External Moment with Known Compressive Stress Calculator

✖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 Stress in Section [f]			+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%
✖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%

✖External Moment is the moment applied externally on the concrete section.ⓘ External Moment with Known Compressive Stress [M]

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Formula

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External Moment with Known Compressive Stress

Formula

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

Example

`"4.00008kN*m"="166.67MPa"*"720000mm⁴"/"30mm"`

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Download General Principles of Prestressed Concrete Formulas PDF

External Moment with Known Compressive Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis
M = f*I_a/y
This formula uses 4 Variables

Variables Used

External Moment - (Measured in Kilonewton Meter) - External Moment is the moment applied externally on the concrete section.
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.
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.
Distance from Centroidal Axis - (Measured in Millimeter) - Distance from Centroidal Axis defines the distance from the extreme fiber of the concrete section to centroidal axis of the section.

STEP 1: Convert Input(s) to Base Unit

Bending Stress in Section: 166.67 Megapascal --> 166670000 Pascal (Check conversion here)
Moment of Inertia of Section: 720000 Millimeter⁴ --> 7.2E-07 Meter⁴ (Check conversion here)
Distance from Centroidal Axis: 30 Millimeter --> 30 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = f*I_a/y --> 166670000*7.2E-07/30

Evaluating ... ...

M = 4.00008

STEP 3: Convert Result to Output's Unit

4000.08 Newton Meter -->4.00008 Kilonewton Meter (Check conversion here)

FINAL ANSWER

4.00008 Kilonewton Meter <-- External Moment

(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

External Moment with Known Compressive Stress Formula

External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis
M = f*I_a/y

What is post tensioned concrete section and post tensioning?

Post-tensioned concrete is a variant of prestressed concrete where the tendons are tensioned after the surrounding concrete structure has been cast. The tendons are not placed in direct contact with the concrete, but are encapsulated within a protective sleeve or duct which is either cast into the concrete structure or placed adjacent to it. At each end of a tendon is an anchorage assembly firmly fixed to the surrounding concrete. Once the concrete has been cast and set, the tendons are tensioned ("stressed") by pulling the tendon ends through the anchorages while pressing against the concrete.

How to Calculate External Moment with Known Compressive Stress?

External Moment with Known Compressive Stress calculator uses External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis to calculate the External Moment, The External Moment with Known Compressive Stress is defined as moment produced due to extra loads on section or due to weight of beam over section. External Moment is denoted by M symbol.

How to calculate External Moment with Known Compressive Stress using this online calculator? To use this online calculator for External Moment with Known Compressive Stress, enter Bending Stress in Section (f), Moment of Inertia of Section (I_a) & Distance from Centroidal Axis (y) and hit the calculate button. Here is how the External Moment with Known Compressive Stress calculation can be explained with given input values -> 0.004 = 166670000*7.2E-07/0.03.

FAQ

What is External Moment with Known Compressive Stress?

The External Moment with Known Compressive Stress is defined as moment produced due to extra loads on section or due to weight of beam over section and is represented as M = f*I_a/y or External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis. 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, Moment of Inertia of section is defined as a property of a two-dimensional plane shape that characterizes its deflection under loading & Distance from Centroidal Axis defines the distance from the extreme fiber of the concrete section to centroidal axis of the section.

How to calculate External Moment with Known Compressive Stress?

The External Moment with Known Compressive Stress is defined as moment produced due to extra loads on section or due to weight of beam over section is calculated using External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis. To calculate External Moment with Known Compressive Stress, you need Bending Stress in Section (f), Moment of Inertia of Section (I_a) & Distance from Centroidal Axis (y). With our tool, you need to enter the respective value for Bending Stress in Section, Moment of Inertia of Section & Distance from Centroidal Axis 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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