Bending stress for strut with axial and transverse point load at center Calculator

✖Bending Moment in Column is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Column [M_b]			+10% -10%
✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis to Extreme Point [c]			+10% -10%
✖Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.ⓘ Column Cross Sectional Area [A_sectional]			+10% -10%
✖Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.ⓘ Least Radius of Gyration Column [r_least]			+10% -10%

✖Bending Stress in Column is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Bending stress for strut with axial and transverse point load at center [σ_b]

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Formula

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Bending stress for strut with axial and transverse point load at center

Formula

`"σ"_{"b"} = ("M"_{"b"}*"c")/("A"_{"sectional"}*("r"_{"least"}^2))`

Example

`"0.000155MPa"=("48N*m"*"10mm")/("1.4m²"*(("47.02mm")^2))`

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Bending stress for strut with axial and transverse point load at center Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σ_b = (M_b*c)/(A_sectional*(r_least^2))
This formula uses 5 Variables

Variables Used

Bending Stress in Column - (Measured in Pascal) - Bending Stress in Column is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.
Bending Moment in Column - (Measured in Newton Meter) - Bending Moment in Column is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Column Cross Sectional Area - (Measured in Square Meter) - Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.
Least Radius of Gyration Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Column: 48 Newton Meter --> 48 Newton Meter No Conversion Required
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required
Least Radius of Gyration Column: 47.02 Millimeter --> 0.04702 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_b = (M_b*c)/(A_sectional*(r_least^2)) --> (48*0.01)/(1.4*(0.04702^2))

Evaluating ... ...

σ_b = 155.077200402673

STEP 3: Convert Result to Output's Unit

155.077200402673 Pascal -->0.000155077200402673 Megapascal (Check conversion here)

FINAL ANSWER

0.000155077200402673 ≈ 0.000155 Megapascal <-- Bending Stress in Column

(Calculation completed in 00.004 seconds)

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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)

Bending stress for strut with axial and transverse point load at center Formula

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 Bending stress for strut with axial and transverse point load at center?

Bending stress for strut with axial and transverse point load at center calculator uses 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)) to calculate the Bending Stress in Column, The Bending stress for strut with axial and transverse point load at center formula is defined as a more specific type of normal stress. When a beam experiences load like that shown in figure one the top fibers of the beam undergo normal compressive stress. Bending Stress in Column is denoted by σ_b symbol.

How to calculate Bending stress for strut with axial and transverse point load at center using this online calculator? To use this online calculator for Bending stress for strut with axial and transverse point load at center, enter Bending Moment in Column (M_b), Distance from Neutral Axis to Extreme Point (c), Column Cross Sectional Area (A_sectional) & Least Radius of Gyration Column (r_least) and hit the calculate button. Here is how the Bending stress for strut with axial and transverse point load at center calculation can be explained with given input values -> 1.6E-10 = (48*0.01)/(1.4*(0.04702^2)).

FAQ

What is Bending stress for strut with axial and transverse point load at center?

The Bending stress for strut with axial and transverse point load at center formula is defined as a more specific type of normal stress. When a beam experiences load like that shown in figure one the top fibers of the beam undergo normal compressive stress and is represented as σ_b = (M_b*c)/(A_sectional*(r_least^2)) or 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)). Bending Moment in Column is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point & Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

How to calculate Bending stress for strut with axial and transverse point load at center?

The Bending stress for strut with axial and transverse point load at center formula is defined as a more specific type of normal stress. When a beam experiences load like that shown in figure one the top fibers of the beam undergo normal compressive stress is calculated using 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)). To calculate Bending stress for strut with axial and transverse point load at center, you need Bending Moment in Column (M_b), Distance from Neutral Axis to Extreme Point (c), Column Cross Sectional Area (A_sectional) & Least Radius of Gyration Column (r_least). With our tool, you need to enter the respective value for Bending Moment in Column, Distance from Neutral Axis to Extreme Point, Column Cross Sectional Area & Least Radius of Gyration Column 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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