Deflection for Axial Compression and Bending Calculator

✖Deflection for Transverse Loading Alone is defined as the deflections caused in the beam due to the transverse load alone.ⓘ Deflection for Transverse Loading Alone [d₀]			+10% -10%
✖Axial Load is a force applied on a structure directly along an axis of the structure.ⓘ Axial Load [P]			+10% -10%
✖Critical Buckling Load is the maximum load that a column can take before deformation.ⓘ Critical Buckling Load [P_c]			+10% -10%

✖Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.ⓘ Deflection for Axial Compression and Bending [δ]

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Deflection for Axial Compression and Bending

Formula

`"δ" = "d"_{"0"}/(1-("P"/"P"_{"c"}))`

Example

`"4.8mm"="4mm"/(1-("2000N"/"12000N"))`

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Deflection for Axial Compression and Bending Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load))
δ = d₀/(1-(P/P_c))
This formula uses 4 Variables

Variables Used

Deflection of Beam - (Measured in Meter) - Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.
Deflection for Transverse Loading Alone - (Measured in Meter) - Deflection for Transverse Loading Alone is defined as the deflections caused in the beam due to the transverse load alone.
Axial Load - (Measured in Newton) - Axial Load is a force applied on a structure directly along an axis of the structure.
Critical Buckling Load - (Measured in Newton) - Critical Buckling Load is the maximum load that a column can take before deformation.

STEP 1: Convert Input(s) to Base Unit

Deflection for Transverse Loading Alone: 4 Millimeter --> 0.004 Meter (Check conversion here)
Axial Load: 2000 Newton --> 2000 Newton No Conversion Required
Critical Buckling Load: 12000 Newton --> 12000 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = d₀/(1-(P/P_c)) --> 0.004/(1-(2000/12000))

Evaluating ... ...

δ = 0.0048

STEP 3: Convert Result to Output's Unit

0.0048 Meter -->4.8 Millimeter (Check conversion here)

FINAL ANSWER

4.8 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Combined Axial and Bending Loads » Deflection for Axial Compression and Bending

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Cummins College of Engineering for Women (CCEW), Pune

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< 19 Combined Axial and Bending Loads Calculators

Neutral Axis to Outermost Fiber Distance given Maximum Stress for Short Beams

Go Distance from Neutral Axis = ((Maximum Stress*Cross Sectional Area*Area Moment of Inertia)-(Axial Load*Area Moment of Inertia))/(Maximum Bending Moment*Cross Sectional Area)

Maximum Stress in Short Beams for Large Deflection

Go Maximum Stress = (Axial Load/Cross Sectional Area)+(((Maximum Bending Moment+Axial Load*Deflection of Beam)*Distance from Neutral Axis)/Area Moment of Inertia)

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams

Go Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))

Maximum Bending Moment given Maximum Stress for Short Beams

Go Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis

Cross-Sectional Area given Maximum Stress for Short Beams

Go Cross Sectional Area = Axial Load/(Maximum Stress-((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia))

Axial Load given Maximum Stress for Short Beams

Go Axial Load = Cross Sectional Area*(Maximum Stress-((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia))

Maximum Stress for Short Beams

Go Maximum Stress = (Axial Load/Cross Sectional Area)+((Maximum Bending Moment*Distance from Neutral Axis)/Area Moment of Inertia)

Young's Modulus given Distance from Extreme Fiber along with Radius and Stress Induced

Go Young's Modulus = ((Radius of Curvature*Fibre Stress at Distance ‘y’ from NA)/Distance from Neutral Axis)

Stress Induced with known Distance from Extreme Fiber, Young's Modulus and Radius of curvature

Go Fibre Stress at Distance ‘y’ from NA = (Young's Modulus*Distance from Neutral Axis)/Radius of Curvature

Distance from Extreme Fiber given Young's Modulus along with Radius and Stress Induced

Go Distance from Neutral Axis = (Radius of Curvature*Fibre Stress at Distance ‘y’ from NA)/Young's Modulus

Deflection for Transverse Loading given Deflection for Axial Bending

Go Deflection for Transverse Loading Alone = Deflection of Beam*(1-(Axial Load/Critical Buckling Load))

Deflection for Axial Compression and Bending

Go Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load))

Distance from Extreme Fiber given Moment of Resistance and Moment of Inertia along with Stress

Go Distance from Neutral Axis = (Area Moment of Inertia*Bending Stress)/Moment of Resistance

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber

Go Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress

Stress Induced using Moment of Resistance, Moment of Inertia and Distance from Extreme Fiber

Go Bending Stress = (Distance from Neutral Axis*Moment of Resistance)/Area Moment of Inertia

Moment of Resistance in Bending Equation

Go Moment of Resistance = (Area Moment of Inertia*Bending Stress)/Distance from Neutral Axis

Young's Modulus using Moment of Resistance, Moment of Inertia and Radius

Go Young's Modulus = (Moment of Resistance*Radius of Curvature)/Area Moment of Inertia

Moment of Resistance given Young's Modulus, Moment of Inertia and Radius

Go Moment of Resistance = (Area Moment of Inertia*Young's Modulus)/Radius of Curvature

Moment of Inertia given Young's Modulus, Moment of Resistance and Radius

Go Area Moment of Inertia = (Moment of Resistance*Radius of Curvature)/Young's Modulus

Deflection for Axial Compression and Bending Formula

Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load))
δ = d₀/(1-(P/P_c))

Define Deflection

Deflection is the degree to which a structural element is displaced under a load (due to its deformation). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load.

How to Calculate Deflection for Axial Compression and Bending?

Deflection for Axial Compression and Bending calculator uses Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load)) to calculate the Deflection of Beam, The Deflection for Axial Compression and Bending formula is defined as the degree to which an element of structure changes shape when a load is applied. Deflection of Beam is denoted by δ symbol.

How to calculate Deflection for Axial Compression and Bending using this online calculator? To use this online calculator for Deflection for Axial Compression and Bending, enter Deflection for Transverse Loading Alone (d₀), Axial Load (P) & Critical Buckling Load (P_c) and hit the calculate button. Here is how the Deflection for Axial Compression and Bending calculation can be explained with given input values -> 0.0048 = 0.004/(1-(2000/12000)).

FAQ

What is Deflection for Axial Compression and Bending?

The Deflection for Axial Compression and Bending formula is defined as the degree to which an element of structure changes shape when a load is applied and is represented as δ = d₀/(1-(P/P_c)) or Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load)). Deflection for Transverse Loading Alone is defined as the deflections caused in the beam due to the transverse load alone, Axial Load is a force applied on a structure directly along an axis of the structure & Critical Buckling Load is the maximum load that a column can take before deformation.

How to calculate Deflection for Axial Compression and Bending?

The Deflection for Axial Compression and Bending formula is defined as the degree to which an element of structure changes shape when a load is applied is calculated using Deflection of Beam = Deflection for Transverse Loading Alone/(1-(Axial Load/Critical Buckling Load)). To calculate Deflection for Axial Compression and Bending, you need Deflection for Transverse Loading Alone (d₀), Axial Load (P) & Critical Buckling Load (P_c). With our tool, you need to enter the respective value for Deflection for Transverse Loading Alone, Axial Load & Critical Buckling Load 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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