✖Coefficient Ay is the non-dimensional coefficient of lateral load term.ⓘ Coefficient Ay [A_y]			+10% -10%
✖Laterally Applied Load is a load that is applied horizontally or laterally to a structural element or soil mass.ⓘ Laterally Applied Load [P_h]			+10% -10%
✖Characteristic Pile Length is the effective length of a pile that provides the necessary load-bearing capacity to support the structure's load.ⓘ Characteristic Pile Length [T]			+10% -10%
✖stiffness of Pile is the ability of a pile to resist deformation under load.ⓘ Stiffness of Pile [EI]			+10% -10%
✖Coefficient By is the non-dimensional coefficient of moment term.ⓘ Coefficient By [B_y]			+10% -10%
✖Moment in Soil is the bending moment induced within a soil mass or a structural element embedded in soil.ⓘ Moment in Soil [M_t]			+10% -10%

✖Lateral Deflection is the movement of a building structure horizontally resulting from loads.ⓘ Lateral Deflection of Pile with Head Free to Move [y]

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Formula

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Lateral Deflection of Pile with Head Free to Move

Formula

`"y" = (("A"_{"y"}*"P"_{"h"}*("T"^3))/"EI")+(("B"_{"y"}*"M"_{"t"}*("T"^2))/"EI")`

Example

`"30.79209"=(("2.01"*"9.32N"*(("1.746m")^3))/"12.0N/m")+(("1.50"*"59N*m"*(("1.746m")^2))/"12.0N/m")`

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Lateral Deflection of Pile with Head Free to Move Solution

STEP 0: Pre-Calculation Summary

Formula Used

Lateral Deflection = ((Coefficient Ay*Laterally Applied Load*(Characteristic Pile Length^3))/Stiffness of Pile)+((Coefficient By*Moment in Soil*(Characteristic Pile Length^2))/Stiffness of Pile)
y = ((A_y*P_h*(T^3))/EI)+((B_y*M_t*(T^2))/EI)
This formula uses 7 Variables

Variables Used

Lateral Deflection - Lateral Deflection is the movement of a building structure horizontally resulting from loads.
Coefficient Ay - Coefficient Ay is the non-dimensional coefficient of lateral load term.
Laterally Applied Load - (Measured in Newton) - Laterally Applied Load is a load that is applied horizontally or laterally to a structural element or soil mass.
Characteristic Pile Length - (Measured in Meter) - Characteristic Pile Length is the effective length of a pile that provides the necessary load-bearing capacity to support the structure's load.
Stiffness of Pile - (Measured in Newton per Meter) - stiffness of Pile is the ability of a pile to resist deformation under load.
Coefficient By - Coefficient By is the non-dimensional coefficient of moment term.
Moment in Soil - (Measured in Joule) - Moment in Soil is the bending moment induced within a soil mass or a structural element embedded in soil.

STEP 1: Convert Input(s) to Base Unit

Coefficient Ay: 2.01 --> No Conversion Required
Laterally Applied Load: 9.32 Newton --> 9.32 Newton No Conversion Required
Characteristic Pile Length: 1.746 Meter --> 1.746 Meter No Conversion Required
Stiffness of Pile: 12 Newton per Meter --> 12 Newton per Meter No Conversion Required
Coefficient By: 1.5 --> No Conversion Required
Moment in Soil: 59 Newton Meter --> 59 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = ((A_y*P_h*(T^3))/EI)+((B_y*M_t*(T^2))/EI) --> ((2.01*9.32*(1.746^3))/12)+((1.5*59*(1.746^2))/12)

Evaluating ... ...

y = 30.7920864199896

STEP 3: Convert Result to Output's Unit

30.7920864199896 --> No Conversion Required

FINAL ANSWER

30.7920864199896 ≈ 30.79209 <-- Lateral Deflection

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Pile Foundations » Laterally Loaded Vertical Piles » Lateral Deflection of Pile with Head Free to Move

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< 7 Laterally Loaded Vertical Piles Calculators

Lateral Deflection of Pile with Head Free to Move

Go Lateral Deflection = ((Coefficient Ay*Laterally Applied Load*(Characteristic Pile Length^3))/Stiffness of Pile)+((Coefficient By*Moment in Soil*(Characteristic Pile Length^2))/Stiffness of Pile)

Negative Moment Imposed on Pile

Go Moment Negative = ((Coefficient Aϑ*Lateral Load*Characteristic Pile Length)/Coefficient Bϑ)-((Angle of Rotation*Stiffness of Pile)/(Coefficient Bϑ*Characteristic Pile Length))

Lateral Deflection for Fixed Head Pile Case

Go Lateral Deflection Fixed Head = ((Laterally Applied Load*(Characteristic Pile Length)^3)/Stiffness of Pile)*(Coefficient Ay-((Coefficient Aϑ*Coefficient By)/Coefficient Bϑ))

Positive Moment Imposed on Pile

Go Moment Positive = (Coefficient of Lateral Load in Positive Moment*Laterally Applied Load*Characteristic Pile Length)+(Coefficient of Moment Term in Positive Moment*Moment in Soil)

Pile Stiffness given Characteristic Pile Length for Laterally Loaded Piles

Go Stiffness of Pile = ((Characteristic Pile Length)^2)*Coefficient of Horizontal Subgrade

Characteristic Pile Length for Laterally Loaded Vertical Piles

Go Characteristic Pile Length = (Stiffness of Pile/Coefficient of Horizontal Subgrade)^0.5

Horizontal Subgrade Reaction Coefficient given Characteristic Pile Length

Go Coefficient of Horizontal Subgrade = Stiffness of Pile/(Characteristic Pile Length)^2

Lateral Deflection of Pile with Head Free to Move Formula

What is Lateral Deflection?

Lateral Deflection is the movement of a building structure horizontally resulting from loads such as wind load, seismic load, cranes, etc. and even small amounts of secondary movement from vertical loads.

How to Calculate Lateral Deflection of Pile with Head Free to Move?

Lateral Deflection of Pile with Head Free to Move calculator uses Lateral Deflection = ((Coefficient Ay*Laterally Applied Load*(Characteristic Pile Length^3))/Stiffness of Pile)+((Coefficient By*Moment in Soil*(Characteristic Pile Length^2))/Stiffness of Pile) to calculate the Lateral Deflection, The Lateral Deflection of Pile with Head Free to Move formula is defined as the horizontal displacement experienced by a pile when the top of the pile is not restrained laterally and is free to move horizontally. In geotechnical engineering, piles are often subjected to lateral forces due to various factors such as wind loads, earth pressure, or seismic forces. Lateral Deflection is denoted by y symbol.

How to calculate Lateral Deflection of Pile with Head Free to Move using this online calculator? To use this online calculator for Lateral Deflection of Pile with Head Free to Move, enter Coefficient Ay (A_y), Laterally Applied Load (P_h), Characteristic Pile Length (T), Stiffness of Pile (EI), Coefficient By (B_y) & Moment in Soil (M_t) and hit the calculate button. Here is how the Lateral Deflection of Pile with Head Free to Move calculation can be explained with given input values -> 30.79209 = ((2.01*9.32*(1.746^3))/12)+((1.5*59*(1.746^2))/12).

FAQ

What is Lateral Deflection of Pile with Head Free to Move?

The Lateral Deflection of Pile with Head Free to Move formula is defined as the horizontal displacement experienced by a pile when the top of the pile is not restrained laterally and is free to move horizontally. In geotechnical engineering, piles are often subjected to lateral forces due to various factors such as wind loads, earth pressure, or seismic forces and is represented as y = ((A_y*P_h*(T^3))/EI)+((B_y*M_t*(T^2))/EI) or Lateral Deflection = ((Coefficient Ay*Laterally Applied Load*(Characteristic Pile Length^3))/Stiffness of Pile)+((Coefficient By*Moment in Soil*(Characteristic Pile Length^2))/Stiffness of Pile). Coefficient Ay is the non-dimensional coefficient of lateral load term, Laterally Applied Load is a load that is applied horizontally or laterally to a structural element or soil mass, Characteristic Pile Length is the effective length of a pile that provides the necessary load-bearing capacity to support the structure's load, stiffness of Pile is the ability of a pile to resist deformation under load, Coefficient By is the non-dimensional coefficient of moment term & Moment in Soil is the bending moment induced within a soil mass or a structural element embedded in soil.

How to calculate Lateral Deflection of Pile with Head Free to Move?

The Lateral Deflection of Pile with Head Free to Move formula is defined as the horizontal displacement experienced by a pile when the top of the pile is not restrained laterally and is free to move horizontally. In geotechnical engineering, piles are often subjected to lateral forces due to various factors such as wind loads, earth pressure, or seismic forces is calculated using Lateral Deflection = ((Coefficient Ay*Laterally Applied Load*(Characteristic Pile Length^3))/Stiffness of Pile)+((Coefficient By*Moment in Soil*(Characteristic Pile Length^2))/Stiffness of Pile). To calculate Lateral Deflection of Pile with Head Free to Move, you need Coefficient Ay (A_y), Laterally Applied Load (P_h), Characteristic Pile Length (T), Stiffness of Pile (EI), Coefficient By (B_y) & Moment in Soil (M_t). With our tool, you need to enter the respective value for Coefficient Ay, Laterally Applied Load, Characteristic Pile Length, Stiffness of Pile, Coefficient By & Moment in Soil 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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