Minimum Vertical Direct Stress Distribution at Base Calculator

✖Total vertical force forces that act in the vertical plane, which is perpendicular to the ground.ⓘ Total Vertical Force [Σ_v]			+10% -10%
✖Base width is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis.ⓘ Base Width [B]			+10% -10%
✖Eccentricity of Resultant Force is a force that does not pass through the Centre of gravity of the body on which it acts or through a point at which the body is fixed.ⓘ Eccentricity of Resultant Force [e]			+10% -10%

✖Minimum vertical direct stress is the stress which is induced due to the applied load when it is perpendicular to the body or structure.ⓘ Minimum Vertical Direct Stress Distribution at Base [ρ_min]

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Formula

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Minimum Vertical Direct Stress Distribution at Base

Formula

`"ρ"_{"min"} = ("Σ"_{"v"}/"B")*(1-(6*"e"/"B"))`

Example

`"8.96kN/m²"=("1400kN"/"25m")*(1-(6*"3.5"/"25m"))`

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Minimum Vertical Direct Stress Distribution at Base Solution

STEP 0: Pre-Calculation Summary

Formula Used

Minimum Vertical Direct Stress = (Total Vertical Force/Base Width)*(1-(6*Eccentricity of Resultant Force/Base Width))
ρ_min = (Σ_v/B)*(1-(6*e/B))
This formula uses 4 Variables

Variables Used

Minimum Vertical Direct Stress - (Measured in Pascal) - Minimum vertical direct stress is the stress which is induced due to the applied load when it is perpendicular to the body or structure.
Total Vertical Force - (Measured in Newton) - Total vertical force forces that act in the vertical plane, which is perpendicular to the ground.
Base Width - (Measured in Meter) - Base width is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis.
Eccentricity of Resultant Force - Eccentricity of Resultant Force is a force that does not pass through the Centre of gravity of the body on which it acts or through a point at which the body is fixed.

STEP 1: Convert Input(s) to Base Unit

Total Vertical Force: 1400 Kilonewton --> 1400000 Newton (Check conversion here)
Base Width: 25 Meter --> 25 Meter No Conversion Required
Eccentricity of Resultant Force: 3.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ_min = (Σ_v/B)*(1-(6*e/B)) --> (1400000/25)*(1-(6*3.5/25))

Evaluating ... ...

ρ_min = 8960

STEP 3: Convert Result to Output's Unit

8960 Pascal -->8.96 Kilonewton per Square Meter (Check conversion here)

FINAL ANSWER

8.96 Kilonewton per Square Meter <-- Minimum Vertical Direct Stress

(Calculation completed in 00.020 seconds)

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Coorg institute of technology (CIT), Kodagu

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< 7 Structural Stability of Gravity Dams Calculators

Shear Friction Factor

Go Shear Friction = ((Coefficient of Friction between Two Surfaces*Total Vertical Force)+(Base Width*Average Shear of Joint))/Horizontal Forces

Maximum Height in Elementary Profile without Exceeding Allowable Compressive Stress of Dam

Go Minimum Possible Height = Allowable Compressive Stress of Dam Material/(Unit Weight of Water*(Specific Gravity of Dam Material-Seepage Coefficient at Base of Dam+1))

Minimum Vertical Direct Stress Distribution at Base

Go Minimum Vertical Direct Stress = (Total Vertical Force/Base Width)*(1-(6*Eccentricity of Resultant Force/Base Width))

Width of Elementary Gravity Dam

Go Base Width = Height of Elementary Dam/sqrt(Specific Gravity of Dam Material-Seepage Coefficient at Base of Dam)

Max Vertical Direct Stress Distribution at Base

Go Vertical Direct Stress = (Total Vertical Force/Base Width)*(1+(6*Eccentricity of Resultant Force/Base Width))

Maximum Possible Height when Uplift is Neglected in Elementary Profile of Gravity Dam

Go Maximum Possible Height = Allowable Compressive Stress of Dam Material/(Unit Weight of Water*(Specific Gravity of Dam Material+1))

Sliding Factor

Go Sliding Factor = Coefficient of Friction between Two Surfaces*Total Vertical Force/Horizontal Forces

Minimum Vertical Direct Stress Distribution at Base Formula

Minimum Vertical Direct Stress = (Total Vertical Force/Base Width)*(1-(6*Eccentricity of Resultant Force/Base Width))
ρ_min = (Σ_v/B)*(1-(6*e/B))

What causes Direct Stress?

The direct stress σz is produced by bending moments or by the bending action of shear loads, while the shear stresses are due to shear and/or torsion of a closed section beam or shear of an open section beam.

What is the Direct Stress formula?

The stresses which are acting normal to the plane of the body are called normal or direct stresses. Direct stress (σd) is produced when applied load acts on a body. Mathematically,

σd= Axial applied compressive or tensile load/Area of cross section = P / A

How to Calculate Minimum Vertical Direct Stress Distribution at Base?

Minimum Vertical Direct Stress Distribution at Base calculator uses Minimum Vertical Direct Stress = (Total Vertical Force/Base Width)*(1-(6*Eccentricity of Resultant Force/Base Width)) to calculate the Minimum Vertical Direct Stress, The Minimum Vertical Direct Stress Distribution at Base formula is defined as the direct stress which is induced due to the applied load when it is perpendicular to the body or structure. Minimum Vertical Direct Stress is denoted by ρ_min symbol.

How to calculate Minimum Vertical Direct Stress Distribution at Base using this online calculator? To use this online calculator for Minimum Vertical Direct Stress Distribution at Base, enter Total Vertical Force (Σ_v), Base Width (B) & Eccentricity of Resultant Force (e) and hit the calculate button. Here is how the Minimum Vertical Direct Stress Distribution at Base calculation can be explained with given input values -> 0.00896 = (1400000/25)*(1-(6*3.5/25)).

FAQ

What is Minimum Vertical Direct Stress Distribution at Base?

The Minimum Vertical Direct Stress Distribution at Base formula is defined as the direct stress which is induced due to the applied load when it is perpendicular to the body or structure and is represented as ρ_min = (Σ_v/B)*(1-(6*e/B)) or Minimum Vertical Direct Stress = (Total Vertical Force/Base Width)*(1-(6*Eccentricity of Resultant Force/Base Width)). Total vertical force forces that act in the vertical plane, which is perpendicular to the ground, Base width is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis & Eccentricity of Resultant Force is a force that does not pass through the Centre of gravity of the body on which it acts or through a point at which the body is fixed.

How to calculate Minimum Vertical Direct Stress Distribution at Base?

The Minimum Vertical Direct Stress Distribution at Base formula is defined as the direct stress which is induced due to the applied load when it is perpendicular to the body or structure is calculated using Minimum Vertical Direct Stress = (Total Vertical Force/Base Width)*(1-(6*Eccentricity of Resultant Force/Base Width)). To calculate Minimum Vertical Direct Stress Distribution at Base, you need Total Vertical Force (Σ_v), Base Width (B) & Eccentricity of Resultant Force (e). With our tool, you need to enter the respective value for Total Vertical Force, Base Width & Eccentricity of Resultant Force 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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