Residual Stress in Beams when Bending Stress is Equal to Yield Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12))
σbeam = -(σ0+(MRec*y)/((b*d^3)/12))
This formula uses 6 Variables
Variables Used
Residual Stress in Beams above Yielding Point - (Measured in Pascal) - Residual Stress in Beams above Yielding Point can be defined as stress fields that exist in the absence of any external loads and are the result of any mechanical process which can cause deformation.
Yield Stress - (Measured in Pascal) - The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.
Recovery Bending Moment - (Measured in Newton Meter) - Recovery Bending Moment can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and the opposite moment is called Recovery bending moment.
Depth Yielded Plastically - (Measured in Meter) - Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber.
Breadth of Rectangular Beam - (Measured in Meter) - Breadth of rectangular beam is the width of the beam.
Depth of Rectangular Beam - (Measured in Meter) - Depth of rectangular beam is the height of the beam.
STEP 1: Convert Input(s) to Base Unit
Yield Stress: 250 Megapascal --> 250000000 Pascal (Check conversion here)
Recovery Bending Moment: -22000000 Newton Millimeter --> -22000 Newton Meter (Check conversion here)
Depth Yielded Plastically: 40.25 Millimeter --> 0.04025 Meter (Check conversion here)
Breadth of Rectangular Beam: 75 Millimeter --> 0.075 Meter (Check conversion here)
Depth of Rectangular Beam: 95 Millimeter --> 0.095 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σbeam = -(σ0+(MRec*y)/((b*d^3)/12)) --> -(250000000+((-22000)*0.04025)/((0.075*0.095^3)/12))
Evaluating ... ...
σbeam = -84751421.4900131
STEP 3: Convert Result to Output's Unit
-84751421.4900131 Pascal -->-84.7514214900131 Megapascal (Check conversion here)
FINAL ANSWER
-84.7514214900131 -84.751421 Megapascal <-- Residual Stress in Beams above Yielding Point
(Calculation completed in 00.004 seconds)

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8 Residual Stresses in Plastic Bending Calculators

Residual Stress in Beam in Fully Plastic State
Go Residual stress in beam in plastic state = -(Yield Stress+(Fully Plastic Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12))
Residual Stress in Beams when Bending Stress is Equal to Yield Stress
Go Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12))
Residual Stress in Beams when Y Lies between 0 and n
Go Residual Stress in beams (Y lies between 0 and η) = (Recovery Bending Moment* Depth Yielded Between 0 and η)/((Depth of Rectangular Beam*Depth of Rectangular Beam^3)/12)
Fully Plastic Recovery Stress in Beams
Go Fully plastic Recovery stress in beams = (Fully Plastic Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)
Recovery Bending Moment
Go Recovery Bending Moment = -((Yield Stress*Breadth of Rectangular Beam* (3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12)
Recovery Stress in Beams
Go Recovery Stress in Beams = (Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)
Fully Plastic Recovery Bending Moment
Go Fully Plastic Recovery Bending Moment = -(Breadth of Rectangular Beam*Depth of Rectangular Beam^2*Yield Stress)/4
Residual Stress in Beam in Fully Plastic State given Recovery Stress
Go Residual stress in beam in plastic state = -(Yield Stress+(Fully plastic Recovery stress in beams))

Residual Stress in Beams when Bending Stress is Equal to Yield Stress Formula

Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12))
σbeam = -(σ0+(MRec*y)/((b*d^3)/12))

Why residual stresses are important for engineering applications?

Residual stresses have a significant impact on the propensity for engineering components and structures to undergo fatigue and fracture, with either a positive (life enhancing) or negative (life reducing) effect that is largely dependent on the sign of the residual stress relative to that of the applied stress.

How to Calculate Residual Stress in Beams when Bending Stress is Equal to Yield Stress?

Residual Stress in Beams when Bending Stress is Equal to Yield Stress calculator uses Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)) to calculate the Residual Stress in Beams above Yielding Point, Residual Stress in Beams when Bending Stress is Equal to Yield Stress is defined as stress fields that exist in the absence of any external loads and are the result of any mechanical process which can cause deformation. Residual Stress in Beams above Yielding Point is denoted by σbeam symbol.

How to calculate Residual Stress in Beams when Bending Stress is Equal to Yield Stress using this online calculator? To use this online calculator for Residual Stress in Beams when Bending Stress is Equal to Yield Stress, enter Yield Stress 0), Recovery Bending Moment (MRec), Depth Yielded Plastically (y), Breadth of Rectangular Beam (b) & Depth of Rectangular Beam (d) and hit the calculate button. Here is how the Residual Stress in Beams when Bending Stress is Equal to Yield Stress calculation can be explained with given input values -> -8.5E-5 = -(250000000+((-22000)*0.04025)/((0.075*0.095^3)/12)).

FAQ

What is Residual Stress in Beams when Bending Stress is Equal to Yield Stress?
Residual Stress in Beams when Bending Stress is Equal to Yield Stress is defined as stress fields that exist in the absence of any external loads and are the result of any mechanical process which can cause deformation and is represented as σbeam = -(σ0+(MRec*y)/((b*d^3)/12)) or Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)). The Yield Stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically, Recovery Bending Moment can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and the opposite moment is called Recovery bending moment, Depth Yielded Plastically is the amount of depth of the beam yielded plastically from it's outermost fiber, Breadth of rectangular beam is the width of the beam & Depth of rectangular beam is the height of the beam.
How to calculate Residual Stress in Beams when Bending Stress is Equal to Yield Stress?
Residual Stress in Beams when Bending Stress is Equal to Yield Stress is defined as stress fields that exist in the absence of any external loads and are the result of any mechanical process which can cause deformation is calculated using Residual Stress in Beams above Yielding Point = -(Yield Stress+(Recovery Bending Moment*Depth Yielded Plastically)/((Breadth of Rectangular Beam*Depth of Rectangular Beam^3)/12)). To calculate Residual Stress in Beams when Bending Stress is Equal to Yield Stress, you need Yield Stress 0), Recovery Bending Moment (MRec), Depth Yielded Plastically (y), Breadth of Rectangular Beam (b) & Depth of Rectangular Beam (d). With our tool, you need to enter the respective value for Yield Stress, Recovery Bending Moment, Depth Yielded Plastically, Breadth of Rectangular Beam & Depth of Rectangular Beam 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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