Maximum Bending Moment given Maximum Stress for Short Beams Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis
Mmax = ((σmax-(P/A))*I)/y
This formula uses 6 Variables
Variables Used
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment occurs where shear force is zero.
Maximum Stress - (Measured in Pascal) - Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks.
Axial Load - (Measured in Newton) - Axial Load is a force applied on a structure directly along an axis of the structure.
Cross Sectional Area - (Measured in Square Meter) - The Cross Sectional Area is the breadth times the depth of the beam structure.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is measured between N.A. and the extreme point.
STEP 1: Convert Input(s) to Base Unit
Maximum Stress: 0.136979 Megapascal --> 136979 Pascal (Check conversion here)
Axial Load: 2000 Newton --> 2000 Newton No Conversion Required
Cross Sectional Area: 0.12 Square Meter --> 0.12 Square Meter No Conversion Required
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required
Distance from Neutral Axis: 25 Millimeter --> 0.025 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mmax = ((σmax-(P/A))*I)/y --> ((136979-(2000/0.12))*0.0016)/0.025
Evaluating ... ...
Mmax = 7699.98933333333
STEP 3: Convert Result to Output's Unit
7699.98933333333 Newton Meter -->7.69998933333333 Kilonewton Meter (Check conversion here)
FINAL ANSWER
7.69998933333333 7.699989 Kilonewton Meter <-- Maximum Bending Moment
(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad
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19 Combined Axial and Bending Loads Calculators

Neutral Axis to Outermost Fiber Distance given Maximum Stress for Short Beams
Go Distance from Neutral Axis = ((Maximum Stress*Cross Sectional Area*Area Moment of Inertia)-(Axial Load*Area Moment of Inertia))/(Maximum Bending Moment*Cross Sectional Area)
Maximum Stress in Short Beams for Large Deflection
Go Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia)
Neutral Axis Moment of Inertia given Maximum Stress for Short Beams
Go Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))
Axial Load given Maximum Stress for Short Beams
Go Axial Load = Cross Sectional Area*(Maximum Stress -((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia))
Maximum Bending Moment given Maximum Stress for Short Beams
Go Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis
Cross-Sectional Area given Maximum Stress for Short Beams
Go Cross Sectional Area = Axial Load/(Maximum Stress-((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia))
Maximum Stress for Short Beams
Go Maximum Stress = (Axial Load/Cross Sectional Area)+((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia)
Young's Modulus given Distance from Extreme Fiber along with Radius and Stress Induced
Go Young's Modulus = ((Radius of Curvature*Fibre Stress at Distance ‘y’ from NA)/Distance from Neutral Axis)
Stress Induced with known Distance from Extreme Fiber, Young's Modulus and Radius of curvature
Go Fibre Stress at Distance ‘y’ from NA = (Young's Modulus*Distance from Neutral Axis)/Radius of Curvature
Distance from Extreme Fiber given Young's Modulus along with Radius and Stress Induced
Go Distance from Neutral Axis = (Radius of Curvature*Fibre Stress at Distance ‘y’ from NA)/Young's Modulus
Deflection for Transverse Loading given Deflection for Axial Bending
Go Deflection for Transverse Loading Alone = Deflection of Beam*(1-(Axial Load/Critical Buckling Load))
Deflection for Axial Compression and Bending
Go Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load))
Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress
Go Distance from Neutral Axis = (Area Moment of Inertia*Bending Stress)/Moment of Resistance
Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber
Go Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress
Stress Induced using Moment of Resistance, Moment of Inertia and Distance from Extreme Fiber
Go Bending Stress = (Distance from Neutral Axis*Moment of Resistance)/Area Moment of Inertia
Moment of Resistance in Bending Equation
Go Moment of Resistance = (Area Moment of Inertia*Bending Stress)/Distance from Neutral Axis
Young's Modulus using Moment of Resistance, Moment of Inertia and Radius
Go Young's Modulus = (Moment of Resistance*Radius of Curvature)/Area Moment of Inertia
Moment of Resistance given Young's Modulus, Moment of Inertia and Radius
Go Moment of Resistance = (Area Moment of Inertia*Young's Modulus)/Radius of Curvature
Moment of Inertia given Young's Modulus, Moment of Resistance and Radius
Go Area Moment of Inertia = (Moment of Resistance*Radius of Curvature)/Young's Modulus

Maximum Bending Moment given Maximum Stress for Short Beams Formula

Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis
Mmax = ((σmax-(P/A))*I)/y

Define Bending Moment

The Bending moment is an internally developed moment to counteract the externally applied loads ( hence to attain equilibrium), developed inside the body which you can not see physically. Please note that it is not an applied moment on the body, it is only developed inside when the body is subjected to some external stimuli.

Define Stress

Stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. Thus, Stress is defined as “The restoring force per unit area of the material”. It is a tensor quantity. Denoted by the Greek letter σ. Measured using Pascal or N/m2.

How to Calculate Maximum Bending Moment given Maximum Stress for Short Beams?

Maximum Bending Moment given Maximum Stress for Short Beams calculator uses Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis to calculate the Maximum Bending Moment, The Maximum Bending Moment given Maximum Stress for Short Beams formula is defined as the bending of the beam or any structure upon the action of the arbitrary load. The maximum bending moment in the beam occurs at the point of maximum stress. Maximum Bending Moment is denoted by Mmax symbol.

How to calculate Maximum Bending Moment given Maximum Stress for Short Beams using this online calculator? To use this online calculator for Maximum Bending Moment given Maximum Stress for Short Beams, enter Maximum Stress max), Axial Load (P), Cross Sectional Area (A), Area Moment of Inertia (I) & Distance from Neutral Axis (y) and hit the calculate button. Here is how the Maximum Bending Moment given Maximum Stress for Short Beams calculation can be explained with given input values -> 0.0077 = ((136979-(2000/0.12))*0.0016)/0.025.

FAQ

What is Maximum Bending Moment given Maximum Stress for Short Beams?
The Maximum Bending Moment given Maximum Stress for Short Beams formula is defined as the bending of the beam or any structure upon the action of the arbitrary load. The maximum bending moment in the beam occurs at the point of maximum stress and is represented as Mmax = ((σmax-(P/A))*I)/y or Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis. Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks, Axial Load is a force applied on a structure directly along an axis of the structure, The Cross Sectional Area is the breadth times the depth of the beam structure, Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane & Distance from Neutral Axis is measured between N.A. and the extreme point.
How to calculate Maximum Bending Moment given Maximum Stress for Short Beams?
The Maximum Bending Moment given Maximum Stress for Short Beams formula is defined as the bending of the beam or any structure upon the action of the arbitrary load. The maximum bending moment in the beam occurs at the point of maximum stress is calculated using Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis. To calculate Maximum Bending Moment given Maximum Stress for Short Beams, you need Maximum Stress max), Axial Load (P), Cross Sectional Area (A), Area Moment of Inertia (I) & Distance from Neutral Axis (y). With our tool, you need to enter the respective value for Maximum Stress, Axial Load, Cross Sectional Area, Area Moment of Inertia & Distance from Neutral 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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