Bending stress in lever of rectangular cross section given bending moment Calculator

✖Bending Moment in Lever is the reaction induced in the lever when an external force or moment is applied to the lever, causing the lever to bend.ⓘ Bending Moment in Lever [M_b]			+10% -10%
✖Width of Lever Arm is the thickness or the width of the lever arm measured perpendicular to the applied force on respective arms.ⓘ Width of Lever Arm [b_l]			+10% -10%
✖Depth of Lever Arm is the thickness of the lever arm measured parallel to the applied force on respective arms.ⓘ Depth of Lever Arm [d]			+10% -10%

✖Bending Stress in Lever Arm or allowable bending stress is the amount of bending stress that can be generated in the lever before its failure or fracture.ⓘ Bending stress in lever of rectangular cross section given bending moment [σ_b]

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Formula

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Bending stress in lever of rectangular cross section given bending moment

Formula

`"σ"_{"b"} = (32*"M"_{"b"})/(pi*"b"_{"l"}*("d"^2))`

Example

`"140.5561N/mm²"=(32*"261050N*mm")/(pi*"14.2mm"*(("36.5mm")^2))`

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Bending stress in lever of rectangular cross section given bending moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Width of Lever Arm*(Depth of Lever Arm^2))
σ_b = (32*M_b)/(pi*b_l*(d^2))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Bending Stress in Lever Arm - (Measured in Pascal) - Bending Stress in Lever Arm or allowable bending stress is the amount of bending stress that can be generated in the lever before its failure or fracture.
Bending Moment in Lever - (Measured in Newton Meter) - Bending Moment in Lever is the reaction induced in the lever when an external force or moment is applied to the lever, causing the lever to bend.
Width of Lever Arm - (Measured in Meter) - Width of Lever Arm is the thickness or the width of the lever arm measured perpendicular to the applied force on respective arms.
Depth of Lever Arm - (Measured in Meter) - Depth of Lever Arm is the thickness of the lever arm measured parallel to the applied force on respective arms.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Lever: 261050 Newton Millimeter --> 261.05 Newton Meter (Check conversion here)
Width of Lever Arm: 14.2 Millimeter --> 0.0142 Meter (Check conversion here)
Depth of Lever Arm: 36.5 Millimeter --> 0.0365 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_b = (32*M_b)/(pi*b_l*(d^2)) --> (32*261.05)/(pi*0.0142*(0.0365^2))

Evaluating ... ...

σ_b = 140556110.214104

STEP 3: Convert Result to Output's Unit

140556110.214104 Pascal -->140.556110214104 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

140.556110214104 ≈ 140.5561 Newton per Square Millimeter <-- Bending Stress in Lever Arm

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Lever » Components of Lever » Bending stress in lever of rectangular cross section given bending moment

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< 15 Components of Lever Calculators

Bending stress in lever of elliptical cross section

Go Bending Stress in Lever Arm = (32*(Effort on Lever*((Length of Effort Arm)-(Diameter of Lever Fulcrum Pin))))/(pi*Minor Axis of Lever Ellipse Section*(Major Axis of Lever Ellipse Section^2))

Reaction Force at Fulcrum of Lever given Effort, Load and Contained Angle

Go Force at Lever Fulcrum Pin = sqrt(Load on lever^2+Effort on Lever^2-2*Load on lever*Effort on Lever*cos(Angle Between Lever Arms))

Bending stress in lever of rectangular cross section

Go Bending Stress in Lever Arm = (32*(Effort on Lever*((Length of Effort Arm)-(Diameter of Lever Fulcrum Pin))))/(pi*Width of Lever Arm*(Depth of Lever Arm^2))

Bending stress in lever of elliptical cross section given bending moment

Go Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Minor Axis of Lever Ellipse Section*(Major Axis of Lever Ellipse Section^2))

Bending stress in lever of rectangular cross section given bending moment

Go Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Width of Lever Arm*(Depth of Lever Arm^2))

Reaction Force at Fulcrum of Lever given Bearing Pressure

Go Force at Lever Fulcrum Pin = Bearing Pressure in Fulcrum Pin of Lever*Diameter of Lever Fulcrum Pin*Length of Lever Fulcrum Pin

Maximum bending moment in lever

Go Bending Moment in Lever = Effort on Lever*((Length of Effort Arm)-(Diameter of Lever Fulcrum Pin))

Effort Force Applied on Lever given Bending Moment

Go Effort on Lever = Bending Moment in Lever/(Length of Effort Arm-Diameter of Lever Fulcrum Pin)

Load using Lengths and Effort

Go Load on lever = Length of Effort Arm*Effort on Lever/Length of Load Arm

Effort using Length and Load

Go Effort on Lever = Length of Load Arm*Load on lever/Length of Effort Arm

Reaction Force at Fulcrum of Right Angled Lever

Go Force at Lever Fulcrum Pin = sqrt(Load on lever^2+Effort on Lever^2)

Leverage

Go Mechanical Advantage of Lever = Length of Effort Arm/Length of Load Arm

Effort using Leverage

Go Effort on Lever = Load on lever/Mechanical Advantage of Lever

Mechanical Advantage

Go Mechanical Advantage of Lever = Load on lever/Effort on Lever

Load using Leverage

Go Load on lever = Effort on Lever*Mechanical Advantage of Lever

Bending stress in lever of rectangular cross section given bending moment Formula

Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Width of Lever Arm*(Depth of Lever Arm^2))
σ_b = (32*M_b)/(pi*b_l*(d^2))

What is a lever?

Simply put, levers are machines used to increase force. We call them "simple machines" because they have only two parts — the handle and the fulcrum. The handle or bar of the lever is called the "arm" - Scissorsit's the part that you push or pull on. The "fulcrum" is the point on which the lever turns or balances. In the case of a fork, the fulcrum is the fingers of your hand. Scissors are really two levers put together. The handle on the toilet flusher is commonly called a fixed lever.

How to Calculate Bending stress in lever of rectangular cross section given bending moment?

Bending stress in lever of rectangular cross section given bending moment calculator uses Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Width of Lever Arm*(Depth of Lever Arm^2)) to calculate the Bending Stress in Lever Arm, The Bending stress in lever of rectangular cross section given bending moment is the amount of bending stress that is generated into the arms of the lever when the lever arms are loaded and bending moments acts onto the arms. Bending Stress in Lever Arm is denoted by σ_b symbol.

How to calculate Bending stress in lever of rectangular cross section given bending moment using this online calculator? To use this online calculator for Bending stress in lever of rectangular cross section given bending moment, enter Bending Moment in Lever (M_b), Width of Lever Arm (b_l) & Depth of Lever Arm (d) and hit the calculate button. Here is how the Bending stress in lever of rectangular cross section given bending moment calculation can be explained with given input values -> 0.000141 = (32*261.05)/(pi*0.0142*(0.0365^2)).

FAQ

What is Bending stress in lever of rectangular cross section given bending moment?

The Bending stress in lever of rectangular cross section given bending moment is the amount of bending stress that is generated into the arms of the lever when the lever arms are loaded and bending moments acts onto the arms and is represented as σ_b = (32*M_b)/(pi*b_l*(d^2)) or Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Width of Lever Arm*(Depth of Lever Arm^2)). Bending Moment in Lever is the reaction induced in the lever when an external force or moment is applied to the lever, causing the lever to bend, Width of Lever Arm is the thickness or the width of the lever arm measured perpendicular to the applied force on respective arms & Depth of Lever Arm is the thickness of the lever arm measured parallel to the applied force on respective arms.

How to calculate Bending stress in lever of rectangular cross section given bending moment?

The Bending stress in lever of rectangular cross section given bending moment is the amount of bending stress that is generated into the arms of the lever when the lever arms are loaded and bending moments acts onto the arms is calculated using Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Width of Lever Arm*(Depth of Lever Arm^2)). To calculate Bending stress in lever of rectangular cross section given bending moment, you need Bending Moment in Lever (M_b), Width of Lever Arm (b_l) & Depth of Lever Arm (d). With our tool, you need to enter the respective value for Bending Moment in Lever, Width of Lever Arm & Depth of Lever Arm 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 Bending Stress in Lever Arm?

In this formula, Bending Stress in Lever Arm uses Bending Moment in Lever, Width of Lever Arm & Depth of Lever Arm. We can use 3 other way(s) to calculate the same, which is/are as follows -

Bending Stress in Lever Arm = (32*(Effort on Lever*((Length of Effort Arm)-(Diameter of Lever Fulcrum Pin))))/(pi*Width of Lever Arm*(Depth of Lever Arm^2))
Bending Stress in Lever Arm = (32*Bending Moment in Lever)/(pi*Minor Axis of Lever Ellipse Section*(Major Axis of Lever Ellipse Section^2))
Bending Stress in Lever Arm = (32*(Effort on Lever*((Length of Effort Arm)-(Diameter of Lever Fulcrum Pin))))/(pi*Minor Axis of Lever Ellipse Section*(Major Axis of Lever Ellipse Section^2))

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