Straight Beam Deflection Calculator

✖Beam Loading Constant is defined as a constant which depends on the loading on the beam.ⓘ Beam Loading Constant [k_b]			+10% -10%
✖Total Beam Load is defined as the total application of force that is acting on the given beam.ⓘ Total Beam Load [T_l]			+10% -10%
✖Beam span is the effective span of the beam.ⓘ Beam Span [l]			+10% -10%
✖The modulus of elasticity of concrete is a characteristic that assesses concrete resistance to deformation under load. It is the ratio of stress to strain.ⓘ Modulus of Elasticity of Concrete [E_c]			+10% -10%
✖Moment of Inertia of the section about an axis parallel to the free surface passing through the centroid of the area.ⓘ Moment of Inertia [I]			+10% -10%
✖Support Condition Constant is defined as a constant which depends on the support conditions.ⓘ Support Condition Constant [k_s]			+10% -10%
✖The shear modulus is the slope of the linear elastic region of the shear stress–strain curve.ⓘ Shear Modulus [G]			+10% -10%
✖The cross-sectional area of beam is the rectangular cross-section.ⓘ Cross-Sectional Area of Beam [A]			+10% -10%

✖The deflection of beam 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.ⓘ Straight Beam Deflection [δ]

⎘ Copy

👎

Formula

✖

Straight Beam Deflection

Formula

`"δ" = (("k"_{"b"}*"T"_{"l"}*("l")^3)/("E"_{"c"}*"I"))+(("k"_{"s"}*"T"_{"l"}*"l")/("G"*"A"))`

Example

`"19.92665mm"=(("0.85"*"10kN"*("3000mm")^3)/("30000MPa"*"3.56kg·m²"))+(("0.75"*"10kN"*"3000mm")/("25000MPa"*"50625mm²"))`

Calculator

LaTeX

Reset

👍

Download Beams, Columns and Other Members Design Methods Formulas PDF PDF Image

Straight Beam Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = ((Beam Loading Constant*Total Beam Load*(Beam Span)^3)/(Modulus of Elasticity of Concrete*Moment of Inertia))+((Support Condition Constant*Total Beam Load*Beam Span)/(Shear Modulus*Cross-Sectional Area of Beam))
δ = ((k_b*T_l*(l)^3)/(E_c*I))+((k_s*T_l*l)/(G*A))
This formula uses 9 Variables

Variables Used

Deflection of Beam - (Measured in Meter) - The deflection of beam 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.
Beam Loading Constant - Beam Loading Constant is defined as a constant which depends on the loading on the beam.
Total Beam Load - (Measured in Kilonewton) - Total Beam Load is defined as the total application of force that is acting on the given beam.
Beam Span - (Measured in Meter) - Beam span is the effective span of the beam.
Modulus of Elasticity of Concrete - (Measured in Megapascal) - The modulus of elasticity of concrete is a characteristic that assesses concrete resistance to deformation under load. It is the ratio of stress to strain.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia of the section about an axis parallel to the free surface passing through the centroid of the area.
Support Condition Constant - Support Condition Constant is defined as a constant which depends on the support conditions.
Shear Modulus - (Measured in Megapascal) - The shear modulus is the slope of the linear elastic region of the shear stress–strain curve.
Cross-Sectional Area of Beam - (Measured in Square Meter) - The cross-sectional area of beam is the rectangular cross-section.

STEP 1: Convert Input(s) to Base Unit

Beam Loading Constant: 0.85 --> No Conversion Required
Total Beam Load: 10 Kilonewton --> 10 Kilonewton No Conversion Required
Beam Span: 3000 Millimeter --> 3 Meter (Check conversion here)
Modulus of Elasticity of Concrete: 30000 Megapascal --> 30000 Megapascal No Conversion Required
Moment of Inertia: 3.56 Kilogram Square Meter --> 3.56 Kilogram Square Meter No Conversion Required
Support Condition Constant: 0.75 --> No Conversion Required
Shear Modulus: 25000 Megapascal --> 25000 Megapascal No Conversion Required
Cross-Sectional Area of Beam: 50625 Square Millimeter --> 0.050625 Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = ((k_b*T_l*(l)^3)/(E_c*I))+((k_s*T_l*l)/(G*A)) --> ((0.85*10*(3)^3)/(30000*3.56))+((0.75*10*3)/(25000*0.050625))

Evaluating ... ...

δ = 0.0199266541822722

STEP 3: Convert Result to Output's Unit

0.0199266541822722 Meter -->19.9266541822722 Millimeter (Check conversion here)

FINAL ANSWER

19.9266541822722 ≈ 19.92665 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Concrete Formulas » Beams, Columns and Other Members Design Methods » Beams » Straight Beam Deflection

Credits

Created by Pranav More

Vellore Institute of Technology, Vellore (VIT, Vellore), Vellore

Pranav More has created this Calculator and 10+ more calculators!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

< 3 Beams Calculators

Straight Beam Deflection

Go Deflection of Beam = ((Beam Loading Constant*Total Beam Load*(Beam Span)^3)/(Modulus of Elasticity of Concrete*Moment of Inertia))+((Support Condition Constant*Total Beam Load*Beam Span)/(Shear Modulus*Cross-Sectional Area of Beam))

Tapered beam Deflection for Uniformly Distributed Load

Go Deflection of Beam = (3*Total Beam Load*Beam Span)/(20*Shear Modulus*Width of Beam*Effective Depth of Beam)

Tapered Beam Deflection for Mid-Span Concentrated Load

Go Deflection of Beam = (3*Total Beam Load*Beam Span)/(10*Shear Modulus*Width of Beam*Effective Depth of Beam)

Straight Beam Deflection Formula

What is Deflection of a Beam?

Deflection of a beam is defined as the displacement of the beam from its original horizontal position when subjected to loads.

What is Shear Deformation?

Shear deformation is very common during the wearing process where the fabric is to be sheared to a more or less degree so as to conform to the new gesture of body movement.

How to Calculate Straight Beam Deflection?

Straight Beam Deflection calculator uses Deflection of Beam = ((Beam Loading Constant*Total Beam Load*(Beam Span)^3)/(Modulus of Elasticity of Concrete*Moment of Inertia))+((Support Condition Constant*Total Beam Load*Beam Span)/(Shear Modulus*Cross-Sectional Area of Beam)) to calculate the Deflection of Beam, The Straight Beam Deflection formula is defined as the displacement of the beam from its original horizontal position when subjected to loads. Deflection of Beam is denoted by δ symbol.

How to calculate Straight Beam Deflection using this online calculator? To use this online calculator for Straight Beam Deflection, enter Beam Loading Constant (k_b), Total Beam Load (T_l), Beam Span (l), Modulus of Elasticity of Concrete (E_c), Moment of Inertia (I), Support Condition Constant (k_s), Shear Modulus (G) & Cross-Sectional Area of Beam (A) and hit the calculate button. Here is how the Straight Beam Deflection calculation can be explained with given input values -> 19926.65 = ((0.85*10000*(3)^3)/(30000000000*3.56))+((0.75*10000*3)/(25000000000*0.050625)).

FAQ

What is Straight Beam Deflection?

The Straight Beam Deflection formula is defined as the displacement of the beam from its original horizontal position when subjected to loads and is represented as δ = ((k_b*T_l*(l)^3)/(E_c*I))+((k_s*T_l*l)/(G*A)) or Deflection of Beam = ((Beam Loading Constant*Total Beam Load*(Beam Span)^3)/(Modulus of Elasticity of Concrete*Moment of Inertia))+((Support Condition Constant*Total Beam Load*Beam Span)/(Shear Modulus*Cross-Sectional Area of Beam)). Beam Loading Constant is defined as a constant which depends on the loading on the beam, Total Beam Load is defined as the total application of force that is acting on the given beam, Beam span is the effective span of the beam, The modulus of elasticity of concrete is a characteristic that assesses concrete resistance to deformation under load. It is the ratio of stress to strain, Moment of Inertia of the section about an axis parallel to the free surface passing through the centroid of the area, Support Condition Constant is defined as a constant which depends on the support conditions, The shear modulus is the slope of the linear elastic region of the shear stress–strain curve & The cross-sectional area of beam is the rectangular cross-section.

How to calculate Straight Beam Deflection?

The Straight Beam Deflection formula is defined as the displacement of the beam from its original horizontal position when subjected to loads is calculated using Deflection of Beam = ((Beam Loading Constant*Total Beam Load*(Beam Span)^3)/(Modulus of Elasticity of Concrete*Moment of Inertia))+((Support Condition Constant*Total Beam Load*Beam Span)/(Shear Modulus*Cross-Sectional Area of Beam)). To calculate Straight Beam Deflection, you need Beam Loading Constant (k_b), Total Beam Load (T_l), Beam Span (l), Modulus of Elasticity of Concrete (E_c), Moment of Inertia (I), Support Condition Constant (k_s), Shear Modulus (G) & Cross-Sectional Area of Beam (A). With our tool, you need to enter the respective value for Beam Loading Constant, Total Beam Load, Beam Span, Modulus of Elasticity of Concrete, Moment of Inertia, Support Condition Constant, Shear Modulus & Cross-Sectional Area of Beam 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 Deflection of Beam?

In this formula, Deflection of Beam uses Beam Loading Constant, Total Beam Load, Beam Span, Modulus of Elasticity of Concrete, Moment of Inertia, Support Condition Constant, Shear Modulus & Cross-Sectional Area of Beam. We can use 2 other way(s) to calculate the same, which is/are as follows -

Deflection of Beam = (3*Total Beam Load*Beam Span)/(20*Shear Modulus*Width of Beam*Effective Depth of Beam)
Deflection of Beam = (3*Total Beam Load*Beam Span)/(10*Shear Modulus*Width of Beam*Effective Depth of Beam)

Home

FREE PDFs

🔍 Search