Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))
Xd = (acos(1-(δc/(acrippling+eload))))/(sqrt(F/(εcolumn*I)))
This formula uses 3 Functions, 7 Variables
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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
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
Distance b/w fixed end and deflection point - (Measured in Meter) - Distance b/w fixed end and deflection point is the distance x between the point of deflection at section and fixed point.
Deflection of Column - (Measured in Meter) - Deflection of Column at free end in terms of moment at the section of column with eccentric load.
Deflection of Free End - (Measured in Meter) - Deflection of Free End is the deflection caused due to crippling load at the free end.
Eccentricity of Load - (Measured in Meter) - Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.
Eccentric load on column - (Measured in Newton) - Eccentric load on column is the load that causes direct stress as well as bending stress.
Modulus of elasticity of column - (Measured in Pascal) - Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
STEP 1: Convert Input(s) to Base Unit
Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Deflection of Free End: 14 Millimeter --> 0.014 Meter (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Eccentric load on column: 40 Newton --> 40 Newton No Conversion Required
Modulus of elasticity of column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Xd = (acos(1-(δc/(acrippling+eload))))/(sqrt(F/(εcolumn*I))) --> (acos(1-(0.012/(0.014+0.0025))))/(sqrt(40/(10560000*1.125)))
Evaluating ... ...
Xd = 705.510791746751
STEP 3: Convert Result to Output's Unit
705.510791746751 Meter -->705510.791746751 Millimeter (Check conversion here)
FINAL ANSWER
705510.791746751 705510.8 Millimeter <-- Distance b/w fixed end and deflection point
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1900+ more calculators!

8 Deflection Calculators

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load
Go Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))
Maximum Initial Deflection given Final Deflection at Distance X from End A of Column
Go Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column))
Final Deflection at Distance X from end A of Column
Go Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)
Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature
Go Maximum initial deflection = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point
Maximum Initial Deflection given Initial Deflection at Distance X from A
Go Maximum initial deflection = Initial Deflection/sin((pi*Distance of deflection from end A)/Length of column)
Initial Deflection at Distance X from end A
Go Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)
Maximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature
Go Maximum initial deflection = Deflection of Column/(1/(1-(Crippling Load/Euler Load)))
Maximum Deflection for Columns with Initial Curvature
Go Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load Formula

Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))
Xd = (acos(1-(δc/(acrippling+eload))))/(sqrt(F/(εcolumn*I)))

Which is example of eccentric loading?

Examples of eccentric loading activities include performing a calf raise off the ledge of a stair, an exercise that has been shown to decrease the risk of Achilles tendon injuries. Another example is the nordic curl exercise, which has been shown to help reduce the risk of hamstring strains.

How to Calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load calculator uses Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))) to calculate the Distance b/w fixed end and deflection point, The Distance of section from fixed end given deflection at section of column with eccentric load formula is defined as the distance of deflected section from the fixed end of the column. Distance b/w fixed end and deflection point is denoted by Xd symbol.

How to calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load using this online calculator? To use this online calculator for Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load, enter Deflection of Column c), Deflection of Free End (acrippling), Eccentricity of Load (eload), Eccentric load on column (F), Modulus of elasticity of column column) & Moment of Inertia (I) and hit the calculate button. Here is how the Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load calculation can be explained with given input values -> 7.1E+8 = (acos(1-(0.012/(0.014+0.0025))))/(sqrt(40/(10560000*1.125))).

FAQ

What is Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?
The Distance of section from fixed end given deflection at section of column with eccentric load formula is defined as the distance of deflected section from the fixed end of the column and is represented as Xd = (acos(1-(δc/(acrippling+eload))))/(sqrt(F/(εcolumn*I))) or Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))). Deflection of Column at free end in terms of moment at the section of column with eccentric load, Deflection of Free End is the deflection caused due to crippling load at the free end, Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load, Eccentric load on column is the load that causes direct stress as well as bending stress, Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load?
The Distance of section from fixed end given deflection at section of column with eccentric load formula is defined as the distance of deflected section from the fixed end of the column is calculated using Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))). To calculate Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load, you need Deflection of Column c), Deflection of Free End (acrippling), Eccentricity of Load (eload), Eccentric load on column (F), Modulus of elasticity of column column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Deflection of Column, Deflection of Free End, Eccentricity of Load, Eccentric load on column, Modulus of elasticity of column & Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!