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Deflection for Hollow Rectangle given Load in Middle Formula

GoDeflection for Solid Rectangle when Load in Middle Formula

GoDeflection for Solid Rectangle when Load is Distributed Formula

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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{Wp \cdot L^{3}}{32 \cdot ((A cs \cdot {d b}^{2}) - (a \cdot d^{2}))}

δ - Deflection of Beam?Wp - Greatest Safe Point Load?L - Length of Beam?A_cs - Cross Sectional Area of Beam?d_b - Depth of Beam?a - Interior Cross-Sectional Area of Beam?d - Interior Depth of Beam?

Deflection for Hollow Rectangle given Load in Middle Example

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Here is how the Deflection for Hollow Rectangle given Load in Middle equation looks like with Values.

Here is how the Deflection for Hollow Rectangle given Load in Middle equation looks like with Units.

Here is how the Deflection for Hollow Rectangle given Load in Middle equation looks like.

52156.7574 = \frac{1.25 \cdot {10.02}^{3}}{32 \cdot ((13 \cdot {10.01}^{2}) - (10 \cdot 10^{2}))}

52156.7574in = \frac{1.25kN \cdot {10.02ft}^{3}}{32 \cdot ((13m² \cdot {10.01in}^{2}) - (10in² \cdot {10in}^{2}))}

52156.7574 = \frac{1.25 \cdot {10.02}^{3}}{32 \cdot ((13 \cdot {10.01}^{2}) - (10 \cdot 10^{2}))}

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Deflection for Hollow Rectangle given Load in Middle Solution

Follow our step by step solution on how to calculate Deflection for Hollow Rectangle given Load in Middle?

FIRST Step Consider the formula

δ = \frac{Wp \cdot L^{3}}{32 \cdot ((A cs \cdot {d b}^{2}) - (a \cdot d^{2}))}

Next Step Substitute values of Variables

∴

δ = \frac{1.25kN \cdot {10.02ft}^{3}}{32 \cdot ((13m² \cdot {10.01in}^{2}) - (10in² \cdot {10in}^{2}))}

Next Step Convert Units

∴

δ = \frac{1250N \cdot {3.0541m}^{3}}{32 \cdot ((13m² \cdot {0.2543m}^{2}) - (0.0065m² \cdot {0.254m}^{2}))}

Next Step Prepare to Evaluate

∴

δ = \frac{1250 \cdot {3.0541}^{3}}{32 \cdot ((13 \cdot {0.2543}^{2}) - (0.0065 \cdot {0.254}^{2}))}

Next Step Evaluate

∴

δ = 1324.78163797662m

Next Step Convert to Output's Unit

∴

δ = 52156.7574004455in

LAST Step Rounding Answer

∴

δ = 52156.7574in

Deflection for Hollow Rectangle given Load in Middle Formula Elements

Variables

Deflection of Beam

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: in

Note: Value should be greater than 0.

Formulas to find Deflection of Beam

Greatest Safe Point Load

The Greatest Safe Point Load refers to the maximum weight or force that can be applied to a structure without causing failure or damage, ensuring structural integrity and safety.

Symbol: Wp

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Greatest Safe Point Load

Length of Beam

Length of Beam is the center to center distance between the supports or the effective length of the beam.

Symbol: L

Measurement: LengthUnit: ft

Note: Value should be greater than 0.

Formulas to find Length of Beam

Cross Sectional Area of Beam

Cross Sectional Area of Beam 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.

Symbol: A_cs

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Beam

Depth of Beam

Depth of Beam is the overall depth of the cross-section of the beam perpendicular to the axis of the beam.

Symbol: d_b

Measurement: LengthUnit: in

Note: Value should be greater than 0.

Formulas to find Depth of Beam

Interior Cross-Sectional Area of Beam

Interior Cross-Sectional Area of Beam is the hollow area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to the axis at a point.

Symbol: a

Measurement: AreaUnit: in²

Note: Value should be greater than 0.

Formulas to find Interior Cross-Sectional Area of Beam

Interior Depth of Beam

Interior Depth of Beam is the depth of the hollow cross section of the beam perpendicular to the axis of the beam.

Symbol: d

Measurement: LengthUnit: in

Note: Value should be greater than 0.

Formulas to find Interior Depth of Beam

Other Formulas to find Deflection of Beam

Go Deflection for Solid Rectangle when Load in Middle

δ = \frac{Wp \cdot L^{3}}{32 \cdot A cs \cdot {d b}^{2}}

Go Deflection for Solid Rectangle when Load is Distributed

δ = \frac{W d \cdot L^{3}}{52 \cdot A cs \cdot {d b}^{2}}

How to Evaluate Deflection for Hollow Rectangle given Load in Middle?

Deflection for Hollow Rectangle given Load in Middle evaluator uses Deflection of Beam = (Greatest Safe Point Load*Length of Beam^3)/(32*((Cross Sectional Area of Beam*Depth of Beam^2)-(Interior Cross-Sectional Area of Beam*Interior Depth of Beam^2))) to evaluate the Deflection of Beam, The Deflection for Hollow Rectangle given Load in Middle formula is defined as the vertical displacement of a point on a hallow rectangular beam loaded in middle. Deflection of Beam is denoted by δ symbol.

How to evaluate Deflection for Hollow Rectangle given Load in Middle using this online evaluator? To use this online evaluator for Deflection for Hollow Rectangle given Load in Middle, enter Greatest Safe Point Load (Wp), Length of Beam (L), Cross Sectional Area of Beam (A_cs), Depth of Beam (d_b), Interior Cross-Sectional Area of Beam (a) & Interior Depth of Beam (d) and hit the calculate button.

FAQs on Deflection for Hollow Rectangle given Load in Middle

What is the formula to find Deflection for Hollow Rectangle given Load in Middle?

The formula of Deflection for Hollow Rectangle given Load in Middle is expressed as Deflection of Beam = (Greatest Safe Point Load*Length of Beam^3)/(32*((Cross Sectional Area of Beam*Depth of Beam^2)-(Interior Cross-Sectional Area of Beam*Interior Depth of Beam^2))). Here is an example- 2.1E+6 = (1250*3.05409600001222^3)/(32*((13*0.254254000001017^2)-(0.00645160000005161*0.254000000001016^2))).

How to calculate Deflection for Hollow Rectangle given Load in Middle?

With Greatest Safe Point Load (Wp), Length of Beam (L), Cross Sectional Area of Beam (A_cs), Depth of Beam (d_b), Interior Cross-Sectional Area of Beam (a) & Interior Depth of Beam (d) we can find Deflection for Hollow Rectangle given Load in Middle using the formula - Deflection of Beam = (Greatest Safe Point Load*Length of Beam^3)/(32*((Cross Sectional Area of Beam*Depth of Beam^2)-(Interior Cross-Sectional Area of Beam*Interior Depth of Beam^2))).

What are the other ways to Calculate Deflection of Beam?

Here are the different ways to Calculate Deflection of Beam-

Deflection of Beam=(Greatest Safe Point Load*Length of Beam^3)/(32*Cross Sectional Area of Beam*Depth of Beam^2)
Deflection of Beam=(Greatest Safe Distributed Load*Length of Beam^3)/(52*Cross Sectional Area of Beam*Depth of Beam^2)
Deflection of Beam=Greatest Safe Distributed Load*(Length of Beam^3)/(52*(Cross Sectional Area of Beam*Depth of Beam^-Interior Cross-Sectional Area of Beam*Interior Depth of Beam^2))

Can the Deflection for Hollow Rectangle given Load in Middle be negative?

No, the Deflection for Hollow Rectangle given Load in Middle, measured in Length cannot be negative.

Which unit is used to measure Deflection for Hollow Rectangle given Load in Middle?

Deflection for Hollow Rectangle given Load in Middle is usually measured using the Inch[in] for Length. Meter[in], Millimeter[in], Kilometer[in] are the few other units in which Deflection for Hollow Rectangle given Load in Middle can be measured.

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Deflection for Hollow Rectangle given Load in Middle Formula

​GoDeflection for Solid Rectangle when Load in Middle Formula

​GoDeflection for Solid Rectangle when Load is Distributed Formula

Deflection for Hollow Rectangle given Load in Middle Example

Deflection for Hollow Rectangle given Load in Middle Solution

Deflection for Hollow Rectangle given Load in Middle Formula Elements

Other Formulas to find Deflection of Beam

How to Evaluate Deflection for Hollow Rectangle given Load in Middle?

FAQs on Deflection for Hollow Rectangle given Load in Middle

Variable Name

GoDeflection for Solid Rectangle when Load in Middle Formula

GoDeflection for Solid Rectangle when Load is Distributed Formula