Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress Calculator

✖Total Shear is defined as the total shear force acting on the body.ⓘ Total Shear [V]			+10% -10%
✖Beam Width for Nominal Shear is the shortest/least measurement of the beam.ⓘ Beam Width for Nominal Shear [b_ns]			+10% -10%
✖Nominal Shear Stress is the shear force generated on the structure due to the force imposed on a given cross-sectional area.ⓘ Nominal Shear Stress [V_n]			+10% -10%

✖Compression to Centroid Reinforcement Distance is the distance from extreme compression surface to the centroid of compression reinforcement.ⓘ Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress [d']

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Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress

Formula

`"d'" = "V"/("b"_{"ns"}*"V"_{"n"})`

Example

`"10mm"="3000N"/("15mm"*"20N/mm²")`

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Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress)
d' = V/(b_ns*V_n)
This formula uses 4 Variables

Variables Used

Compression to Centroid Reinforcement Distance - (Measured in Meter) - Compression to Centroid Reinforcement Distance is the distance from extreme compression surface to the centroid of compression reinforcement.
Total Shear - (Measured in Newton) - Total Shear is defined as the total shear force acting on the body.
Beam Width for Nominal Shear - (Measured in Meter) - Beam Width for Nominal Shear is the shortest/least measurement of the beam.
Nominal Shear Stress - (Measured in Pascal) - Nominal Shear Stress is the shear force generated on the structure due to the force imposed on a given cross-sectional area.

STEP 1: Convert Input(s) to Base Unit

Total Shear: 3000 Newton --> 3000 Newton No Conversion Required
Beam Width for Nominal Shear: 15 Millimeter --> 0.015 Meter (Check conversion here)
Nominal Shear Stress: 20 Newton per Square Millimeter --> 20000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d' = V/(b_ns*V_n) --> 3000/(0.015*20000000)

Evaluating ... ...

d' = 0.01

STEP 3: Convert Result to Output's Unit

0.01 Meter -->10 Millimeter (Check conversion here)

FINAL ANSWER

10 Millimeter <-- Compression to Centroid Reinforcement Distance

(Calculation completed in 00.020 seconds)

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Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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Bhilai Institute of Technology (BIT), Raipur

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< 13 Allowable Shear Calculators

Stirrups Spacing given Stirrup Leg Area for Group of Bars Bent up Different Distances

Go Stirrup Spacing = (Stirrup Area*Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance*(sin(Angle at which Stirrup is Inclined)+cos(Angle at which Stirrup is Inclined)))/(Excess Shear given Stirrup Leg Area for Bars Bent)

Excess Shear given Stirrup Leg Area for Group of Bars Bent up Different Distances

Go Excess Shear given Stirrup Leg Area for Bars Bent = (Stirrup Area*Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance*(sin(Angle at which Stirrup is Inclined)+cos(Angle at which Stirrup is Inclined)))/(Stirrup Spacing)

Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances

Go Stirrup Area = (Excess Shear given Stirrup Leg Area for Bars Bent*Stirrup Spacing)/(Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance*(cos(Angle at which Stirrup is Inclined)+sin(Angle at which Stirrup is Inclined)))

Vertical Stirrup Leg Area when Single Bar is Bent at Angle a

Go Stirrup Area = Excess Shear given Vertical Stirrup Leg Area/(Allowable Stress in Stirrup Steel*sin(Angle at which Stirrup is Inclined))

Excess Shear given Vertical Stirrup Leg Area for Single Bar Bent at Angle a

Go Excess Shear given Vertical Stirrup Leg Area = Stirrup Area*Allowable Stress in Stirrup Steel*sin(Angle at which Stirrup is Inclined)

Distance from Extreme Compression to Centroid given Area in Legs of Vertical Stirrup

Go Compression to Centroid Reinforcement Distance = (Excess Shear*Stirrup Spacing)/(Allowable Stress in Stirrup Steel*Stirrup Area)

Allowable Stress in Stirrup Steel given Area in Legs of Vertical Stirrup

Go Allowable Stress in Stirrup Steel = (Excess Shear*Stirrup Spacing)/(Stirrup Area*Compression to Centroid Reinforcement Distance)

Excess Shear given Area in Legs of Vertical Stirrup

Go Excess Shear = (Stirrup Area*Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance)/(Stirrup Spacing)

Area Required in Legs of Vertical Stirrup

Go Stirrup Area = (Excess Shear*Stirrup Spacing)/(Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance)

Stirrups Spacing using Area in Legs of Vertical Stirrup

Go Stirrup Spacing = (Stirrup Area*Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance)/Excess Shear

Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress

Go Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress)

Nominal Unit Shear Stress

Go Nominal Shear Stress = Total Shear/(Beam Width for Nominal Shear*Compression to Centroid Reinforcement Distance)

Shear given Nominal Unit Shear Stress

Go Total Shear = Beam Width for Nominal Shear*Compression to Centroid Reinforcement Distance*Nominal Shear Stress

Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress Formula

Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress)
d' = V/(b_ns*V_n)

What is Nominal Unit Shear Stress?

Nominal unit shear stress is the stress which is provided by concrete where diagonal cracking results from high tensile stress in the web.

How to Calculate Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress?

Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress calculator uses Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress) to calculate the Compression to Centroid Reinforcement Distance, The Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress formula is defined as it is used to calculate the distance from the extreme compression end to the centroid of a beam, in (mm). Compression to Centroid Reinforcement Distance is denoted by d' symbol.

How to calculate Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress using this online calculator? To use this online calculator for Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress, enter Total Shear (V), Beam Width for Nominal Shear (b_ns) & Nominal Shear Stress (V_n) and hit the calculate button. Here is how the Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress calculation can be explained with given input values -> 10000 = 3000/(0.015*20000000).

FAQ

What is Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress?

The Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress formula is defined as it is used to calculate the distance from the extreme compression end to the centroid of a beam, in (mm) and is represented as d' = V/(b_ns*V_n) or Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress). Total Shear is defined as the total shear force acting on the body, Beam Width for Nominal Shear is the shortest/least measurement of the beam & Nominal Shear Stress is the shear force generated on the structure due to the force imposed on a given cross-sectional area.

How to calculate Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress?

The Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress formula is defined as it is used to calculate the distance from the extreme compression end to the centroid of a beam, in (mm) is calculated using Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress). To calculate Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress, you need Total Shear (V), Beam Width for Nominal Shear (b_ns) & Nominal Shear Stress (V_n). With our tool, you need to enter the respective value for Total Shear, Beam Width for Nominal Shear & Nominal Shear Stress 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 Compression to Centroid Reinforcement Distance?

In this formula, Compression to Centroid Reinforcement Distance uses Total Shear, Beam Width for Nominal Shear & Nominal Shear Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

Compression to Centroid Reinforcement Distance = (Excess Shear*Stirrup Spacing)/(Allowable Stress in Stirrup Steel*Stirrup Area)

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