Eccentricity for Vertical Normal Stress at Downstream Face Calculator

✖Vertical Stress at a Point is the stress acting perpendicular to the surface.ⓘ Vertical Stress at a Point [σ_z]			+10% -10%
✖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 Downstream is the distance from point of application of resultant to center of base.ⓘ Eccentricity for Vertical Normal Stress at Downstream Face [e_d]

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Formula

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Eccentricity for Vertical Normal Stress at Downstream Face

Formula

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

Example

`"19.72667"=(1+("2.5Pa"/("15N"/(144*"2.2m"))))*"2.2m"/6`

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Eccentricity for Vertical Normal Stress at Downstream Face Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Eccentricity at Downstream - Eccentricity at Downstream is the distance from point of application of resultant to center of base.
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.

STEP 1: Convert Input(s) to Base Unit

Vertical Stress at a Point: 2.5 Pascal --> 2.5 Pascal No Conversion Required
Vertical Component of Force: 15 Newton --> 15 Newton No Conversion Required
Thickness of Dam: 2.2 Meter --> 2.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_d = (1+(σ_z/(F_v/(144*T))))*T/6 --> (1+(2.5/(15/(144*2.2))))*2.2/6

Evaluating ... ...

e_d = 19.7266666666667

STEP 3: Convert Result to Output's Unit

19.7266666666667 --> No Conversion Required

FINAL ANSWER

19.7266666666667 ≈ 19.72667 <-- Eccentricity at Downstream

(Calculation completed in 00.020 seconds)

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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

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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)

Eccentricity for Vertical Normal Stress at Downstream Face Formula

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

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How to Calculate Eccentricity for Vertical Normal Stress at Downstream Face?

Eccentricity for Vertical Normal Stress at Downstream Face calculator uses Eccentricity at Downstream = (1+(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6 to calculate the Eccentricity at Downstream, Eccentricity for Vertical Normal Stress at Downstream Face is defined as distance from the centroid. Eccentricity at Downstream is denoted by e_d symbol.

How to calculate Eccentricity for Vertical Normal Stress at Downstream Face using this online calculator? To use this online calculator for Eccentricity for Vertical Normal Stress at Downstream Face, enter Vertical Stress at a Point (σ_z), Vertical Component of Force (F_v) & Thickness of Dam (T) and hit the calculate button. Here is how the Eccentricity for Vertical Normal Stress at Downstream Face calculation can be explained with given input values -> 19.72667 = (1+(2.5/(15/(144*2.2))))*2.2/6.

FAQ

What is Eccentricity for Vertical Normal Stress at Downstream Face?

Eccentricity for Vertical Normal Stress at Downstream Face is defined as distance from the centroid and is represented as e_d = (1+(σ_z/(F_v/(144*T))))*T/6 or Eccentricity at Downstream = (1+(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6. Vertical Stress at a Point is the stress acting perpendicular to the surface, 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.

How to calculate Eccentricity for Vertical Normal Stress at Downstream Face?

Eccentricity for Vertical Normal Stress at Downstream Face is defined as distance from the centroid is calculated using Eccentricity at Downstream = (1+(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6. To calculate Eccentricity for Vertical Normal Stress at Downstream Face, you need Vertical Stress at a Point (σ_z), Vertical Component of Force (F_v) & Thickness of Dam (T). With our tool, you need to enter the respective value for Vertical Stress at a Point, Vertical Component of Force & Thickness of Dam 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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