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Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Formula

GoMaximum Bending Stress if Maximum Bending Moment is given for Strut with Axial and Point Load Formula

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Maximum Bending Stress is the highest stress experienced by a material when subjected to bending forces. It occurs at the point on a beam or structural element where the bending moment is greatest. Check FAQs

σb max = (\frac{P compressive}{A sectional}) + ((W p \cdot ((\frac{\sqrt{I \cdot \frac{ε column}{P compressive}}}{2 \cdot P compressive}) \cdot \tan ((\frac{l column}{2}) \cdot (\sqrt{\frac{P compressive}{I \cdot \frac{ε column}{P compressive}}})))) \cdot \frac{c}{A sectional \cdot (k^{2})})

σb^max - Maximum Bending Stress?P_compressive - Column Compressive Load?A_sectional - Column Cross Sectional Area?W_p - Greatest Safe Load?I - Moment of Inertia in Column?ε_column - Modulus of Elasticity?l_column - Column Length?c - Distance from Neutral Axis to Extreme Point?k - Least Radius of Gyration of Column?

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Example

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Here is how the Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center equation looks like with Values.

Here is how the Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center equation looks like with Units.

Here is how the Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center equation looks like.

0.0003 = (\frac{0.4}{1.4}) + ((0.1 \cdot ((\frac{\sqrt{5600 \cdot \frac{10.56}{0.4}}}{2 \cdot 0.4}) \cdot \tan ((\frac{5000}{2}) \cdot (\sqrt{\frac{0.4}{5600 \cdot \frac{10.56}{0.4}}})))) \cdot \frac{10}{1.4 \cdot ({2.9277}^{2})})

0.0003MPa = (\frac{0.4kN}{1.4m²}) + ((0.1kN \cdot ((\frac{\sqrt{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}{2 \cdot 0.4kN}) \cdot \tan ((\frac{5000mm}{2}) \cdot (\sqrt{\frac{0.4kN}{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}})))) \cdot \frac{10mm}{1.4m² \cdot ({2.9277mm}^{2})})

0.0003 = (\frac{0.4}{1.4}) + ((0.1 \cdot ((\frac{\sqrt{5600 \cdot \frac{10.56}{0.4}}}{2 \cdot 0.4}) \cdot \tan ((\frac{5000}{2}) \cdot (\sqrt{\frac{0.4}{5600 \cdot \frac{10.56}{0.4}}})))) \cdot \frac{10}{1.4 \cdot ({2.9277}^{2})})

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Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Solution

Follow our step by step solution on how to calculate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

FIRST Step Consider the formula

σb max = (\frac{P compressive}{A sectional}) + ((W p \cdot ((\frac{\sqrt{I \cdot \frac{ε column}{P compressive}}}{2 \cdot P compressive}) \cdot \tan ((\frac{l column}{2}) \cdot (\sqrt{\frac{P compressive}{I \cdot \frac{ε column}{P compressive}}})))) \cdot \frac{c}{A sectional \cdot (k^{2})})

Next Step Substitute values of Variables

∴

σb max = (\frac{0.4kN}{1.4m²}) + ((0.1kN \cdot ((\frac{\sqrt{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}}{2 \cdot 0.4kN}) \cdot \tan ((\frac{5000mm}{2}) \cdot (\sqrt{\frac{0.4kN}{5600cm⁴ \cdot \frac{10.56MPa}{0.4kN}}})))) \cdot \frac{10mm}{1.4m² \cdot ({2.9277mm}^{2})})

Next Step Convert Units

∴

σb max = (\frac{400N}{1.4m²}) + ((100N \cdot ((\frac{\sqrt{5.6E-5m⁴ \cdot \frac{1.1E+7Pa}{400N}}}{2 \cdot 400N}) \cdot \tan ((\frac{5m}{2}) \cdot (\sqrt{\frac{400N}{5.6E-5m⁴ \cdot \frac{1.1E+7Pa}{400N}}})))) \cdot \frac{0.01m}{1.4m² \cdot ({0.0029m}^{2})})

Next Step Prepare to Evaluate

∴

σb max = (\frac{400}{1.4}) + ((100 \cdot ((\frac{\sqrt{5.6E-5 \cdot \frac{1.1E+7}{400}}}{2 \cdot 400}) \cdot \tan ((\frac{5}{2}) \cdot (\sqrt{\frac{400}{5.6E-5 \cdot \frac{1.1E+7}{400}}})))) \cdot \frac{0.01}{1.4 \cdot ({0.0029}^{2})})

Next Step Evaluate

∴

σb max = 322.309786460362Pa

Next Step Convert to Output's Unit

∴

σb max = 0.000322309786460362MPa

LAST Step Rounding Answer

∴

σb max = 0.0003MPa

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Formula Elements

Variables

Functions

Maximum Bending Stress

Maximum Bending Stress is the highest stress experienced by a material when subjected to bending forces. It occurs at the point on a beam or structural element where the bending moment is greatest.

Symbol: σb^max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Bending Stress

Column Compressive Load

Column Compressive Load is the load applied to a column that is compressive in nature.

Symbol: P_compressive

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Column Compressive Load

Column Cross Sectional Area

Column Cross Sectional Area is the area of a column that is obtained when a column is sliced perpendicular to some specified axis at a point.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Column Cross Sectional Area

Greatest Safe Load

Greatest Safe Load is the maximum safe point load allowable at the center of the beam.

Symbol: W_p

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Greatest Safe Load

Moment of Inertia in Column

Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia in Column

Modulus of Elasticity

Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

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_column

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

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

Least Radius of Gyration of Column

Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.

Symbol: k

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration of Column

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Maximum Bending Stress

Go Maximum Bending Stress if Maximum Bending Moment is given for Strut with Axial and Point Load

σb max = \frac{M max \cdot c}{A sectional \cdot (k^{2})}

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre category

Go Bending Moment at Section for Strut with Axial and Transverse Point Load at Center

M b = - (P compressive \cdot δ) - (W p \cdot \frac{x}{2})

Go Compressive Axial Load for Strut with Axial and Transverse Point Load at Center

P compressive = - \frac{M b + (W p \cdot \frac{x}{2})}{δ}

How to Evaluate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center evaluator uses Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))) to evaluate the Maximum Bending Stress, The Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum stress experienced by a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, taking into account the strut's geometric and material properties. Maximum Bending Stress is denoted by σb^max symbol.

How to evaluate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center using this online evaluator? To use this online evaluator for Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center, enter Column Compressive Load (P_compressive), Column Cross Sectional Area (A_sectional), Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Length (l_column), Distance from Neutral Axis to Extreme Point (c) & Least Radius of Gyration of Column (k) and hit the calculate button.

FAQs on Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center

What is the formula to find Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

The formula of Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center is expressed as Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))). Here is an example- 2.9E-10 = (400/1.4)+((100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))))*(0.01)/(1.4*(0.0029277^2))).

How to calculate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

With Column Compressive Load (P_compressive), Column Cross Sectional Area (A_sectional), Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Length (l_column), Distance from Neutral Axis to Extreme Point (c) & Least Radius of Gyration of Column (k) we can find Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center using the formula - Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))). This formula also uses Tangent (tan), Square Root (sqrt) function(s).

What are the other ways to Calculate Maximum Bending Stress?

Here are the different ways to Calculate Maximum Bending Stress-

Maximum Bending Stress=(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))

Can the Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center be negative?

No, the Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center, measured in Pressure cannot be negative.

Which unit is used to measure Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center can be measured.

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Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Formula

​GoMaximum Bending Stress if Maximum Bending Moment is given for Strut with Axial and Point Load Formula

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Example

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Solution

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Formula Elements

Other Formulas to find Maximum Bending Stress

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre category

How to Evaluate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

FAQs on Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center

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GoMaximum Bending Stress if Maximum Bending Moment is given for Strut with Axial and Point Load Formula