Stirrup Area given Support Angle Calculator

✖Strength of Shear reinforcements are designed to withstand shear or diagonal stresses acting on the structure.ⓘ Strength of Shear Reinforcement [Vs]			+10% -10%
✖Yield Strength of Reinforcement is stress at which a predetermined amount of permanent deformation occurs.ⓘ Yield Strength of Reinforcement [f_y]			+10% -10%
✖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.ⓘ Angle at which Stirrup is inclined [α]			+10% -10%

✖Stirrup Area is the total cross-sectional area of the stirrup bars used.ⓘ Stirrup Area given Support Angle [A_v]

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Formula

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Stirrup Area given Support Angle

Formula

`"A"_{"v"} = ("Vs")/("f"_{"y"})*sin("α")`

Example

`"10010.01mm²"=("200kN")/("9.99MPa")*sin("30°")`

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Download Design for Beams and Ultimate Strength for Rectangular Beams with Tension Reinforcement Formulas PDF

Stirrup Area given Support Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined)
A_v = (Vs)/(f_y)*sin(α)
This formula uses 1 Functions, 4 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)

Variables Used

Stirrup Area - (Measured in Square Meter) - Stirrup Area is the total cross-sectional area of the stirrup bars used.
Strength of Shear Reinforcement - (Measured in Newton) - Strength of Shear reinforcements are designed to withstand shear or diagonal stresses acting on the structure.
Yield Strength of Reinforcement - (Measured in Pascal) - Yield Strength of Reinforcement is stress at which a predetermined amount of permanent deformation occurs.
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

Strength of Shear Reinforcement: 200 Kilonewton --> 200000 Newton (Check conversion here)
Yield Strength of Reinforcement: 9.99 Megapascal --> 9990000 Pascal (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

A_v = (Vs)/(f_y)*sin(α) --> (200000)/(9990000)*sin(0.5235987755982)

Evaluating ... ...

A_v = 0.01001001001001

STEP 3: Convert Result to Output's Unit

0.01001001001001 Square Meter -->10010.01001001 Square Millimeter (Check conversion here)

FINAL ANSWER

10010.01001001 ≈ 10010.01 Square Millimeter <-- Stirrup Area

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 12 Shear Reinforcement Calculators

Nominal Shear Strength of Concrete

Go Nominal Shear Strength of Concrete = (1.9*sqrt(28 Day Compressive Strength of Concrete)+((2500*Reinforcement Ratio of Web Section)*((Shear Force in considered Section*Centroidal Distance of Tension Reinforcement)/Bending Moment of Considered Section)))*(Width of Beam Web*Centroidal Distance of Tension Reinforcement)

Stirrup Area given Stirrup Spacing in Practical Design

Go Stirrup Area = (Stirrup Spacing)*(Design of Shear Stress-(2*Capacity Reduction Factor*sqrt(28 Day Compressive Strength of Concrete)*Effective Depth of Beam*Breadth of Web))/(Capacity Reduction Factor*Yield Strength of Reinforcement*Effective Depth of Beam)

Stirrup Spacing for Practical Design

Go Stirrup Spacing = (Stirrup Area*Capacity Reduction Factor*Yield Strength of Steel*Effective Depth of Beam)/((Design of Shear Stress)-((2*Capacity Reduction Factor)*sqrt(28 Day Compressive Strength of Concrete)*Breadth of Web*Effective Depth of Beam))

Stirrups area for Inclined Stirrups

Go Stirrup Area = (Strength of Shear Reinforcement*Stirrup Spacing)/((sin(Angle at which Stirrup is inclined)+cos(Angle at which Stirrup is inclined))*Yield Strength of Reinforcement*Effective Depth of Beam)

Area of Steel Required in Vertical Stirrups

Go Area of Steel required = (Nominal Shear Strength by Reinforcement*Stirrup Spacing)/(Yield Strength of Steel*Centroidal Distance of Tension Reinforcement)

Stirrup Area given Support Angle

Go Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined)

Nominal Reinforcement Shear Strength for Stirrup Area with Support Angle

Go Nominal Shear Strength by Reinforcement = Stirrup Area*Yield Strength of Steel*sin(Angle at which Stirrup is inclined)

Bar Diameter given Development Length for Hooked Bar

Go Bar Diameter = ((Development Length)*(sqrt(28 Day Compressive Strength of Concrete)))/1200

Development Length for Hooked Bar

Go Development Length = (1200*Bar Diameter)/sqrt(28 Day Compressive Strength of Concrete)

Ultimate Shear Capacity of Beam Section

Go Ultimate Shear Capacity = (Nominal Shear Strength of Concrete+Nominal Shear Strength by Reinforcement)

Nominal Shear Strength Provided by Reinforcement

Go Nominal Shear Strength by Reinforcement = Ultimate Shear Capacity-Nominal Shear Strength of Concrete

28 Day Concrete Compressive Strength given Development Length for Hooked Bar

Go 28 Day Compressive Strength of Concrete = ((1200*Bar Diameter)/(Development Length))^2

Stirrup Area given Support Angle Formula

Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined)
A_v = (Vs)/(f_y)*sin(α)

What is a Stirrup?

A stirrup is a steel bar bent into a "U" or box shape and installed perpendicular to, or at an angle to the longitudinal reinforcement. and properly anchored in RCC members.

Why do we give Stirrups?

Stirrups are placed at proper intervals to beams to prevent them from deformation/shear failure of beam. This is done to prevent shear failure which is usually diagonal in case of cracks in beams.

How to Calculate Stirrup Area given Support Angle?

Stirrup Area given Support Angle calculator uses Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined) to calculate the Stirrup Area, The Stirrup Area given Support Angle is defined as the area required when a single bar or a group of parallel bars are all bent up at the same distance from the support at an angle with the longitudinal axis of the member. Stirrup Area is denoted by A_v symbol.

How to calculate Stirrup Area given Support Angle using this online calculator? To use this online calculator for Stirrup Area given Support Angle, enter Strength of Shear Reinforcement (Vs), Yield Strength of Reinforcement (f_y) & Angle at which Stirrup is inclined (α) and hit the calculate button. Here is how the Stirrup Area given Support Angle calculation can be explained with given input values -> 1E+10 = (200000)/(9990000)*sin(0.5235987755982).

FAQ

What is Stirrup Area given Support Angle?

The Stirrup Area given Support Angle is defined as the area required when a single bar or a group of parallel bars are all bent up at the same distance from the support at an angle with the longitudinal axis of the member and is represented as A_v = (Vs)/(f_y)*sin(α) or Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined). Strength of Shear reinforcements are designed to withstand shear or diagonal stresses acting on the structure, Yield Strength of Reinforcement is stress at which a predetermined amount of permanent deformation occurs & 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 Stirrup Area given Support Angle?

The Stirrup Area given Support Angle is defined as the area required when a single bar or a group of parallel bars are all bent up at the same distance from the support at an angle with the longitudinal axis of the member is calculated using Stirrup Area = (Strength of Shear Reinforcement)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined). To calculate Stirrup Area given Support Angle, you need Strength of Shear Reinforcement (Vs), Yield Strength of Reinforcement (f_y) & Angle at which Stirrup is inclined (α). With our tool, you need to enter the respective value for Strength of Shear Reinforcement, Yield Strength of Reinforcement & 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 Strength of Shear Reinforcement, Yield Strength of Reinforcement & Angle at which Stirrup is inclined. We can use 2 other way(s) to calculate the same, which is/are as follows -

Stirrup Area = (Stirrup Spacing)*(Design of Shear Stress-(2*Capacity Reduction Factor*sqrt(28 Day Compressive Strength of Concrete)*Effective Depth of Beam*Breadth of Web))/(Capacity Reduction Factor*Yield Strength of Reinforcement*Effective Depth of Beam)
Stirrup Area = (Strength of Shear Reinforcement*Stirrup Spacing)/((sin(Angle at which Stirrup is inclined)+cos(Angle at which Stirrup is inclined))*Yield Strength of Reinforcement*Effective Depth of Beam)

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