Length of Arc of Slice Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of Arc = Total Normal Force/Normal Stress in Pascal
l = P/ฯƒnormal
This formula uses 3 Variables
Variables Used
Length of Arc - (Measured in Meter) - Length of Arc of the slice taken into consideration.
Total Normal Force - (Measured in Newton) - Total normal force acting at the base of the slice.
Normal Stress in Pascal - (Measured in Pascal) - Normal Stress in Pascal is defined as the stress produced by the perpendicular action of a force on a given area.
STEP 1: Convert Input(s) to Base Unit
Total Normal Force: 150 Newton --> 150 Newton No Conversion Required
Normal Stress in Pascal: 15.71 Pascal --> 15.71 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = P/ฯƒnormal --> 150/15.71
Evaluating ... ...
l = 9.54805856142584
STEP 3: Convert Result to Output's Unit
9.54805856142584 Meter --> No Conversion Required
FINAL ANSWER
9.54805856142584 โ‰ˆ 9.548059 Meter <-- Length of Arc
(Calculation completed in 00.004 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
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25 Slope Stability Analysis using Bishops Method Calculators

Weight of Slice given Total Normal Force Acting on Slice
Go Weight of Slice = (Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))-Vertical Shear Force+Vertical Shear Force at other Section
Resultant Vertical Shear Force on Section N+1
Go Vertical Shear Force at other Section = Weight of Slice+Vertical Shear Force-(Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))
Resultant Vertical Shear Force on Section N
Go Vertical Shear Force = (Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))-Weight of Slice+Vertical Shear Force at other Section
Effective Cohesion of Soil given Shear Force in Bishop's Analysis
Go Effective Cohesion = ((Shear Force on Slice in Soil Mechanics*Factor of Safety)-((Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Arc
Factor of Safety given Shear Force in Bishop's Analysis
Go Factor of Safety = ((Effective Cohesion*Length of Arc) +(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics
Effective Angle of Internal Friction given Shear Force in Bishop's Analysis
Go Effective Angle of Internal Friction = atan(((Shear Force on Slice in Soil Mechanics*Factor of Safety)-(Effective Cohesion*Length of Arc))/(Total Normal Force-(Upward Force*Length of Arc)))
Effective Cohesion of Soil given Normal Stress on Slice
Go Effective Cohesion = Shear Strength of Soil in Pascal-((Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))
Normal Stress on Slice given Shear Strength
Go Normal Stress in Pascal = ((Shear Strength of Soil in Pascal-Cohesion in Soil)/tan((Effective Angle of Internal Friction*pi)/180))+Upward Force
Effective Angle of Internal Friction given Shear Strength
Go Effective Angle of Internal Friction = atan((Shear Strength-Effective Cohesion)/(Normal Stress in Mega Pascal-Upward Force))
Radius of Arc when Total Shear Force on Slice is Available
Go Radius of Soil Section = (Total Weight of Slice in Soil Mechanics*Horizontal Distance)/Total Shear Force in Soil Mechanics
Total Weight of Slice given Total Shear Force on Slice
Go Total Weight of Slice in Soil Mechanics = (Total Shear Force in Soil Mechanics*Radius of Soil Section)/Horizontal Distance
Horizontal Distance of Slice from Centre of Rotation
Go Horizontal Distance = (Total Shear Force in Soil Mechanics*Radius of Soil Section)/Total Weight of Slice in Soil Mechanics
Factor of Safety given by Bishop
Go Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio)
Pore Pressure Ratio given Horizontal Width
Go Pore Pressure Ratio = (Upward Force*Width of Soil Section)/Total Weight of Slice in Soil Mechanics
Unit weight of Soil given Pore Pressure Ratio
Go Unit Weight of Soil = (Upward Force in Seepage Analysis/(Pore Pressure Ratio*Height of Slice))
Height of Slice given Pore Pressure Ratio
Go Height of Slice = (Upward Force in Seepage Analysis/(Pore Pressure Ratio*Unit Weight of Soil))
Pore Pressure Ratio given Unit Weight
Go Pore Pressure Ratio = (Upward Force in Seepage Analysis/(Unit Weight of Soil*Height of Slice))
Length of Arc of Slice given Effective Stress
Go Length of Arc = Total Normal Force/(Effective Normal Stress+Total Pore Pressure)
Pore Pressure given Effective Stress on Slice
Go Total Pore Pressure = (Total Normal Force/Length of Arc)-Effective Normal Stress
Effective Stress on Slice
Go Effective Normal Stress = (Total Normal Force/Length of Arc)-Total Pore Pressure
Length of Arc of Slice given Shear Force in Bishop's Analysis
Go Length of Arc = Shear Force on Slice in Soil Mechanics/Shear Stress of Soil in Pascal
Change in Pore Pressure given Overall Pore Pressure Coefficient
Go Change in Pore Pressure = Change in Normal Stress*Pore Pressure Coefficient Overall
Change in Normal Stress given Overall Pore Pressure Coefficient
Go Change in Normal Stress = Change in Pore Pressure/Pore Pressure Coefficient Overall
Normal Stress on Slice
Go Normal Stress in Pascal = Total Normal Force/Length of Arc
Length of Arc of Slice
Go Length of Arc = Total Normal Force/Normal Stress in Pascal

Length of Arc of Slice Formula

Length of Arc = Total Normal Force/Normal Stress in Pascal
l = P/ฯƒnormal

What is Normal Stress?

A normal stress is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area.

How to Calculate Length of Arc of Slice?

Length of Arc of Slice calculator uses Length of Arc = Total Normal Force/Normal Stress in Pascal to calculate the Length of Arc, The Length of Arc of Slice is defined as the value of length of arc of slice when we have prior information of other parameters used. Length of Arc is denoted by l symbol.

How to calculate Length of Arc of Slice using this online calculator? To use this online calculator for Length of Arc of Slice, enter Total Normal Force (P) & Normal Stress in Pascal (ฯƒnormal) and hit the calculate button. Here is how the Length of Arc of Slice calculation can be explained with given input values -> 187.5 = 150/15.71.

FAQ

What is Length of Arc of Slice?
The Length of Arc of Slice is defined as the value of length of arc of slice when we have prior information of other parameters used and is represented as l = P/ฯƒnormal or Length of Arc = Total Normal Force/Normal Stress in Pascal. Total normal force acting at the base of the slice & Normal Stress in Pascal is defined as the stress produced by the perpendicular action of a force on a given area.
How to calculate Length of Arc of Slice?
The Length of Arc of Slice is defined as the value of length of arc of slice when we have prior information of other parameters used is calculated using Length of Arc = Total Normal Force/Normal Stress in Pascal. To calculate Length of Arc of Slice, you need Total Normal Force (P) & Normal Stress in Pascal (ฯƒnormal). With our tool, you need to enter the respective value for Total Normal Force & Normal Stress in Pascal 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 Length of Arc?
In this formula, Length of Arc uses Total Normal Force & Normal Stress in Pascal. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Length of Arc = Total Normal Force/(Effective Normal Stress+Total Pore Pressure)
  • Length of Arc = Shear Force on Slice in Soil Mechanics/Shear Stress of Soil in Pascal
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