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Spacing of Closed Stirrups for Torsion under Working Stress Design Formula

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Stirrup Spacing is the approximate minimum spacing between two bars in a section. Check FAQs

s = \frac{3 \cdot A t \cdot α t \cdot x 1 \cdot y 1 \cdot f v}{τ torsional - T u} \cdot Σx 2 y

s - Stirrup Spacing?A_t - Area of One Leg of Closed Stirrup?α_t - Coefficient?x₁ - Shorter Dimension Legs of Closed Stirrup?y₁ - Longer Dimension Legs of Closed Stirrup?f_v - Allowable Stress in Stirrup Steel?τ_torsional - Torsional Stress?T_u - Maximum Allowable Torsion?Σx²y - Sum for Component Rectangles of Section?

Spacing of Closed Stirrups for Torsion under Working Stress Design Example

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Here is how the Spacing of Closed Stirrups for Torsion under Working Stress Design equation looks like with Values.

Here is how the Spacing of Closed Stirrups for Torsion under Working Stress Design equation looks like with Units.

Here is how the Spacing of Closed Stirrups for Torsion under Working Stress Design equation looks like.

46.1672 = \frac{3 \cdot 100.0001 \cdot 3.5 \cdot 250 \cdot 500.0001 \cdot 35}{12 - 10} \cdot 20.1

46.1672mm = \frac{3 \cdot 100.0001mm² \cdot 3.5 \cdot 250mm \cdot 500.0001mm \cdot 35MPa}{12MPa - 10MPa} \cdot 20.1

46.1672 = \frac{3 \cdot 100.0001 \cdot 3.5 \cdot 250 \cdot 500.0001 \cdot 35}{12 - 10} \cdot 20.1

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Spacing of Closed Stirrups for Torsion under Working Stress Design Solution

Follow our step by step solution on how to calculate Spacing of Closed Stirrups for Torsion under Working Stress Design?

FIRST Step Consider the formula

s = \frac{3 \cdot A t \cdot α t \cdot x 1 \cdot y 1 \cdot f v}{τ torsional - T u} \cdot Σx 2 y

Next Step Substitute values of Variables

∴

s = \frac{3 \cdot 100.0001mm² \cdot 3.5 \cdot 250mm \cdot 500.0001mm \cdot 35MPa}{12MPa - 10MPa} \cdot 20.1

Next Step Convert Units

∴

s = \frac{3 \cdot 0.0001m² \cdot 3.5 \cdot 0.25m \cdot 0.5m \cdot 3.5E+7Pa}{1.2E+7Pa - 1E+7Pa} \cdot 20.1

Next Step Prepare to Evaluate

∴

s = \frac{3 \cdot 0.0001 \cdot 3.5 \cdot 0.25 \cdot 0.5 \cdot 3.5E+7}{1.2E+7 - 1E+7} \cdot 20.1

Next Step Evaluate

∴

s = 0.0461672475173539m

Next Step Convert to Output's Unit

∴

s = 46.1672475173539mm

LAST Step Rounding Answer

∴

s = 46.1672mm

Spacing of Closed Stirrups for Torsion under Working Stress Design Formula Elements

Variables

Stirrup Spacing

Stirrup Spacing is the approximate minimum spacing between two bars in a section.

Symbol: s

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Area of One Leg of Closed Stirrup

Area of One Leg of Closed Stirrup is the cross-sectional surface inside the reinforcing loop of a structural element.

Symbol: A_t

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Coefficient

Coefficient αt in Spacing of closed stirrups for torsion.

Symbol: α_t

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Shorter Dimension Legs of Closed Stirrup

Shorter Dimension Legs of Closed Stirrup whose main function is to hold the given RCC structure in its location.

Symbol: x₁

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Longer Dimension Legs of Closed Stirrup

Longer Dimension Legs of Closed Stirrup is the vertical length of the bent steel bars used in reinforced concrete construction.

Symbol: y₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Allowable Stress in Stirrup Steel

Allowable stress in stirrup steel is 55% of those for ultimate strength design.

Symbol: f_v

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Torsional Stress

Torsional Stress is the shear stress produced in the shaft due to the twisting.

Symbol: τ_torsional

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Maximum Allowable Torsion

Maximum Allowable Torsion in the section is the stress produced in the shaft due to the twisting.

Symbol: T_u

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

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.

Symbol: Σx²y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Formula and 2000+ more formulas!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

Other formulas in Working Stress Design for Torsion category

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T = 0.55 \cdot (0.5 \cdot f' c \cdot Σx 2 y)

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

Spacing of Closed Stirrups for Torsion under Working Stress Design evaluator 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 evaluate 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 evaluate Spacing of Closed Stirrups for Torsion under Working Stress Design using this online evaluator? To use this online evaluator 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.

FAQs on Spacing of Closed Stirrups for Torsion under Working Stress Design

What is the formula to find Spacing of Closed Stirrups for Torsion under Working Stress Design?

The formula of Spacing of Closed Stirrups for Torsion under Working Stress Design is expressed as 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. Here is an example- 45937.56 = (3*0.00010000011*3.5*0.25*0.5000001*35000000)/(12000000-10000000)*20.1.

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

With 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) we can find Spacing of Closed Stirrups for Torsion under Working Stress Design using the formula - 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.

Can the Spacing of Closed Stirrups for Torsion under Working Stress Design be negative?

No, the Spacing of Closed Stirrups for Torsion under Working Stress Design, measured in Length cannot be negative.

Which unit is used to measure Spacing of Closed Stirrups for Torsion under Working Stress Design?

Spacing of Closed Stirrups for Torsion under Working Stress Design is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Spacing of Closed Stirrups for Torsion under Working Stress Design can be measured.

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Spacing of Closed Stirrups for Torsion under Working Stress Design Formula

Spacing of Closed Stirrups for Torsion under Working Stress Design Example

Spacing of Closed Stirrups for Torsion under Working Stress Design Solution

Spacing of Closed Stirrups for Torsion under Working Stress Design Formula Elements

Credits

Other formulas in Working Stress Design for Torsion category

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

FAQs on Spacing of Closed Stirrups for Torsion under Working Stress Design

Variable Name