Transverse point load given maximum bending moment for strut Solution

STEP 0: Pre-Calculation Summary
Formula Used
Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))
Wp = M/(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive)))))
This formula uses 2 Functions, 6 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(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
Greatest Safe Load - (Measured in Newton) - Greatest Safe Load is the maximum safe point load allowable at the center of the beam.
Maximum Bending Moment In Column - (Measured in Newton Meter) - Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment.
Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Column Compressive load - (Measured in Newton) - Column Compressive load is the load applied to a column that is compressive in nature.
Column Length - (Measured in Meter) - Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
STEP 1: Convert Input(s) to Base Unit
Maximum Bending Moment In Column: 16 Newton Meter --> 16 Newton Meter No Conversion Required
Moment of Inertia Column: 5600 Centimeter⁴ --> 5.6E-05 Meter⁴ (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Column Compressive load: 0.4 Kilonewton --> 400 Newton (Check conversion here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Wp = M/(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive))))) --> 16/(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))
Evaluating ... ...
Wp = 36434.3568330503
STEP 3: Convert Result to Output's Unit
36434.3568330503 Newton -->36.4343568330503 Kilonewton (Check conversion here)
FINAL ANSWER
36.4343568330503 36.43436 Kilonewton <-- Greatest Safe Load
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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23 Strut Subjected To Compressive Axial Thrust And A Transverse Point Load At The Centre Calculators

Radius of gyration given maximum stress induced for strut with axial and point load
Go Least Radius of Gyration Column = sqrt(((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*((Maximum bending stress-(Column Compressive load/Column Cross Sectional Area))))))
Distance of extreme layer from neutral axis given maximum stress induced for strut
Go Distance from Neutral Axis to Extreme Point = (Maximum bending stress-(Column Compressive load/Column Cross Sectional Area))*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))))
Maximum stress induced for strut with axial and transverse point load at center
Go Maximum bending stress = (Column Compressive load/Column Cross Sectional Area)+((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration Column^2)))
Cross-sectional area given maximum stress induced for strut with axial and point load
Go Column Cross Sectional Area = (Column Compressive load/Maximum bending stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum bending stress*(Least Radius of Gyration Column^2)))
Maximum deflection for strut with axial and transverse point load at center
Go Deflection at Section = Greatest Safe Load*((((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))-(Column Length/(4*Column Compressive load)))
Transverse point load given maximum deflection for strut
Go Greatest Safe Load = Deflection at Section/((((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))-(Column Length/(4*Column Compressive load)))
Maximum bending moment for strut with axial and transverse point load at center
Go Maximum Bending Moment In Column = Greatest Safe Load*(((sqrt(Moment of Inertia Column* Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))
Transverse point load given maximum bending moment for strut
Go Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))
Radius of gyration if maximum bending moment is given for strut with axial and point load
Go Least Radius of Gyration Column = sqrt((Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*Maximum bending stress))
Radius of gyration given bending stress for strut with axial and transverse point load
Go Least Radius of Gyration Column = sqrt((Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*Column Cross Sectional Area))
Deflection at section for strut with axial and transverse point load at center
Go Deflection at Section = Column Compressive load-(Bending Moment in Column+(Greatest Safe Load*Distance of deflection from end A/2))/(Column Compressive load)
Distance of extreme layer from neutral axis if max bending moment is given for strut with point load
Go Distance from Neutral Axis to Extreme Point = Maximum bending stress*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Maximum Bending Moment In Column)
Maximum bending stress if maximum bending moment is given for strut with axial and point load
Go Maximum bending stress = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration Column^2))
Maximum bending moment if maximum bending stress is given for strut with axial and point load
Go Maximum Bending Moment In Column = Maximum bending stress*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Distance from Neutral Axis to Extreme Point)
Cross sectional area if maximum bending moment is given for strut with axial and point load
Go Column Cross Sectional Area = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/((Least Radius of Gyration Column^2)*Maximum bending stress)
Bending moment given bending stress for strut with axial and transverse point load at center
Go Bending Moment in Column = Bending Stress in Column*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Distance from Neutral Axis to Extreme Point)
Cross-sectional area given bending stress for strut with axial and transverse point load
Go Column Cross Sectional Area = (Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*(Least Radius of Gyration Column^2))
Distance of extreme layer from neutral axis given bending stress for strut
Go Distance from Neutral Axis to Extreme Point = Bending Stress in Column*(Column Cross Sectional Area*(Least Radius of Gyration Column^2))/(Bending Moment in Column)
Bending stress for strut with axial and transverse point load at center
Go Bending Stress in Column = (Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration Column^2))
Distance of deflection from end A for strut with axial and transverse point load at center
Go Distance of deflection from end A = (-Bending Moment in Column-(Column Compressive load*Deflection at Section))*2/(Greatest Safe Load)
Compressive axial load for strut with axial and transverse point load at center
Go Column Compressive load = -(Bending Moment in Column+(Greatest Safe Load*Distance of deflection from end A/2))/(Deflection at Section)
Transverse point load for strut with axial and transverse point load at center
Go Greatest Safe Load = (-Bending Moment in Column-(Column Compressive load*Deflection at Section))*2/(Distance of deflection from end A)
Bending moment at section for strut with axial and transverse point load at center
Go Bending Moment in Column = -(Column Compressive load*Deflection at Section)-(Greatest Safe Load*Distance of deflection from end A/2)

Transverse point load given maximum bending moment for strut Formula

Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))
Wp = M/(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive)))))

What is transverse point loading?

Transverse loading is a load applied vertically to the plane of the longitudinal axis of a configuration, such as a wind load. It causes the material to bend and rebound from its original position, with inner tensile and compressive straining associated with the change in curvature of the material.

How to Calculate Transverse point load given maximum bending moment for strut?

Transverse point load given maximum bending moment for strut calculator uses Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))) to calculate the Greatest Safe Load, The Transverse point load given maximum bending moment for strut formula is defined as a load applied vertically to the plane of the longitudinal axis of a configuration, such as a wind load. Greatest Safe Load is denoted by Wp symbol.

How to calculate Transverse point load given maximum bending moment for strut using this online calculator? To use this online calculator for Transverse point load given maximum bending moment for strut, enter Maximum Bending Moment In Column (M), Moment of Inertia Column (I), Modulus of Elasticity Column column), Column Compressive load (Pcompressive) & Column Length (lcolumn) and hit the calculate button. Here is how the Transverse point load given maximum bending moment for strut calculation can be explained with given input values -> 0.036434 = 16/(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))).

FAQ

What is Transverse point load given maximum bending moment for strut?
The Transverse point load given maximum bending moment for strut formula is defined as a load applied vertically to the plane of the longitudinal axis of a configuration, such as a wind load and is represented as Wp = M/(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive))))) or Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))). Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment, Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis, Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it, Column Compressive load is the load applied to a column that is compressive in nature & Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
How to calculate Transverse point load given maximum bending moment for strut?
The Transverse point load given maximum bending moment for strut formula is defined as a load applied vertically to the plane of the longitudinal axis of a configuration, such as a wind load is calculated using Greatest Safe Load = Maximum Bending Moment In Column/(((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))))). To calculate Transverse point load given maximum bending moment for strut, you need Maximum Bending Moment In Column (M), Moment of Inertia Column (I), Modulus of Elasticity Column column), Column Compressive load (Pcompressive) & Column Length (lcolumn). With our tool, you need to enter the respective value for Maximum Bending Moment In Column, Moment of Inertia Column, Modulus of Elasticity Column, Column Compressive load & Column Length 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 Greatest Safe Load?
In this formula, Greatest Safe Load uses Maximum Bending Moment In Column, Moment of Inertia Column, Modulus of Elasticity Column, Column Compressive load & Column Length. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Greatest Safe Load = (-Bending Moment in Column-(Column Compressive load*Deflection at Section))*2/(Distance of deflection from end A)
  • Greatest Safe Load = Deflection at Section/((((sqrt(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load))/(2*Column Compressive load))*tan((Column Length/2)*(sqrt(Column Compressive load/(Moment of Inertia Column*Modulus of Elasticity Column/Column Compressive load)))))-(Column Length/(4*Column Compressive load)))
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