Stirrups area for Inclined Stirrups Calculator

✖Strength of Shear reinforcements are designed to withstand shear or diagonal stresses acting on the structure.ⓘ Strength of Shear Reinforcement [Vs]			+10% -10%
✖Stirrup Spacing is the approximate minimum spacing between two bars in a section.ⓘ Stirrup Spacing [s]			+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%
✖Yield Strength of Reinforcement is stress at which a predetermined amount of permanent deformation occurs.ⓘ Yield Strength of Reinforcement [f_y]			+10% -10%
✖Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.ⓘ Effective Depth of Beam [d_eff]			+10% -10%

✖Stirrup Area is the total cross-sectional area of the stirrup bars used.ⓘ Stirrups area for Inclined Stirrups [A_v]

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Formula

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Stirrups area for Inclined Stirrups

Formula

`"A"_{"v"} = ("Vs"*"s")/((sin("α")+cos("α"))*"f"_{"y"}*"d"_{"eff"})`

Example

`"183.5623mm²"=("200kN"*"50.1mm")/((sin("30°")+cos("30°"))*"9.99MPa"*"4m")`

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Stirrups area for Inclined Stirrups Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
A_v = (Vs*s)/((sin(α)+cos(α))*f_y*d_eff)
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.
Strength of Shear Reinforcement - (Measured in Newton) - Strength of Shear reinforcements are designed to withstand shear or diagonal stresses acting on the structure.
Stirrup Spacing - (Measured in Meter) - Stirrup Spacing is the approximate minimum spacing between two bars in a section.
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.
Yield Strength of Reinforcement - (Measured in Pascal) - Yield Strength of Reinforcement is stress at which a predetermined amount of permanent deformation occurs.
Effective Depth of Beam - (Measured in Meter) - Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.

STEP 1: Convert Input(s) to Base Unit

Strength of Shear Reinforcement: 200 Kilonewton --> 200000 Newton (Check conversion here)
Stirrup Spacing: 50.1 Millimeter --> 0.0501 Meter (Check conversion here)
Angle at which Stirrup is inclined: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Yield Strength of Reinforcement: 9.99 Megapascal --> 9990000 Pascal (Check conversion here)
Effective Depth of Beam: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_v = (Vs*s)/((sin(α)+cos(α))*f_y*d_eff) --> (200000*0.0501)/((sin(0.5235987755982)+cos(0.5235987755982))*9990000*4)

Evaluating ... ...

A_v = 0.000183562289585589

STEP 3: Convert Result to Output's Unit

0.000183562289585589 Square Meter -->183.562289585589 Square Millimeter (Check conversion here)

FINAL ANSWER

183.562289585589 ≈ 183.5623 Square Millimeter <-- Stirrup Area

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Structural Engineering » Concrete Structures » Design for Beams and Ultimate Strength for Rectangular Beams with Tension Reinforcement » Shear Reinforcement » Stirrups area for Inclined Stirrups

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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

Stirrups area for Inclined Stirrups Formula

What is a Stirrup?

A stirrup is the reinforcement used to resist shear and diagonal tension stresses in a concrete structural member.

What is the Purpose of Using Stirrups?

The main purpose of stirrup is to hold the primary reinforcement bars. They also prevent columns and beams from buckling.

How to Calculate Stirrups area for Inclined Stirrups?

Stirrups area for Inclined Stirrups calculator uses 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) to calculate the Stirrup Area, The Stirrups area for Inclined Stirrups defined as area cut by a plane normal to the axis of the bars when bars are bent at different distances from support. Stirrup Area is denoted by A_v symbol.

How to calculate Stirrups area for Inclined Stirrups using this online calculator? To use this online calculator for Stirrups area for Inclined Stirrups, enter Strength of Shear Reinforcement (Vs), Stirrup Spacing (s), Angle at which Stirrup is inclined (α), Yield Strength of Reinforcement (f_y) & Effective Depth of Beam (d_eff) and hit the calculate button. Here is how the Stirrups area for Inclined Stirrups calculation can be explained with given input values -> 1.8E+8 = (200000*0.0501)/((sin(0.5235987755982)+cos(0.5235987755982))*9990000*4).

FAQ

What is Stirrups area for Inclined Stirrups?

The Stirrups area for Inclined Stirrups defined as area cut by a plane normal to the axis of the bars when bars are bent at different distances from support and is represented as A_v = (Vs*s)/((sin(α)+cos(α))*f_y*d_eff) or 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). Strength of Shear reinforcements are designed to withstand shear or diagonal stresses acting on the structure, Stirrup Spacing is the approximate minimum spacing between two bars in a section, 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, Yield Strength of Reinforcement is stress at which a predetermined amount of permanent deformation occurs & Effective Depth of Beam is the distance from the centroid of tension steel to the outermost face of the compression fiber.

How to calculate Stirrups area for Inclined Stirrups?

The Stirrups area for Inclined Stirrups defined as area cut by a plane normal to the axis of the bars when bars are bent at different distances from support is calculated using 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). To calculate Stirrups area for Inclined Stirrups, you need Strength of Shear Reinforcement (Vs), Stirrup Spacing (s), Angle at which Stirrup is inclined (α), Yield Strength of Reinforcement (f_y) & Effective Depth of Beam (d_eff). With our tool, you need to enter the respective value for Strength of Shear Reinforcement, Stirrup Spacing, Angle at which Stirrup is inclined, Yield Strength of Reinforcement & Effective Depth of Beam 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, Stirrup Spacing, Angle at which Stirrup is inclined, Yield Strength of Reinforcement & Effective Depth of Beam. 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)/(Yield Strength of Reinforcement)*sin(Angle at which Stirrup is inclined)

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