Maximum Stress in Short Beams for Large Deflection Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia)
σmax = (P/A)+(((Mmax+P*δ)*y)/I)
This formula uses 7 Variables
Variables Used
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.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment occurs where shear force is zero.
Deflection of Beam - (Measured in Meter) - Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is measured between N.A. and the extreme point.
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.
STEP 1: Convert Input(s) to Base Unit
Axial Load: 2000 Newton --> 2000 Newton No Conversion Required
Cross Sectional Area: 0.12 Square Meter --> 0.12 Square Meter No Conversion Required
Maximum Bending Moment: 7.7 Kilonewton Meter --> 7700 Newton Meter (Check conversion here)
Deflection of Beam: 5 Millimeter --> 0.005 Meter (Check conversion here)
Distance from Neutral Axis: 25 Millimeter --> 0.025 Meter (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σmax = (P/A)+(((Mmax+P*δ)*y)/I) --> (2000/0.12)+(((7700+2000*0.005)*0.025)/0.0016)
Evaluating ... ...
σmax = 137135.416666667
STEP 3: Convert Result to Output's Unit
137135.416666667 Pascal -->0.137135416666667 Megapascal (Check conversion here)
FINAL ANSWER
0.137135416666667 0.137135 Megapascal <-- Maximum Stress
(Calculation completed in 00.004 seconds)

Credits

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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 Stress in Short Beams for Large Deflection Formula

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

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 Stress in Short Beams for Large Deflection?

Maximum Stress in Short Beams for Large Deflection calculator uses Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia) to calculate the Maximum Stress, Maximum Stress in Short Beams for Large Deflection formula is defined as force per unit area that the force acts upon. Thus, Stresses are either tensile or compressive. While the test is conducted, both the stress and strain are recorded. Maximum Stress is denoted by σmax symbol.

How to calculate Maximum Stress in Short Beams for Large Deflection using this online calculator? To use this online calculator for Maximum Stress in Short Beams for Large Deflection, enter Axial Load (P), Cross Sectional Area (A), Maximum Bending Moment (Mmax), Deflection of Beam (δ), Distance from Neutral Axis (y) & Area Moment of Inertia (I) and hit the calculate button. Here is how the Maximum Stress in Short Beams for Large Deflection calculation can be explained with given input values -> 1.4E-7 = (2000/0.12)+(((7700+2000*0.005)*0.025)/0.0016).

FAQ

What is Maximum Stress in Short Beams for Large Deflection?
Maximum Stress in Short Beams for Large Deflection formula is defined as force per unit area that the force acts upon. Thus, Stresses are either tensile or compressive. While the test is conducted, both the stress and strain are recorded and is represented as σmax = (P/A)+(((Mmax+P*δ)*y)/I) or Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia). 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, Maximum Bending Moment occurs where shear force is zero, Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body, Distance from Neutral Axis is measured between N.A. and the extreme point & 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.
How to calculate Maximum Stress in Short Beams for Large Deflection?
Maximum Stress in Short Beams for Large Deflection formula is defined as force per unit area that the force acts upon. Thus, Stresses are either tensile or compressive. While the test is conducted, both the stress and strain are recorded is calculated using Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia). To calculate Maximum Stress in Short Beams for Large Deflection, you need Axial Load (P), Cross Sectional Area (A), Maximum Bending Moment (Mmax), Deflection of Beam (δ), Distance from Neutral Axis (y) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Axial Load, Cross Sectional Area, Maximum Bending Moment, Deflection of Beam, Distance from Neutral Axis & Area Moment of Inertia 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 Maximum Stress?
In this formula, Maximum Stress uses Axial Load, Cross Sectional Area, Maximum Bending Moment, Deflection of Beam, Distance from Neutral Axis & Area Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Maximum Stress = (Axial Load/Cross Sectional Area)+((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia)
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