Shear Stress in Fulcrum Pin of Rocker Arm Calculator

✖Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.ⓘ Total Force on Rocker Arm of Exhaust Valve [P_e]			+10% -10%
✖Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.ⓘ Force on Roller Pin [P_c]			+10% -10%
✖Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.ⓘ Angle Between Rocker Arms [θ]			+10% -10%
✖Diameter of Fulcrum Pin is the diameter of the pin used at the fulcrum joint.ⓘ Diameter of Fulcrum Pin [d₁]			+10% -10%

✖Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.ⓘ Shear Stress in Fulcrum Pin of Rocker Arm [τ_f]

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Shear Stress in Fulcrum Pin of Rocker Arm Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress in Fulcrum Pin = (2*(sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Diameter of Fulcrum Pin^2))
τ_f = (2*(sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)))/(pi*d₁^2))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Shear Stress in Fulcrum Pin - (Measured in Pascal) - Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.
Total Force on Rocker Arm of Exhaust Valve - (Measured in Newton) - Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.
Force on Roller Pin - (Measured in Newton) - Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.
Angle Between Rocker Arms - (Measured in Radian) - Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.
Diameter of Fulcrum Pin - (Measured in Meter) - Diameter of Fulcrum Pin is the diameter of the pin used at the fulcrum joint.

STEP 1: Convert Input(s) to Base Unit

Total Force on Rocker Arm of Exhaust Valve: 1926 Newton --> 1926 Newton No Conversion Required
Force on Roller Pin: 1925 Newton --> 1925 Newton No Conversion Required
Angle Between Rocker Arms: 135 Degree --> 2.3561944901919 Radian (Check conversion here)
Diameter of Fulcrum Pin: 25 Millimeter --> 0.025 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_f = (2*(sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)))/(pi*d₁^2)) --> (2*(sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*0.025^2))

Evaluating ... ...

τ_f = 3624006.5394509

STEP 3: Convert Result to Output's Unit

3624006.5394509 Pascal -->3.6240065394509 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

3.6240065394509 ≈ 3.624007 Newton per Square Millimeter <-- Shear Stress in Fulcrum Pin

(Calculation completed in 00.004 seconds)

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Home » Physics » IC Engine » Design of IC Engine Components » Rocker Arm » Mechanical » Design of Fulcrum Pin » Shear Stress in Fulcrum Pin of Rocker Arm

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Created by Saurabh Patil

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

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< Design of Fulcrum Pin Calculators

Angle between Two Arms of Rocker Arm

LaTeX Go Angle Between Rocker Arms = pi-arccos(-(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-Force at Fulcrum Pin^2)/(2*Total Force on Rocker Arm of Exhaust Valve*Force on Roller Pin))

Reaction at Fulcrum Pin of Rocker Arm

LaTeX Go Force at Fulcrum Pin = sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms))

Reaction at Fulcrum Pin of Rocker Arm for Equal Arm Lengths

LaTeX Go Force at Fulcrum Pin = Total Force on Rocker Arm of Exhaust Valve*sqrt(2*(1-cos(Angle Between Rocker Arms)))

Bearing Pressure at Fulcrum Pin of Rocker Arm

LaTeX Go Bearing Pressure for Fulcrum Pin = (Force at Fulcrum Pin)/(Diameter of Fulcrum Pin*Length of Fulcrum Pin)

Shear Stress in Fulcrum Pin of Rocker Arm Formula

LaTeX Go

Design of Rocker Arm

It is a two-arm lever with the fulcrum in the middle. One end of the rocker arm that is actuated by the cam is forked and carries a roller. The other arm of the rocker arm consists of a plain boss where a tappet is screwed. In order to reduce the weight and inertia force, the cross-section of the rocker arm is I-section. The arms of the rocker arm are made of uniform strength by tapering the width and depth dimensions. However, the thickness of the web and flanges is kept uniform. Rocker arms are made of grey cast iron, malleable cast iron, or cast steel.

How to Calculate Shear Stress in Fulcrum Pin of Rocker Arm?

Shear Stress in Fulcrum Pin of Rocker Arm calculator uses Shear Stress in Fulcrum Pin = (2*(sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Diameter of Fulcrum Pin^2)) to calculate the Shear Stress in Fulcrum Pin, The Shear stress in fulcrum pin of rocker arm is the shear stress-induced into the fulcrum pin, the force per unit area tending to cause deformation of the pin by slippage along a plane or planes parallel to the imposed stress. Here the force is acting on two arms of the rocker arm. Shear Stress in Fulcrum Pin is denoted by τ_f symbol.

How to calculate Shear Stress in Fulcrum Pin of Rocker Arm using this online calculator? To use this online calculator for Shear Stress in Fulcrum Pin of Rocker Arm, enter Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c), Angle Between Rocker Arms (θ) & Diameter of Fulcrum Pin (d₁) and hit the calculate button. Here is how the Shear Stress in Fulcrum Pin of Rocker Arm calculation can be explained with given input values -> 3.6E-6 = (2*(sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)))/(pi*0.025^2)).

FAQ

What is Shear Stress in Fulcrum Pin of Rocker Arm?

The Shear stress in fulcrum pin of rocker arm is the shear stress-induced into the fulcrum pin, the force per unit area tending to cause deformation of the pin by slippage along a plane or planes parallel to the imposed stress. Here the force is acting on two arms of the rocker arm and is represented as τ_f = (2*(sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)))/(pi*d₁^2)) or Shear Stress in Fulcrum Pin = (2*(sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Diameter of Fulcrum Pin^2)). Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve, Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint, Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms & Diameter of Fulcrum Pin is the diameter of the pin used at the fulcrum joint.

How to calculate Shear Stress in Fulcrum Pin of Rocker Arm?

The Shear stress in fulcrum pin of rocker arm is the shear stress-induced into the fulcrum pin, the force per unit area tending to cause deformation of the pin by slippage along a plane or planes parallel to the imposed stress. Here the force is acting on two arms of the rocker arm is calculated using Shear Stress in Fulcrum Pin = (2*(sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Diameter of Fulcrum Pin^2)). To calculate Shear Stress in Fulcrum Pin of Rocker Arm, you need Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c), Angle Between Rocker Arms (θ) & Diameter of Fulcrum Pin (d₁). With our tool, you need to enter the respective value for Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin, Angle Between Rocker Arms & Diameter of Fulcrum Pin 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 Shear Stress in Fulcrum Pin?

In this formula, Shear Stress in Fulcrum Pin uses Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin, Angle Between Rocker Arms & Diameter of Fulcrum Pin. We can use 1 other way(s) to calculate the same, which is/are as follows -

Shear Stress in Fulcrum Pin = (2*Force at Fulcrum Pin)/(pi*Diameter of Fulcrum Pin^2)

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