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Eccentricity given Vertical Normal Stress at Upstream Face Formula

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Eccentricity at Upstream is the distance from point of application of resultant to center of base. Check FAQs

e u = (1 - (\frac{σ z}{\frac{F v}{144 \cdot T}})) \cdot \frac{T}{6}

e_u - Eccentricity at Upstream?σ_z - Vertical Stress at a Point?F_v - Vertical Component of Force?T - Thickness of Dam?

Eccentricity given Vertical Normal Stress at Upstream Face Example

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Here is how the Eccentricity given Vertical Normal Stress at Upstream Face equation looks like with Values.

Here is how the Eccentricity given Vertical Normal Stress at Upstream Face equation looks like with Units.

Here is how the Eccentricity given Vertical Normal Stress at Upstream Face equation looks like.

-18.9933 = (1 - (\frac{2.5}{\frac{15}{144 \cdot 2.2}})) \cdot \frac{2.2}{6}

-18.9933 = (1 - (\frac{2.5Pa}{\frac{15N}{144 \cdot 2.2m}})) \cdot \frac{2.2m}{6}

-18.9933 = (1 - (\frac{2.5}{\frac{15}{144 \cdot 2.2}})) \cdot \frac{2.2}{6}

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Eccentricity given Vertical Normal Stress at Upstream Face Solution

Follow our step by step solution on how to calculate Eccentricity given Vertical Normal Stress at Upstream Face?

FIRST Step Consider the formula

e u = (1 - (\frac{σ z}{\frac{F v}{144 \cdot T}})) \cdot \frac{T}{6}

Next Step Substitute values of Variables

∴

e u = (1 - (\frac{2.5Pa}{\frac{15N}{144 \cdot 2.2m}})) \cdot \frac{2.2m}{6}

Next Step Prepare to Evaluate

∴

e u = (1 - (\frac{2.5}{\frac{15}{144 \cdot 2.2}})) \cdot \frac{2.2}{6}

Next Step Evaluate

∴

e u = -18.9933333333333

LAST Step Rounding Answer

∴

e u = -18.9933

Eccentricity given Vertical Normal Stress at Upstream Face Formula Elements

Variables

Eccentricity at Upstream

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

Symbol: e_u

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Eccentricity at Upstream

Vertical Stress at a Point

Vertical Stress at a Point is the stress acting perpendicular to the surface.

Symbol: σ_z

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Vertical Stress at a Point

Vertical Component of Force

Vertical component of force is the resolved force acting along the vertical direction.

Symbol: F_v

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Vertical Component of Force

Thickness of Dam

Thickness of Dam is the measurement or extent of dam from side to side.

Symbol: T

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Thickness of Dam

Other formulas in Gravity Dam category

Go Water Pressure in Gravity Dam

P W = 0.5 \cdot ρ Water \cdot ({H S}^{2})

Go Density of Water given Water Pressure in Gravity Dam

ρ Water = \frac{P W}{0.5} \cdot ({H S}^{2})

Go Vertical Normal Stress at Downstream Face

σ z = (\frac{F v}{144 \cdot T}) \cdot (1 + (\frac{6 \cdot e d}{T}))

Go Total Vertical Force given Vertical Normal Stress at Downstream Face

F v = \frac{σ z}{(\frac{1}{144 \cdot T}) \cdot (1 + (\frac{6 \cdot e d}{T}))}

How to Evaluate Eccentricity given Vertical Normal Stress at Upstream Face?

Eccentricity given Vertical Normal Stress at Upstream Face evaluator uses Eccentricity at Upstream = (1-(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6 to evaluate the Eccentricity at Upstream, Eccentricity given Vertical Normal Stress at Upstream Face is defined as distance from point of application of resultant to center of base. Eccentricity at Upstream is denoted by e_u symbol.

How to evaluate Eccentricity given Vertical Normal Stress at Upstream Face using this online evaluator? To use this online evaluator for Eccentricity given Vertical Normal Stress at Upstream Face, enter Vertical Stress at a Point (σ_z), Vertical Component of Force (F_v) & Thickness of Dam (T) and hit the calculate button.

FAQs on Eccentricity given Vertical Normal Stress at Upstream Face

What is the formula to find Eccentricity given Vertical Normal Stress at Upstream Face?

The formula of Eccentricity given Vertical Normal Stress at Upstream Face is expressed as Eccentricity at Upstream = (1-(Vertical Stress at a Point/(Vertical Component of Force/(144*Thickness of Dam))))*Thickness of Dam/6. Here is an example- -18.993333 = (1-(2.5/(15/(144*2.2))))*2.2/6.

How to calculate Eccentricity given Vertical Normal Stress at Upstream Face?

With Vertical Stress at a Point (σ_z), Vertical Component of Force (F_v) & Thickness of Dam (T) we can find Eccentricity given Vertical Normal Stress at Upstream Face using the formula - 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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Eccentricity given Vertical Normal Stress at Upstream Face Formula

Eccentricity given Vertical Normal Stress at Upstream Face Example

Eccentricity given Vertical Normal Stress at Upstream Face Solution

Eccentricity given Vertical Normal Stress at Upstream Face Formula Elements

Other formulas in Gravity Dam category

How to Evaluate Eccentricity given Vertical Normal Stress at Upstream Face?

FAQs on Eccentricity given Vertical Normal Stress at Upstream Face

Variable Name