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Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Formula

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Deflection at Section is the lateral displacement at the section of the column. Check FAQs

δ = \frac{- M t + H \cdot (l - x)}{P}

δ - Deflection at Section?M_t - Moment of Section?H - Horizontal Reaction?l - Column Length?x - Distance b/w Fixed End and Deflection Point?P - Column Crippling Load?

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Example

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Here is how the Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged equation looks like with Values.

Here is how the Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged equation looks like with Units.

Here is how the Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged equation looks like.

1333.3167 = \frac{- 50 + 2 \cdot (5000 - 3000)}{3}

1333.3167mm = \frac{- 50N*mm + 2kN \cdot (5000mm - 3000mm)}{3kN}

1333.3167 = \frac{- 50 + 2 \cdot (5000 - 3000)}{3}

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Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Solution

Follow our step by step solution on how to calculate Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged?

FIRST Step Consider the formula

δ = \frac{- M t + H \cdot (l - x)}{P}

Next Step Substitute values of Variables

∴

δ = \frac{- 50N*mm + 2kN \cdot (5000mm - 3000mm)}{3kN}

Next Step Convert Units

∴

δ = \frac{- 0.05N*m + 2000N \cdot (5m - 3m)}{3000N}

Next Step Prepare to Evaluate

∴

δ = \frac{- 0.05 + 2000 \cdot (5 - 3)}{3000}

Next Step Evaluate

∴

δ = 1.33331666666667m

Next Step Convert to Output's Unit

∴

δ = 1333.31666666667mm

LAST Step Rounding Answer

∴

δ = 1333.3167mm

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Formula Elements

Variables

Deflection at Section

Deflection at Section is the lateral displacement at the section of the column.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Deflection at Section

Moment of Section

The Moment of Section is an overturning effect (tends to bend or turn the member) created by the force(load) acting on a structural member.

Symbol: M_t

Measurement: Moment of ForceUnit: N*mm

Note: Value can be positive or negative.

Formulas to find Moment of Section

Horizontal Reaction

Horizontal Reaction is used to balance the bending moment due to vertical reactions and dead load, live load, etc.

Symbol: H

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Horizontal Reaction

Column Length

Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

Distance b/w Fixed End and Deflection Point

Distance b/w Fixed End and Deflection Point is the distance x between the point of deflection at section and fixed point.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance b/w Fixed End and Deflection Point

Column Crippling Load

Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Column Crippling Load

Other formulas in One End of Column is Fixed and Other is Hinged category

Go Moment at Section if One End of Column is Fixed and Other is Hinged

M t = - P \cdot δ + H \cdot (l - x)

Go Crippling Load given Moment at Section if One End of Column is Fixed and Other is Hinged

P = \frac{- M t + H \cdot (l - x)}{δ}

Go Horizontal Reaction given Moment at Section if One End of Column is Fixed and Other is Hinged

H = \frac{M t + P \cdot δ}{l - x}

Go Length of Column given Moment at Section if One End of Column is Fixed and Other is Hinged

l = \frac{M t + P \cdot δ}{H} + x

How to Evaluate Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged?

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged evaluator uses Deflection at Section = (-Moment of Section+Horizontal Reaction*(Column Length-Distance b/w Fixed End and Deflection Point))/Column Crippling Load to evaluate the Deflection at Section, Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged formula is defined as a measure of the lateral displacement of a column section when one end is fixed and the other is hinged, providing insight into the column's structural behavior under load. Deflection at Section is denoted by δ symbol.

How to evaluate Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged using this online evaluator? To use this online evaluator for Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged, enter Moment of Section (M_t), Horizontal Reaction (H), Column Length (l), Distance b/w Fixed End and Deflection Point (x) & Column Crippling Load (P) and hit the calculate button.

FAQs on Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged

What is the formula to find Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged?

The formula of Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged is expressed as Deflection at Section = (-Moment of Section+Horizontal Reaction*(Column Length-Distance b/w Fixed End and Deflection Point))/Column Crippling Load. Here is an example- 1.3E+6 = (-0.05+2000*(5-3))/3000.

How to calculate Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged?

With Moment of Section (M_t), Horizontal Reaction (H), Column Length (l), Distance b/w Fixed End and Deflection Point (x) & Column Crippling Load (P) we can find Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged using the formula - Deflection at Section = (-Moment of Section+Horizontal Reaction*(Column Length-Distance b/w Fixed End and Deflection Point))/Column Crippling Load.

Can the Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged be negative?

Yes, the Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged, measured in Length can be negative.

Which unit is used to measure Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged?

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged can be measured.

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Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Formula

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Example

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Solution

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged Formula Elements

Other formulas in One End of Column is Fixed and Other is Hinged category

How to Evaluate Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged?

FAQs on Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged

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