Bending stress in lever of elliptical cross section Calculator

✖Effort on Lever is the force applied on the input of the lever to overcome the resistance to get the work done by the machine.ⓘ Effort on Lever [P]			+10% -10%
✖Length of effort arm is defined as the length of the arm of the lever onto which the effort force is applied.ⓘ Length of Effort Arm [l₁]			+10% -10%
✖Diameter of Lever Fulcrum Pin is the diameter of the pin used at the fulcrum joint of a lever.ⓘ Diameter of Lever Fulcrum Pin [d₁]			+10% -10%
✖Minor Axis of Lever Ellipse Section is the line segment that is perpendicular to the major axis and intersects at the center of the elliptical cross-section of a lever.ⓘ Minor Axis of Lever Ellipse Section [b]			+10% -10%
✖Major Axis of Lever Ellipse Section is the line segment that crosses both the focal points of the elliptical cross-section of a lever.ⓘ Major Axis of Lever Ellipse Section [a]			+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 elliptical cross section [σ_b]

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Formula

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Bending stress in lever of elliptical cross section

Formula

`"σ"_{"b"} = (32*("P"*(("l"_{"1"})-("d"_{"1"}))))/(pi*"b"*("a"^2))`

Example

`"141.7247N/mm²"=(32*("294N"*(("900mm")-("11.6mm"))))/(pi*"13mm"*(("38mm")^2))`

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Bending stress in lever of elliptical cross section Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σ_b = (32*(P*((l₁)-(d₁))))/(pi*b*(a^2))
This formula uses 1 Constants, 6 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.
Effort on Lever - (Measured in Newton) - Effort on Lever is the force applied on the input of the lever to overcome the resistance to get the work done by the machine.
Length of Effort Arm - (Measured in Meter) - Length of effort arm is defined as the length of the arm of the lever onto which the effort force is applied.
Diameter of Lever Fulcrum Pin - (Measured in Meter) - Diameter of Lever Fulcrum Pin is the diameter of the pin used at the fulcrum joint of a lever.
Minor Axis of Lever Ellipse Section - (Measured in Meter) - Minor Axis of Lever Ellipse Section is the line segment that is perpendicular to the major axis and intersects at the center of the elliptical cross-section of a lever.
Major Axis of Lever Ellipse Section - (Measured in Meter) - Major Axis of Lever Ellipse Section is the line segment that crosses both the focal points of the elliptical cross-section of a lever.

STEP 1: Convert Input(s) to Base Unit

Effort on Lever: 294 Newton --> 294 Newton No Conversion Required
Length of Effort Arm: 900 Millimeter --> 0.9 Meter (Check conversion here)
Diameter of Lever Fulcrum Pin: 11.6 Millimeter --> 0.0116 Meter (Check conversion here)
Minor Axis of Lever Ellipse Section: 13 Millimeter --> 0.013 Meter (Check conversion here)
Major Axis of Lever Ellipse Section: 38 Millimeter --> 0.038 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_b = (32*(P*((l₁)-(d₁))))/(pi*b*(a^2)) --> (32*(294*((0.9)-(0.0116))))/(pi*0.013*(0.038^2))

Evaluating ... ...

σ_b = 141724665.413833

STEP 3: Convert Result to Output's Unit

141724665.413833 Pascal -->141.724665413833 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

141.724665413833 ≈ 141.7247 Newton per Square Millimeter <-- Bending Stress in Lever Arm

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Lever » Components of Lever » Bending stress in lever of elliptical cross section

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

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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 elliptical cross section Formula

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 elliptical cross section?

Bending stress in lever of elliptical cross section calculator uses 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)) to calculate the Bending Stress in Lever Arm, The Bending stress in lever of elliptical cross section is the amount of bending stress that is generated into the arms of the lever when the lever arms are loaded and bending moments act onto the arms. Bending Stress in Lever Arm is denoted by σ_b symbol.

How to calculate Bending stress in lever of elliptical cross section using this online calculator? To use this online calculator for Bending stress in lever of elliptical cross section, enter Effort on Lever (P), Length of Effort Arm (l₁), Diameter of Lever Fulcrum Pin (d₁), Minor Axis of Lever Ellipse Section (b) & Major Axis of Lever Ellipse Section (a) and hit the calculate button. Here is how the Bending stress in lever of elliptical cross section calculation can be explained with given input values -> 0.000142 = (32*(294*((0.9)-(0.0116))))/(pi*0.013*(0.038^2)).

FAQ

What is Bending stress in lever of elliptical cross section?

The Bending stress in lever of elliptical cross section is the amount of bending stress that is generated into the arms of the lever when the lever arms are loaded and bending moments act onto the arms and is represented as σ_b = (32*(P*((l₁)-(d₁))))/(pi*b*(a^2)) or 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)). Effort on Lever is the force applied on the input of the lever to overcome the resistance to get the work done by the machine, Length of effort arm is defined as the length of the arm of the lever onto which the effort force is applied, Diameter of Lever Fulcrum Pin is the diameter of the pin used at the fulcrum joint of a lever, Minor Axis of Lever Ellipse Section is the line segment that is perpendicular to the major axis and intersects at the center of the elliptical cross-section of a lever & Major Axis of Lever Ellipse Section is the line segment that crosses both the focal points of the elliptical cross-section of a lever.

How to calculate Bending stress in lever of elliptical cross section?

The Bending stress in lever of elliptical cross section is the amount of bending stress that is generated into the arms of the lever when the lever arms are loaded and bending moments act onto the arms is calculated using 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)). To calculate Bending stress in lever of elliptical cross section, you need Effort on Lever (P), Length of Effort Arm (l₁), Diameter of Lever Fulcrum Pin (d₁), Minor Axis of Lever Ellipse Section (b) & Major Axis of Lever Ellipse Section (a). With our tool, you need to enter the respective value for Effort on Lever, Length of Effort Arm, Diameter of Lever Fulcrum Pin, Minor Axis of Lever Ellipse Section & Major Axis of Lever Ellipse Section 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 Effort on Lever, Length of Effort Arm, Diameter of Lever Fulcrum Pin, Minor Axis of Lever Ellipse Section & Major Axis of Lever Ellipse Section. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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