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

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Av = (V'LAB*s)/(fv*d'*(cos(α)+sin(α)))
This formula uses 2 Functions, 6 Variables
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Stirrup Area - (Measured in Square Meter) - Stirrup Area is the total cross-sectional area of the stirrup bars used.
Excess Shear given Stirrup Leg Area for Bars Bent - (Measured in Pascal) - Excess Shear given Stirrup Leg Area for Bars Bent is a measure that can be evaluated numerically and can be used in an assessment of the possible magnitude and relative likelihood of seismic activity.
Stirrup Spacing - (Measured in Meter) - Stirrup Spacing is the approximate minimum spacing between two bars in a section.
Allowable Stress in Stirrup Steel - (Measured in Pascal) - Allowable stress in stirrup steel is 55% of those for ultimate strength design.
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.
Angle at which Stirrup is Inclined - (Measured in Radian) - Angle at which Stirrup is Inclined series constitutes bars that are bent up at different distances from the support or when the stirrup is inclined.
STEP 1: Convert Input(s) to Base Unit
Excess Shear given Stirrup Leg Area for Bars Bent: 4785 Newton per Square Meter --> 4785 Pascal (Check conversion ​here)
Stirrup Spacing: 50.1 Millimeter --> 0.0501 Meter (Check conversion ​here)
Allowable Stress in Stirrup Steel: 35 Megapascal --> 35000000 Pascal (Check conversion ​here)
Compression to Centroid Reinforcement Distance: 10.1 Millimeter --> 0.0101 Meter (Check conversion ​here)
Angle at which Stirrup is Inclined: 30 Degree --> 0.5235987755982 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Av = (V'LAB*s)/(fv*d'*(cos(α)+sin(α))) --> (4785*0.0501)/(35000000*0.0101*(cos(0.5235987755982)+sin(0.5235987755982)))
Evaluating ... ...
Av = 0.00049644538054392
STEP 3: Convert Result to Output's Unit
0.00049644538054392 Square Meter -->496.44538054392 Square Millimeter (Check conversion ​here)
FINAL ANSWER
496.44538054392 496.4454 Square Millimeter <-- Stirrup Area
(Calculation completed in 00.004 seconds)

Credits

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Created by Ishita Goyal
Meerut Institute of Engineering and Technology (MIET), Meerut
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Verified by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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Allowable Shear Calculators

Area Required in Legs of Vertical Stirrup
​ LaTeX ​ Go Stirrup Area = (Excess Shear*Stirrup Spacing)/(Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance)
Distance from Extreme Compression to Centroid given Nominal Unit Shear Stress
​ LaTeX ​ Go Compression to Centroid Reinforcement Distance = Total Shear/(Beam Width for Nominal Shear*Nominal Shear Stress)
Nominal Unit Shear Stress
​ LaTeX ​ Go Nominal Shear Stress = Total Shear/(Beam Width for Nominal Shear*Compression to Centroid Reinforcement Distance)
Shear given Nominal Unit Shear Stress
​ LaTeX ​ Go Total Shear = Beam Width for Nominal Shear*Compression to Centroid Reinforcement Distance*Nominal Shear Stress

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

​LaTeX ​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)))
Av = (V'LAB*s)/(fv*d'*(cos(α)+sin(α)))

What is Bent-Up Bar?

The bent-up bar is the main reinforcement bent at a suitable angle to act as shear reinforcement. They are bent up to the supports where greater compressive force occurs.

How to Calculate Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances?

Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances calculator uses 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))) to calculate the Stirrup Area, The Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances formula is defined as the area of the vertical stirrup which is required to resist the shear. Stirrup Area is denoted by Av symbol.

How to calculate Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances using this online calculator? To use this online calculator for Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances, enter Excess Shear given Stirrup Leg Area for Bars Bent (V'LAB), Stirrup Spacing (s), Allowable Stress in Stirrup Steel (fv), Compression to Centroid Reinforcement Distance (d') & Angle at which Stirrup is Inclined (α) and hit the calculate button. Here is how the Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances calculation can be explained with given input values -> 5E+8 = (4785*0.0501)/(35000000*0.0101*(cos(0.5235987755982)+sin(0.5235987755982))).

FAQ

What is Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances?
The Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances formula is defined as the area of the vertical stirrup which is required to resist the shear and is represented as Av = (V'LAB*s)/(fv*d'*(cos(α)+sin(α))) or 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))). Excess Shear given Stirrup Leg Area for Bars Bent is a measure that can be evaluated numerically and can be used in an assessment of the possible magnitude and relative likelihood of seismic activity, Stirrup Spacing is the approximate minimum spacing between two bars in a section, Allowable stress in stirrup steel is 55% of those for ultimate strength design, Compression to Centroid Reinforcement Distance is the distance from extreme compression surface to the centroid of compression reinforcement & Angle at which Stirrup is Inclined series constitutes bars that are bent up at different distances from the support or when the stirrup is inclined.
How to calculate Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances?
The Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances formula is defined as the area of the vertical stirrup which is required to resist the shear is calculated using 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))). To calculate Vertical Stirrup Leg Area when Group of Bars is Bent at Different Distances, you need Excess Shear given Stirrup Leg Area for Bars Bent (V'LAB), Stirrup Spacing (s), Allowable Stress in Stirrup Steel (fv), Compression to Centroid Reinforcement Distance (d') & Angle at which Stirrup is Inclined (α). With our tool, you need to enter the respective value for Excess Shear given Stirrup Leg Area for Bars Bent, Stirrup Spacing, Allowable Stress in Stirrup Steel, Compression to Centroid Reinforcement Distance & Angle at which Stirrup is Inclined 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 Stirrup Area?
In this formula, Stirrup Area uses Excess Shear given Stirrup Leg Area for Bars Bent, Stirrup Spacing, Allowable Stress in Stirrup Steel, Compression to Centroid Reinforcement Distance & Angle at which Stirrup is Inclined. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Stirrup Area = (Excess Shear*Stirrup Spacing)/(Allowable Stress in Stirrup Steel*Compression to Centroid Reinforcement Distance)
  • Stirrup Area = Excess Shear given Vertical Stirrup Leg Area/(Allowable Stress in Stirrup Steel*sin(Angle at which Stirrup is Inclined))
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