Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Calculator

✖Bending Moment about X-Axis is defined as the bending moment about principal axis XX.ⓘ Bending Moment about X-Axis [M_x]			+10% -10%
✖Distance from Point to XX Axis is the distance of the point to XX axis where stress is to be computed.ⓘ Distance from Point to XX Axis [y]			+10% -10%
✖Maximum Stress is defined as force per unit area that the force acts upon.ⓘ Maximum Stress [f_Max]			+10% -10%
✖Bending Moment about Y-Axis is defined as the bending moment about principal axis YY.ⓘ Bending Moment about Y-Axis [M_y]			+10% -10%
✖Distance from Point to YY Axis is the distance from the point to the YY axis where stress is to be computed.ⓘ Distance from Point to YY Axis [x]			+10% -10%
✖Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.ⓘ Moment of Inertia about Y-Axis [I_y]			+10% -10%

✖Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.ⓘ Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending [I_x]

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Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis)))
I_x = (M_x*y)/(f_Max-((M_y*x)/(I_y)))
This formula uses 7 Variables

Variables Used

Moment of Inertia about X-Axis - (Measured in Kilogram Square Meter) - Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.
Bending Moment about X-Axis - (Measured in Newton Meter) - Bending Moment about X-Axis is defined as the bending moment about principal axis XX.
Distance from Point to XX Axis - (Measured in Millimeter) - Distance from Point to XX Axis is the distance of the point to XX axis where stress is to be computed.
Maximum Stress - (Measured in Pascal) - Maximum Stress is defined as force per unit area that the force acts upon.
Bending Moment about Y-Axis - (Measured in Newton Meter) - Bending Moment about Y-Axis is defined as the bending moment about principal axis YY.
Distance from Point to YY Axis - (Measured in Millimeter) - Distance from Point to YY Axis is the distance from the point to the YY axis where stress is to be computed.
Moment of Inertia about Y-Axis - (Measured in Kilogram Square Meter) - Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.

STEP 1: Convert Input(s) to Base Unit

Bending Moment about X-Axis: 239 Newton Meter --> 239 Newton Meter No Conversion Required
Distance from Point to XX Axis: 169 Millimeter --> 169 Millimeter No Conversion Required
Maximum Stress: 1430 Newton per Square Meter --> 1430 Pascal (Check conversion here)
Bending Moment about Y-Axis: 307 Newton Meter --> 307 Newton Meter No Conversion Required
Distance from Point to YY Axis: 104 Millimeter --> 104 Millimeter No Conversion Required
Moment of Inertia about Y-Axis: 50 Kilogram Square Meter --> 50 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_x = (M_x*y)/(f_Max-((M_y*x)/(I_y))) --> (239*169)/(1430-((307*104)/(50)))

Evaluating ... ...

I_x = 51.0348226018397

STEP 3: Convert Result to Output's Unit

51.0348226018397 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

51.0348226018397 ≈ 51.03482 Kilogram Square Meter <-- Moment of Inertia about X-Axis

(Calculation completed in 00.004 seconds)

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< Unsymmetrical Bending Calculators

Bending Moment about Axis XX given Maximum Stress in Unsymmetrical Bending

LaTeX Go Bending Moment about X-Axis = (Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/Moment of Inertia about Y-Axis))*Moment of Inertia about X-Axis/(Distance from Point to XX Axis)

Bending Moment about Axis YY given Maximum Stress in Unsymmetrical Bending

LaTeX Go Bending Moment about Y-Axis = (Maximum Stress-((Bending Moment about X-Axis*Distance from Point to XX Axis)/Moment of Inertia about X-Axis))*Moment of Inertia about Y-Axis/(Distance from Point to YY Axis)

Maximum Stress in Unsymmetrical Bending

LaTeX Go Maximum Stress = ((Bending Moment about X-Axis*Distance from Point to XX Axis)/Moment of Inertia about X-Axis)+((Bending Moment about Y-Axis*Distance from Point to YY Axis)/Moment of Inertia about Y-Axis)

Distance from YY axis to stress point given Maximum Stress in Unsymmetrical Bending

LaTeX Go Distance from Point to YY Axis = (Maximum Stress-((Bending Moment about X-Axis*Distance from Point to XX Axis)/Moment of Inertia about X-Axis))*Moment of Inertia about Y-Axis/Bending Moment about Y-Axis

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Formula

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What is Unsymmetrical Bending?

If the load line on a beam does not coincide with one of the principal axes of the section, the bending takes place in a plane different from the plane of principal axes. This type of bending is known as unsymmetrical bending.

How to Calculate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending calculator uses Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis))) to calculate the Moment of Inertia about X-Axis, Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending formula is defined as the second moment of the area distribution with respect to the bending axis, crucial for calculating maximum stress in the asymmetrically loaded structure. Moment of Inertia about X-Axis is denoted by I_x symbol.

How to calculate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending using this online calculator? To use this online calculator for Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending, enter Bending Moment about X-Axis (M_x), Distance from Point to XX Axis (y), Maximum Stress (f_Max), Bending Moment about Y-Axis (M_y), Distance from Point to YY Axis (x) & Moment of Inertia about Y-Axis (I_y) and hit the calculate button. Here is how the Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending calculation can be explained with given input values -> -63.402191 = (239*0.169)/(1430-((307*0.104)/(50))).

FAQ

What is Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending formula is defined as the second moment of the area distribution with respect to the bending axis, crucial for calculating maximum stress in the asymmetrically loaded structure and is represented as I_x = (M_x*y)/(f_Max-((M_y*x)/(I_y))) or Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis))). Bending Moment about X-Axis is defined as the bending moment about principal axis XX, Distance from Point to XX Axis is the distance of the point to XX axis where stress is to be computed, Maximum Stress is defined as force per unit area that the force acts upon, Bending Moment about Y-Axis is defined as the bending moment about principal axis YY, Distance from Point to YY Axis is the distance from the point to the YY axis where stress is to be computed & Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.

How to calculate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending formula is defined as the second moment of the area distribution with respect to the bending axis, crucial for calculating maximum stress in the asymmetrically loaded structure is calculated using Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis))). To calculate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending, you need Bending Moment about X-Axis (M_x), Distance from Point to XX Axis (y), Maximum Stress (f_Max), Bending Moment about Y-Axis (M_y), Distance from Point to YY Axis (x) & Moment of Inertia about Y-Axis (I_y). With our tool, you need to enter the respective value for Bending Moment about X-Axis, Distance from Point to XX Axis, Maximum Stress, Bending Moment about Y-Axis, Distance from Point to YY Axis & Moment of Inertia about Y-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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