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Straight Beam Deflection Formula

GoTapered beam Deflection for Uniformly Distributed Load Formula

GoTapered Beam Deflection for Mid-Span Concentrated Load Formula

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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. Check FAQs

δ = (\frac{k b \cdot T l \cdot {(l)}^{3}}{E c \cdot I}) + (\frac{k s \cdot T l \cdot l}{G \cdot A})

δ - Deflection of Beam?k_b - Beam Loading Constant?T_l - Total Beam Load?l - Beam Span?E_c - Modulus of Elasticity of Concrete?I - Moment of Inertia?k_s - Support Condition Constant?G - Shear Modulus?A - Cross-Sectional Area of Beam?

Straight Beam Deflection Example

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Here is how the Straight Beam Deflection equation looks like with Values.

Here is how the Straight Beam Deflection equation looks like with Units.

Here is how the Straight Beam Deflection equation looks like.

19.9267 = (\frac{0.85 \cdot 10 \cdot {(3000)}^{3}}{30000 \cdot 3.56}) + (\frac{0.75 \cdot 10 \cdot 3000}{25000 \cdot 50625})

19.9267mm = (\frac{0.85 \cdot 10kN \cdot {(3000mm)}^{3}}{30000MPa \cdot 3.56kg·m²}) + (\frac{0.75 \cdot 10kN \cdot 3000mm}{25000MPa \cdot 50625mm²})

19.9267 = (\frac{0.85 \cdot 10 \cdot {(3000)}^{3}}{30000 \cdot 3.56}) + (\frac{0.75 \cdot 10 \cdot 3000}{25000 \cdot 50625})

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Home » Engineering » Civil » Concrete Formulas » Straight Beam Deflection

Straight Beam Deflection Solution

Follow our step by step solution on how to calculate Straight Beam Deflection?

FIRST Step Consider the formula

δ = (\frac{k b \cdot T l \cdot {(l)}^{3}}{E c \cdot I}) + (\frac{k s \cdot T l \cdot l}{G \cdot A})

Next Step Substitute values of Variables

∴

δ = (\frac{0.85 \cdot 10kN \cdot {(3000mm)}^{3}}{30000MPa \cdot 3.56kg·m²}) + (\frac{0.75 \cdot 10kN \cdot 3000mm}{25000MPa \cdot 50625mm²})

Next Step Convert Units

∴

δ = (\frac{0.85 \cdot 10kN \cdot {(3m)}^{3}}{30000MPa \cdot 3.56kg·m²}) + (\frac{0.75 \cdot 10kN \cdot 3m}{25000MPa \cdot 0.0506m²})

Next Step Prepare to Evaluate

∴

δ = (\frac{0.85 \cdot 10 \cdot {(3)}^{3}}{30000 \cdot 3.56}) + (\frac{0.75 \cdot 10 \cdot 3}{25000 \cdot 0.0506})

Next Step Evaluate

∴

δ = 0.0199266541822722m

Next Step Convert to Output's Unit

∴

δ = 19.9266541822722mm

LAST Step Rounding Answer

∴

δ = 19.9267mm

Straight Beam Deflection Formula Elements

Variables

Deflection of Beam

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.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Beam Loading Constant

Beam Loading Constant is defined as a constant which depends on the loading on the beam.

Symbol: k_b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Total Beam Load

Total Beam Load is defined as the total application of force that is acting on the given beam.

Symbol: T_l

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Beam Span

Beam span is the effective span of the beam.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Modulus of Elasticity of Concrete

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.

Symbol: E_c

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Moment of Inertia

Moment of Inertia of the section about an axis parallel to the free surface passing through the centroid of the area.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Support Condition Constant

Support Condition Constant is defined as a constant which depends on the support conditions.

Symbol: k_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Shear Modulus

The shear modulus is the slope of the linear elastic region of the shear stress–strain curve.

Symbol: G

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Cross-Sectional Area of Beam

The cross-sectional area of beam is the rectangular cross-section.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value can be positive or negative.

Credits

Created by Pranav More

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

Pranav More has created this Formula and 10+ more formulas!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has verified this Formula and 700+ more formulas!

Other Formulas to find Deflection of Beam

Go Tapered beam Deflection for Uniformly Distributed Load

δ = \frac{3 \cdot T l \cdot l}{20 \cdot G \cdot b \cdot d}

Go Tapered Beam Deflection for Mid-Span Concentrated Load

δ = \frac{3 \cdot T l \cdot l}{10 \cdot G \cdot b \cdot d}

How to Evaluate Straight Beam Deflection?

Straight Beam Deflection evaluator 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 evaluate 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 evaluate Straight Beam Deflection using this online evaluator? To use this online evaluator 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.

FAQs on Straight Beam Deflection

What is the formula to find Straight Beam Deflection?

The formula of Straight Beam Deflection is expressed as 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)). Here is an example- 19926.65 = ((0.85*10000*(3)^3)/(30000000000*3.56))+((0.75*10000*3)/(25000000000*0.050625)).

How to calculate Straight Beam Deflection?

With 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) we can find Straight Beam Deflection using the formula - 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)).

What are the other ways to Calculate Deflection of Beam?

Here are the different ways to Calculate Deflection of Beam-

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)

Can the Straight Beam Deflection be negative?

Yes, the Straight Beam Deflection, measured in Length can be negative.

Which unit is used to measure Straight Beam Deflection?

Straight Beam Deflection is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Straight Beam Deflection can be measured.