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 = ((kb*Tl*(l)^3)/(Ec*I))+((ks*Tl*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.
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
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 = ((kb*Tl*(l)^3)/(Ec*I))+((ks*Tl*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)
19.9266541822722 19.92665 Millimeter <-- Deflection of Beam
(Calculation completed in 00.004 seconds)
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<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

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 = ((kb*Tl*(l)^3)/(Ec*I))+((ks*Tl*l)/(G*A))

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 (kb), Total Beam Load (Tl), Beam Span (l), Modulus of Elasticity of Concrete (Ec), Moment of Inertia (I), Support Condition Constant (ks), 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?
How to calculate Straight Beam Deflection?
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)
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