Spacing of Closed Stirrups for Torsion under Working Stress Design Calculator

✖Area of One Leg of Closed Stirrup is the cross-sectional surface inside the reinforcing loop of a structural element.ⓘ Area of One Leg of Closed Stirrup [A_t]			+10% -10%
✖Coefficient αt in Spacing of closed stirrups for torsion.ⓘ Coefficient [α_t]			+10% -10%
✖Shorter Dimension Legs of Closed Stirrup whose main function is to hold the given RCC structure in its location.ⓘ Shorter Dimension Legs of Closed Stirrup [x₁]			+10% -10%
✖Longer Dimension Legs of Closed Stirrup is the vertical length of the bent steel bars used in reinforced concrete construction.ⓘ Longer Dimension Legs of Closed Stirrup [y₁]			+10% -10%
✖Allowable stress in stirrup steel is 55% of those for ultimate strength design.ⓘ Allowable Stress in Stirrup Steel [f_v]			+10% -10%
✖Torsional Stress is the shear stress produced in the shaft due to the twisting.ⓘ Torsional Stress [τ_torsional]			+10% -10%
✖Maximum Allowable Torsion in the section is the stress produced in the shaft due to the twisting.ⓘ Maximum Allowable Torsion [T_u]			+10% -10%
✖Sum for Component Rectangles of Section of the product of square of the shorter side and the longer side of each rectangle.ⓘ Sum for Component Rectangles of Section [Σx²y]			+10% -10%

✖Stirrup Spacing is the approximate minimum spacing between two bars in a section.ⓘ Spacing of Closed Stirrups for Torsion under Working Stress Design [s]

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Formula

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Spacing of Closed Stirrups for Torsion under Working Stress Design

Formula

`"s" = (3*"A"_{"t"}*"α"_{"t"}*"x"_{"1"}*"y"_{"1"}*"f"_{"v"})/("τ"_{"torsional"}-"T"_{"u"})*("Σx"^{"2"}"y")`

Example

`"46.16725mm"=(3*"100.00011mm²"*"3.5"*"250mm"*"500.0001mm"*"35MPa")/("12MPa"-"10MPa")*"20.1"`

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Spacing of Closed Stirrups for Torsion under Working Stress Design Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stirrup Spacing = (3*Area of One Leg of Closed Stirrup*Coefficient*Shorter Dimension Legs of Closed Stirrup*Longer Dimension Legs of Closed Stirrup*Allowable Stress in Stirrup Steel)/(Torsional Stress-Maximum Allowable Torsion)*Sum for Component Rectangles of Section
s = (3*A_t*α_t*x₁*y₁*f_v)/(τ_torsional-T_u)*Σx²y
This formula uses 9 Variables

Variables Used

Stirrup Spacing - (Measured in Meter) - Stirrup Spacing is the approximate minimum spacing between two bars in a section.
Area of One Leg of Closed Stirrup - (Measured in Square Meter) - Area of One Leg of Closed Stirrup is the cross-sectional surface inside the reinforcing loop of a structural element.
Coefficient - Coefficient αt in Spacing of closed stirrups for torsion.
Shorter Dimension Legs of Closed Stirrup - (Measured in Meter) - Shorter Dimension Legs of Closed Stirrup whose main function is to hold the given RCC structure in its location.
Longer Dimension Legs of Closed Stirrup - (Measured in Meter) - Longer Dimension Legs of Closed Stirrup is the vertical length of the bent steel bars used in reinforced concrete construction.
Allowable Stress in Stirrup Steel - (Measured in Pascal) - Allowable stress in stirrup steel is 55% of those for ultimate strength design.
Torsional Stress - (Measured in Pascal) - Torsional Stress is the shear stress produced in the shaft due to the twisting.
Maximum Allowable Torsion - (Measured in Pascal) - Maximum Allowable Torsion in the section is the stress produced in the shaft due to the twisting.
Sum for Component Rectangles of Section - Sum for Component Rectangles of Section of the product of square of the shorter side and the longer side of each rectangle.

STEP 1: Convert Input(s) to Base Unit

Area of One Leg of Closed Stirrup: 100.00011 Square Millimeter --> 0.00010000011 Square Meter (Check conversion here)
Coefficient: 3.5 --> No Conversion Required
Shorter Dimension Legs of Closed Stirrup: 250 Millimeter --> 0.25 Meter (Check conversion here)
Longer Dimension Legs of Closed Stirrup: 500.0001 Millimeter --> 0.5000001 Meter (Check conversion here)
Allowable Stress in Stirrup Steel: 35 Megapascal --> 35000000 Pascal (Check conversion here)
Torsional Stress: 12 Megapascal --> 12000000 Pascal (Check conversion here)
Maximum Allowable Torsion: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Sum for Component Rectangles of Section: 20.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

s = (3*A_t*α_t*x₁*y₁*f_v)/(τ_torsional-T_u)*Σx²y --> (3*0.00010000011*3.5*0.25*0.5000001*35000000)/(12000000-10000000)*20.1

Evaluating ... ...

s = 0.0461672475173539

STEP 3: Convert Result to Output's Unit

0.0461672475173539 Meter -->46.1672475173539 Millimeter (Check conversion here)

FINAL ANSWER

46.1672475173539 ≈ 46.16725 Millimeter <-- Stirrup Spacing

(Calculation completed in 00.004 seconds)

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< 2 Working Stress Design for Torsion Calculators

Spacing of Closed Stirrups for Torsion under Working Stress Design

Go Stirrup Spacing = (3*Area of One Leg of Closed Stirrup*Coefficient*Shorter Dimension Legs of Closed Stirrup*Longer Dimension Legs of Closed Stirrup*Allowable Stress in Stirrup Steel)/(Torsional Stress-Maximum Allowable Torsion)*Sum for Component Rectangles of Section

Maximum Torsion due to Service Load for Torsion Effects

Go Maximum Torsion = 0.55*(0.5*Specified 28-Day Compressive Strength of Concrete*Sum for Component Rectangles of Section)

Spacing of Closed Stirrups for Torsion under Working Stress Design Formula

What is a Stirrup?

Stirrup refers to a closed loop of reinforcement bar. Its main purpose is to hold the reinforcement bars together in an RCC structure.

What is the difference in application between open stirrups and closed stirrups?

Open stirrups are provided principally to resist shear forces in concrete beams and they are applied in locations in which the effect of torsion is insignificant. However, when concrete beams are designed to resist a substantial amount of torsion, closed stirrups should be used instead.

How to Calculate Spacing of Closed Stirrups for Torsion under Working Stress Design?

Spacing of Closed Stirrups for Torsion under Working Stress Design calculator uses Stirrup Spacing = (3*Area of One Leg of Closed Stirrup*Coefficient*Shorter Dimension Legs of Closed Stirrup*Longer Dimension Legs of Closed Stirrup*Allowable Stress in Stirrup Steel)/(Torsional Stress-Maximum Allowable Torsion)*Sum for Component Rectangles of Section to calculate the Stirrup Spacing, The Spacing of Closed Stirrups for Torsion under Working Stress Design formula is defined by the parameters shorter and longer dimensions of closed stirrups, allowable stress in the stirrup area, Torsional stress, Allowable Torsion stress on Concrete and sum for the component rectangles of the section of the product of the square of the shorter side and the longer side of each rectangle. Stirrup Spacing is denoted by s symbol.

How to calculate Spacing of Closed Stirrups for Torsion under Working Stress Design using this online calculator? To use this online calculator for Spacing of Closed Stirrups for Torsion under Working Stress Design, enter Area of One Leg of Closed Stirrup (A_t), Coefficient (α_t), Shorter Dimension Legs of Closed Stirrup (x₁), Longer Dimension Legs of Closed Stirrup (y₁), Allowable Stress in Stirrup Steel (f_v), Torsional Stress (τ_torsional), Maximum Allowable Torsion (T_u) & Sum for Component Rectangles of Section (Σx²y) and hit the calculate button. Here is how the Spacing of Closed Stirrups for Torsion under Working Stress Design calculation can be explained with given input values -> 45937.56 = (3*0.00010000011*3.5*0.25*0.5000001*35000000)/(12000000-10000000)*20.1.

FAQ

What is Spacing of Closed Stirrups for Torsion under Working Stress Design?

The Spacing of Closed Stirrups for Torsion under Working Stress Design formula is defined by the parameters shorter and longer dimensions of closed stirrups, allowable stress in the stirrup area, Torsional stress, Allowable Torsion stress on Concrete and sum for the component rectangles of the section of the product of the square of the shorter side and the longer side of each rectangle and is represented as s = (3*A_t*α_t*x₁*y₁*f_v)/(τ_torsional-T_u)*Σx²y or Stirrup Spacing = (3*Area of One Leg of Closed Stirrup*Coefficient*Shorter Dimension Legs of Closed Stirrup*Longer Dimension Legs of Closed Stirrup*Allowable Stress in Stirrup Steel)/(Torsional Stress-Maximum Allowable Torsion)*Sum for Component Rectangles of Section. Area of One Leg of Closed Stirrup is the cross-sectional surface inside the reinforcing loop of a structural element, Coefficient αt in Spacing of closed stirrups for torsion, Shorter Dimension Legs of Closed Stirrup whose main function is to hold the given RCC structure in its location, Longer Dimension Legs of Closed Stirrup is the vertical length of the bent steel bars used in reinforced concrete construction, Allowable stress in stirrup steel is 55% of those for ultimate strength design, Torsional Stress is the shear stress produced in the shaft due to the twisting, Maximum Allowable Torsion in the section is the stress produced in the shaft due to the twisting & Sum for Component Rectangles of Section of the product of square of the shorter side and the longer side of each rectangle.

How to calculate Spacing of Closed Stirrups for Torsion under Working Stress Design?

The Spacing of Closed Stirrups for Torsion under Working Stress Design formula is defined by the parameters shorter and longer dimensions of closed stirrups, allowable stress in the stirrup area, Torsional stress, Allowable Torsion stress on Concrete and sum for the component rectangles of the section of the product of the square of the shorter side and the longer side of each rectangle is calculated using Stirrup Spacing = (3*Area of One Leg of Closed Stirrup*Coefficient*Shorter Dimension Legs of Closed Stirrup*Longer Dimension Legs of Closed Stirrup*Allowable Stress in Stirrup Steel)/(Torsional Stress-Maximum Allowable Torsion)*Sum for Component Rectangles of Section. To calculate Spacing of Closed Stirrups for Torsion under Working Stress Design, you need Area of One Leg of Closed Stirrup (A_t), Coefficient (α_t), Shorter Dimension Legs of Closed Stirrup (x₁), Longer Dimension Legs of Closed Stirrup (y₁), Allowable Stress in Stirrup Steel (f_v), Torsional Stress (τ_torsional), Maximum Allowable Torsion (T_u) & Sum for Component Rectangles of Section (Σx²y). With our tool, you need to enter the respective value for Area of One Leg of Closed Stirrup, Coefficient, Shorter Dimension Legs of Closed Stirrup, Longer Dimension Legs of Closed Stirrup, Allowable Stress in Stirrup Steel, Torsional Stress, Maximum Allowable Torsion & Sum for Component Rectangles of Section 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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