Vertical Normal Stress at Upstream Face Calculator

✖Vertical component of force is the resolved force acting along the vertical direction.ⓘ Vertical Component of Force [F_v]			+10% -10%
✖Thickness of Dam is the measurement or extent of dam from side to side.ⓘ Thickness of Dam [T]			+10% -10%
✖Eccentricity at Upstream is the distance from point of application of resultant to center of base.ⓘ Eccentricity at Upstream [e_u]			+10% -10%

✖Vertical Stress at a Point is the stress acting perpendicular to the surface.ⓘ Vertical Normal Stress at Upstream Face [σ_z]

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Formula

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Vertical Normal Stress at Upstream Face

Formula

`"σ"_{"z"} = ("F"_{"v"}/(144*"T"))*(1-((6*"e"_{"u"})/"T"))`

Example

`"2.500861Pa"=("15N"/(144*"2.2m"))*(1-((6*"-19")/"2.2m"))`

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Vertical Normal Stress at Upstream Face Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam))
σ_z = (F_v/(144*T))*(1-((6*e_u)/T))
This formula uses 4 Variables

Variables Used

Vertical Stress at a Point - (Measured in Pascal) - Vertical Stress at a Point is the stress acting perpendicular to the surface.
Vertical Component of Force - (Measured in Newton) - Vertical component of force is the resolved force acting along the vertical direction.
Thickness of Dam - (Measured in Meter) - Thickness of Dam is the measurement or extent of dam from side to side.
Eccentricity at Upstream - Eccentricity at Upstream is the distance from point of application of resultant to center of base.

STEP 1: Convert Input(s) to Base Unit

Vertical Component of Force: 15 Newton --> 15 Newton No Conversion Required
Thickness of Dam: 2.2 Meter --> 2.2 Meter No Conversion Required
Eccentricity at Upstream: -19 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_z = (F_v/(144*T))*(1-((6*e_u)/T)) --> (15/(144*2.2))*(1-((6*(-19))/2.2))

Evaluating ... ...

σ_z = 2.5008608815427

STEP 3: Convert Result to Output's Unit

2.5008608815427 Pascal --> No Conversion Required

FINAL ANSWER

2.5008608815427 ≈ 2.500861 Pascal <-- Vertical Stress at a Point

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Birsa Institute of Technology (BIT), Sindri

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< 8 Gravity Dam Calculators

Total Vertical Force given Vertical Normal Stress at Downstream Face

Go Vertical Component of Force = Vertical Stress at a Point/((1/(144*Thickness of Dam))*(1+((6*Eccentricity at Downstream)/Thickness of Dam)))

Total Vertical Force for Vertical Normal Stress at Upstream Face

Go Vertical Component of Force = Vertical Stress at a Point/((1/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam)))

Vertical Normal Stress at Downstream Face

Go Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1+((6*Eccentricity at Downstream)/Thickness of Dam))

Eccentricity for Vertical Normal Stress at Downstream Face

Go Eccentricity at Downstream = (1+(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6

Vertical Normal Stress at Upstream Face

Go Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam))

Eccentricity given Vertical Normal Stress at Upstream Face

Go Eccentricity at Upstream = (1-(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6

Density of Water given Water Pressure in Gravity Dam

Go Water Density = Water Pressure in Gravity Dam/0.5*(Height of Section^2)

Water Pressure in Gravity Dam

Go Water Pressure in Gravity Dam = 0.5*Water Density*(Height of Section^2)

Vertical Normal Stress at Upstream Face Formula

Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam))
σ_z = (F_v/(144*T))*(1-((6*e_u)/T))

What is Safe Bearing Capacity of the Soil?

Safe bearing capacity of soil field test is done to check the capacity of the soil to withstand loads .The maximum load per unit area which the soil can bear without any displacement or settlements is designated as the “Safe bearing capacity of the soil.”

How to Calculate Vertical Normal Stress at Upstream Face?

Vertical Normal Stress at Upstream Face calculator uses Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam)) to calculate the Vertical Stress at a Point, Vertical Normal Stress at Upstream Face formula is defined as the minimum bearing capacity of the soil in tension. Vertical Stress at a Point is denoted by σ_z symbol.

How to calculate Vertical Normal Stress at Upstream Face using this online calculator? To use this online calculator for Vertical Normal Stress at Upstream Face, enter Vertical Component of Force (F_v), Thickness of Dam (T) & Eccentricity at Upstream (e_u) and hit the calculate button. Here is how the Vertical Normal Stress at Upstream Face calculation can be explained with given input values -> -2.406164 = (15/(144*2.2))*(1-((6*(-19))/2.2)).

FAQ

What is Vertical Normal Stress at Upstream Face?

Vertical Normal Stress at Upstream Face formula is defined as the minimum bearing capacity of the soil in tension and is represented as σ_z = (F_v/(144*T))*(1-((6*e_u)/T)) or Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam)). Vertical component of force is the resolved force acting along the vertical direction, Thickness of Dam is the measurement or extent of dam from side to side & Eccentricity at Upstream is the distance from point of application of resultant to center of base.

How to calculate Vertical Normal Stress at Upstream Face?

Vertical Normal Stress at Upstream Face formula is defined as the minimum bearing capacity of the soil in tension is calculated using Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1-((6*Eccentricity at Upstream)/Thickness of Dam)). To calculate Vertical Normal Stress at Upstream Face, you need Vertical Component of Force (F_v), Thickness of Dam (T) & Eccentricity at Upstream (e_u). With our tool, you need to enter the respective value for Vertical Component of Force, Thickness of Dam & Eccentricity at Upstream and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Vertical Stress at a Point?

In this formula, Vertical Stress at a Point uses Vertical Component of Force, Thickness of Dam & Eccentricity at Upstream. We can use 1 other way(s) to calculate the same, which is/are as follows -

Vertical Stress at a Point = (Vertical Component of Force/(144*Thickness of Dam))*(1+((6*Eccentricity at Downstream)/Thickness of Dam))

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