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Vertical Stress at a Point is the stress acting perpendicular to the surface. Check FAQs
σz=(z⋅γ⋅cos((I)))
σz - Vertical Stress at a Point?z - Depth of Prism?γ - Unit Weight of Soil?I - Angle of Inclination?

Vertical Stress on Surface of Prism given Unit Weight of Soil Example

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Here is how the Vertical Stress on Surface of Prism given Unit Weight of Soil equation looks like with Values.

Here is how the Vertical Stress on Surface of Prism given Unit Weight of Soil equation looks like with Units.

Here is how the Vertical Stress on Surface of Prism given Unit Weight of Soil equation looks like.

9.377Edit=(3Edit⋅18Edit⋅cos((80Edit)))
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Vertical Stress on Surface of Prism given Unit Weight of Soil Solution

Follow our step by step solution on how to calculate Vertical Stress on Surface of Prism given Unit Weight of Soil?

FIRST Step Consider the formula
σz=(z⋅γ⋅cos((I)))
Next Step Substitute values of Variables
∴ σz=(3m⋅18kN/m³⋅cos((80°)))
Next Step Convert Units
∴ σz=(3m⋅18kN/m³⋅cos((1.3963rad)))
Next Step Prepare to Evaluate
∴ σz=(3⋅18⋅cos((1.3963)))
Next Step Evaluate
∴σz=9377001.59402826Pa
Next Step Convert to Output's Unit
∴σz=9.37700159402826MPa
LAST Step Rounding Answer
∴σz=9.377MPa

Vertical Stress on Surface of Prism given Unit Weight of Soil Formula Elements

Variables
Functions
Vertical Stress at a Point
Vertical Stress at a Point is the stress acting perpendicular to the surface.
Symbol: σz
Measurement: PressureUnit: MPa
Note: Value should be greater than 0.
Formulas to find Vertical Stress at a PointOpen Variable
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 PrismOpen Variable
Unit Weight of Soil
Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Symbol: γ
Measurement: Specific WeightUnit: kN/m³
Note: Value should be greater than 0.
Formulas to find Unit Weight of SoilOpen Variable
Angle of Inclination
Angle of Inclination 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 InclinationOpen Variable
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 Vertical Stress at a Point

​Go Vertical Stress on Surface of Prism
σz=Wb

Other formulas in Stability Analysis of Infinite Slopes in Prism category

​Go Weight of Soil Prism in Stability Analysis
W=(γ⋅z⋅b⋅cos((I)))
​Go Unit Weight of Soil given Weight of Soil Prism
γ=Wz⋅b⋅cos((I))
​Go Inclined Length along Slope given Weight of Soil Prism
b=Wγ⋅z⋅cos((I))
​Go Depth of Prism given Weight of Soil Prism
z=Wγ⋅b⋅cos((I))

How to Evaluate Vertical Stress on Surface of Prism given Unit Weight of Soil?

Vertical Stress on Surface of Prism given Unit Weight of Soil evaluator uses Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination))) to evaluate the Vertical Stress at a Point, The Vertical Stress on Surface of Prism given Unit Weight of Soil is defined as the product of unit weight of soil and depth below the surface. Vertical Stress at a Point is denoted by σz symbol.

How to evaluate Vertical Stress on Surface of Prism given Unit Weight of Soil using this online evaluator? To use this online evaluator for Vertical Stress on Surface of Prism given Unit Weight of Soil, enter Depth of Prism (z), Unit Weight of Soil (γ) & Angle of Inclination (I) and hit the calculate button.

FAQs on Vertical Stress on Surface of Prism given Unit Weight of Soil

What is the formula to find Vertical Stress on Surface of Prism given Unit Weight of Soil?
The formula of Vertical Stress on Surface of Prism given Unit Weight of Soil is expressed as Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination))). Here is an example- 9.4E-9 = (3*18000*cos((1.3962634015952))).
How to calculate Vertical Stress on Surface of Prism given Unit Weight of Soil?
With Depth of Prism (z), Unit Weight of Soil (γ) & Angle of Inclination (I) we can find Vertical Stress on Surface of Prism given Unit Weight of Soil using the formula - Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination))). This formula also uses Cosine (cos) function(s).
What are the other ways to Calculate Vertical Stress at a Point?
Here are the different ways to Calculate Vertical Stress at a Point-
  • Vertical Stress at a Point=Weight of Prism/Inclined LengthOpenImg
Can the Vertical Stress on Surface of Prism given Unit Weight of Soil be negative?
No, the Vertical Stress on Surface of Prism given Unit Weight of Soil, measured in Pressure cannot be negative.
Which unit is used to measure Vertical Stress on Surface of Prism given Unit Weight of Soil?
Vertical Stress on Surface of Prism given Unit Weight of Soil is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Vertical Stress on Surface of Prism given Unit Weight of Soil can be measured.
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