Compressive Stress due to External Moment Calculator

✖The Bending Moment in Prestress is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Prestress [M_b]			+10% -10%
✖Distance from Centroidal Axis defines the distance from the extreme fiber of the concrete section to centroidal axis of the section.ⓘ Distance from Centroidal Axis [y]			+10% -10%
✖Moment of Inertia of section is defined as a property of a two-dimensional plane shape that characterizes its deflection under loading.ⓘ Moment of Inertia of Section [I_a]			+10% -10%

✖Bending Stress in Section in the prestressed concrete section is the internal resistance of the section. Here it can be due to axial force, moment and eccentric load.ⓘ Compressive Stress due to External Moment [f]

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Formula

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Compressive Stress due to External Moment

Formula

`"f" = "M"_{"b"}*("y"/"I"_{"a"})`

Example

`"166.6667MPa"="4kN*m"*("30mm"/"720000mm⁴")`

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Download General Principles of Prestressed Concrete Formulas PDF

Compressive Stress due to External Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section)
f = M_b*(y/I_a)
This formula uses 4 Variables

Variables Used

Bending Stress in Section - (Measured in Pascal) - Bending Stress in Section in the prestressed concrete section is the internal resistance of the section. Here it can be due to axial force, moment and eccentric load.
Bending Moment in Prestress - (Measured in Newton Meter) - The Bending Moment in Prestress is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Distance from Centroidal Axis - (Measured in Meter) - Distance from Centroidal Axis defines the distance from the extreme fiber of the concrete section to centroidal axis of the section.
Moment of Inertia of Section - (Measured in Meter⁴) - Moment of Inertia of section is defined as a property of a two-dimensional plane shape that characterizes its deflection under loading.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Prestress: 4 Kilonewton Meter --> 4000 Newton Meter (Check conversion here)
Distance from Centroidal Axis: 30 Millimeter --> 0.03 Meter (Check conversion here)
Moment of Inertia of Section: 720000 Millimeter⁴ --> 7.2E-07 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = M_b*(y/I_a) --> 4000*(0.03/7.2E-07)

Evaluating ... ...

f = 166666666.666667

STEP 3: Convert Result to Output's Unit

166666666.666667 Pascal -->166.666666666667 Megapascal (Check conversion here)

FINAL ANSWER

166.666666666667 ≈ 166.6667 Megapascal <-- Bending Stress in Section

(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad

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< 12 General Principles of Prestressed Concrete Calculators

Resulting Stress due to Moment and Prestress and Eccentric Strands

Go Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(External Moment*Distance from Centroidal Axis/Moment of Inertia of Section)+(Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section)

Resulting Stress due to Moment and Prestressing Force

Go Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(Bending Moment in Prestress*Distance from Centroidal Axis/Moment of Inertia of Section)

Stress due to Prestress Moment

Go Bending Stress in Section = Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section

Compressive Stress due to External Moment

Go Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section)

Length of Span given Uniform Load

Go Span Length = sqrt(8*Sag Length of Cable*Prestressing Force/Uniform Load)

External Moment with Known Compressive Stress

Go External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis

Prestressing Force given Uniform Load

Go Prestressing Force = Uniform Load*Span Length^2/(8*Sag Length of Cable)

Sag of Parabola given Uniform Load

Go Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force)

Upward Uniform Load using Load Balancing Method

Go Uniform Load = 8*Prestressing Force*Sag Length of Cable/Span Length^2

Cross Sectional Area given Compressive Stress

Go Area of Beam Section = Prestressing Force/Compressive Stress in Prestress

Uniform Compressive Stress due to Prestress

Go Compressive Stress in Prestress = Prestressing Force/Area of Beam Section

Prestressing Force given Compressive Stress

Go Prestressing Force = Area of Beam Section*Compressive Stress in Prestress

Compressive Stress due to External Moment Formula

Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section)
f = M_b*(y/I_a)

What is Pre-Tensioned Concrete Section?

Pre-Tensioned Concrete is a variant of prestressed concrete where the tendons are tensioned prior to the concrete being cast. The concrete bonds to the tendons as it cures, following which the end-anchoring of the tendons is released, and the tendon tension forces are transferred to the concrete as compression by static friction. Pre-tensioned concrete is most commonly used for the fabrication of structural beams, floor slabs, hollow-core planks, balconies, lintels, driven piles, water tanks and concrete pipes.

How to Calculate Compressive Stress due to External Moment?

Compressive Stress due to External Moment calculator uses Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section) to calculate the Bending Stress in Section, The Compressive Stress due to External Moment is defined when the concrete section is subjected to an external moment M due to load or weight on beam. Bending Stress in Section is denoted by f symbol.

How to calculate Compressive Stress due to External Moment using this online calculator? To use this online calculator for Compressive Stress due to External Moment, enter Bending Moment in Prestress (M_b), Distance from Centroidal Axis (y) & Moment of Inertia of Section (I_a) and hit the calculate button. Here is how the Compressive Stress due to External Moment calculation can be explained with given input values -> 0.000167 = 4000*(0.03/7.2E-07).

FAQ

What is Compressive Stress due to External Moment?

The Compressive Stress due to External Moment is defined when the concrete section is subjected to an external moment M due to load or weight on beam and is represented as f = M_b*(y/I_a) or Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section). The Bending Moment in Prestress is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Distance from Centroidal Axis defines the distance from the extreme fiber of the concrete section to centroidal axis of the section & Moment of Inertia of section is defined as a property of a two-dimensional plane shape that characterizes its deflection under loading.

How to calculate Compressive Stress due to External Moment?

The Compressive Stress due to External Moment is defined when the concrete section is subjected to an external moment M due to load or weight on beam is calculated using Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section). To calculate Compressive Stress due to External Moment, you need Bending Moment in Prestress (M_b), Distance from Centroidal Axis (y) & Moment of Inertia of Section (I_a). With our tool, you need to enter the respective value for Bending Moment in Prestress, Distance from Centroidal Axis & Moment of Inertia of Section 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 Bending Stress in Section?

In this formula, Bending Stress in Section uses Bending Moment in Prestress, Distance from Centroidal Axis & Moment of Inertia of Section. We can use 1 other way(s) to calculate the same, which is/are as follows -

Bending Stress in Section = Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section

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