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Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Formula

GoMaximum Initial Deflection given Initial Deflection at Distance X from A Formula

GoMaximum Initial Deflection given Final Deflection at Distance X from End A of Column Formula

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Maximum Initial Deflection is the degree to which a structural element is displaced under a load. Check FAQs

C = (1 - (\frac{σ}{σ E})) \cdot ((\frac{σ max}{σ}) - 1) \cdot \frac{{k G}^{2}}{c}

C - Maximum Initial Deflection?σ - Direct Stress?σ_E - Euler Stress?σ_max - Maximum Stress at Crack Tip?k_G - Radius of Gyration?c - Distance from Neutral Axis to Extreme Point?

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Example

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Here is how the Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature equation looks like with Values.

Here is how the Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature equation looks like with Units.

Here is how the Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature equation looks like.

12674.9997 = (1 - (\frac{8E-6}{0.3})) \cdot ((\frac{6E-5}{8E-6}) - 1) \cdot \frac{312^{2}}{49.9187}

12674.9997mm = (1 - (\frac{8E-6MPa}{0.3MPa})) \cdot ((\frac{6E-5MPa}{8E-6MPa}) - 1) \cdot \frac{{312mm}^{2}}{49.9187mm}

12674.9997 = (1 - (\frac{8E-6}{0.3})) \cdot ((\frac{6E-5}{8E-6}) - 1) \cdot \frac{312^{2}}{49.9187}

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Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Solution

Follow our step by step solution on how to calculate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

FIRST Step Consider the formula

C = (1 - (\frac{σ}{σ E})) \cdot ((\frac{σ max}{σ}) - 1) \cdot \frac{{k G}^{2}}{c}

Next Step Substitute values of Variables

∴

C = (1 - (\frac{8E-6MPa}{0.3MPa})) \cdot ((\frac{6E-5MPa}{8E-6MPa}) - 1) \cdot \frac{{312mm}^{2}}{49.9187mm}

Next Step Convert Units

∴

C = (1 - (\frac{8Pa}{300000Pa})) \cdot ((\frac{60Pa}{8Pa}) - 1) \cdot \frac{{0.312m}^{2}}{0.0499m}

Next Step Prepare to Evaluate

∴

C = (1 - (\frac{8}{300000})) \cdot ((\frac{60}{8}) - 1) \cdot \frac{{0.312}^{2}}{0.0499}

Next Step Evaluate

∴

C = 12.6749996953044m

Next Step Convert to Output's Unit

∴

C = 12674.9996953044mm

LAST Step Rounding Answer

∴

C = 12674.9997mm

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Formula Elements

Variables

Maximum Initial Deflection

Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

Symbol: C

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Maximum Initial Deflection

Direct Stress

Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material.

Symbol: σ

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Direct Stress

Euler Stress

Euler stress is the stress in column with curvature due to Euler load.

Symbol: σ_E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Euler Stress

Maximum Stress at Crack Tip

Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.

Symbol: σ_max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress at Crack Tip

Radius of Gyration

Radius of Gyration is the radial distance from the axis of rotation at which the entire area or mass can be assumed to be concentrated to produce the same moment of inertia.

Symbol: k_G

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Distance from Neutral Axis to Extreme Point

Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.

Symbol: c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis to Extreme Point

Other Formulas to find Maximum Initial Deflection

Go Maximum Initial Deflection given Initial Deflection at Distance X from A

C = \frac{y'}{\sin (\frac{π \cdot x}{l})}

Go Maximum Initial Deflection given Final Deflection at Distance X from End A of Column

C = \frac{δ c}{(\frac{1}{1 - (\frac{P}{P E})}) \cdot \sin (\frac{π \cdot x}{l})}

Go Maximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature

C = \frac{δ c}{\frac{1}{1 - (\frac{P}{P E})}}

Other formulas in Columns With Initial Curvature category

Go Value of Distance 'X' given Initial Deflection at Distance X from end A

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

Go Length of Column given Initial Deflection at Distance X from end A

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Euler Load

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{π^{2} \cdot I}

How to Evaluate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature evaluator uses Maximum Initial Deflection = (1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point to evaluate the Maximum Initial Deflection, The Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the maximum initial deflection that occurs in columns with initial curvature when subjected to maximum stress, taking into account the effects of initial curvature on the column's behavior. Maximum Initial Deflection is denoted by C symbol.

How to evaluate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature using this online evaluator? To use this online evaluator for Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature, enter Direct Stress (σ), Euler Stress (σ_E), Maximum Stress at Crack Tip (σ_max), Radius of Gyration (k_G) & Distance from Neutral Axis to Extreme Point (c) and hit the calculate button.

FAQs on Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature

What is the formula to find Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

The formula of Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature is expressed as Maximum Initial Deflection = (1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point. Here is an example- 300000 = (1-(8/300000))*((60/8)-1)*(0.312^2)/0.04991867.

How to calculate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

With Direct Stress (σ), Euler Stress (σ_E), Maximum Stress at Crack Tip (σ_max), Radius of Gyration (k_G) & Distance from Neutral Axis to Extreme Point (c) we can find Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature using the formula - Maximum Initial Deflection = (1-(Direct Stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct Stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point.

What are the other ways to Calculate Maximum Initial Deflection?

Here are the different ways to Calculate Maximum Initial Deflection-

Maximum Initial Deflection=Initial Deflection/sin((pi*Distance of Deflection from end A)/Length of Column)
Maximum Initial Deflection=Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of Deflection from end A)/Length of Column))
Maximum Initial Deflection=Deflection of Column/(1/(1-(Crippling Load/Euler Load)))

Can the Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature be negative?

Yes, the Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature, measured in Length can be negative.

Which unit is used to measure Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature can be measured.

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Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Formula

​GoMaximum Initial Deflection given Initial Deflection at Distance X from A Formula

​GoMaximum Initial Deflection given Final Deflection at Distance X from End A of Column Formula

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Example

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Solution

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Formula Elements

Other Formulas to find Maximum Initial Deflection

Other formulas in Columns With Initial Curvature category

How to Evaluate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

FAQs on Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature

Variable Name

GoMaximum Initial Deflection given Initial Deflection at Distance X from A Formula

GoMaximum Initial Deflection given Final Deflection at Distance X from End A of Column Formula