter[kN/m²], Newton per Square Millimeter[kN/m²] are the few other units in which Normal Stress Component given Submerged Unit Weight and Depth of Prism can be measured.

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Normal Stress Component given Submerged Unit Weight and Depth of Prism Formula

​GoNormal Stress Component given Saturated Unit Weight Formula

​GoNormal Stress Component given Effective Normal Stress Formula

Normal Stress Component given Submerged Unit Weight and Depth of Prism Example

Normal Stress Component given Submerged Unit Weight and Depth of Prism Solution

Normal Stress Component given Submerged Unit Weight and Depth of Prism Formula Elements

Other Formulas to find Normal Stress in Soil Mechanics

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Normal Stress Component given Submerged Unit Weight and Depth of Prism?

FAQs on Normal Stress Component given Submerged Unit Weight and Depth of Prism

Variable Name

GoNormal Stress Component given Saturated Unit Weight Formula

GoNormal Stress Component given Effective Normal Stress Formula