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Beam Depth for given Column Load Formula

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The Depth of Section is the depth of the rectangular cross-section of the beam perpendicular to the axis of consideration. Check FAQs

D = \frac{N \cdot (3 \cdot {(\frac{t w}{t f})}^{1.5})}{(\frac{R}{(67.5 \cdot {t w}^{\frac{3}{2}}) \cdot \sqrt{F y \cdot t f}} - 1)}

D - Depth of Section?N - Bearing or Plate Length?t_w - Web Thickness?t_f - Flange Thickness?R - Concentrated Load of Reaction?F_y - Yield Stress of Steel?

Beam Depth for given Column Load Example

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Here is how the Beam Depth for given Column Load equation looks like with Values.

Here is how the Beam Depth for given Column Load equation looks like with Units.

Here is how the Beam Depth for given Column Load equation looks like.

147.9322 = \frac{160 \cdot (3 \cdot {(\frac{100}{15})}^{1.5})}{(\frac{235}{(67.5 \cdot 100^{\frac{3}{2}}) \cdot \sqrt{250 \cdot 15}} - 1)}

147.9322mm = \frac{160mm \cdot (3 \cdot {(\frac{100mm}{15mm})}^{1.5})}{(\frac{235kN}{(67.5 \cdot {100mm}^{\frac{3}{2}}) \cdot \sqrt{250MPa \cdot 15mm}} - 1)}

147.9322 = \frac{160 \cdot (3 \cdot {(\frac{100}{15})}^{1.5})}{(\frac{235}{(67.5 \cdot 100^{\frac{3}{2}}) \cdot \sqrt{250 \cdot 15}} - 1)}

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Beam Depth for given Column Load Solution

Follow our step by step solution on how to calculate Beam Depth for given Column Load?

FIRST Step Consider the formula

D = \frac{N \cdot (3 \cdot {(\frac{t w}{t f})}^{1.5})}{(\frac{R}{(67.5 \cdot {t w}^{\frac{3}{2}}) \cdot \sqrt{F y \cdot t f}} - 1)}

Next Step Substitute values of Variables

∴

D = \frac{160mm \cdot (3 \cdot {(\frac{100mm}{15mm})}^{1.5})}{(\frac{235kN}{(67.5 \cdot {100mm}^{\frac{3}{2}}) \cdot \sqrt{250MPa \cdot 15mm}} - 1)}

Next Step Convert Units

∴

D = \frac{0.16m \cdot (3 \cdot {(\frac{0.1m}{0.015m})}^{1.5})}{(\frac{235000N}{(67.5 \cdot {0.1m}^{\frac{3}{2}}) \cdot \sqrt{2.5E+8Pa \cdot 0.015m}} - 1)}

Next Step Prepare to Evaluate

∴

D = \frac{0.16 \cdot (3 \cdot {(\frac{0.1}{0.015})}^{1.5})}{(\frac{235000}{(67.5 \cdot {0.1}^{\frac{3}{2}}) \cdot \sqrt{2.5E+8 \cdot 0.015}} - 1)}

Next Step Evaluate

∴

D = 0.147932249989211m

Next Step Convert to Output's Unit

∴

D = 147.932249989211mm

LAST Step Rounding Answer

∴

D = 147.9322mm

Beam Depth for given Column Load Formula Elements

Variables

Functions

Depth of Section

The Depth of Section is the depth of the rectangular cross-section of the beam perpendicular to the axis of consideration.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Section

Bearing or Plate Length

Bearing or Plate Length is the length along the beam under which a high concentration of stresses due to concentrated loads is transferred to the supporting structure below.

Symbol: N

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Bearing or Plate Length

Web Thickness

Web Thickness is the thickness of the web section in the member of I section.

Symbol: t_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Web Thickness

Flange Thickness

The Flange Thickness is the thickness of a flange in a protruded ridge, lip or rim, either external or internal of a beam such as an I-beam or a T-beam.

Symbol: t_f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Flange Thickness

Concentrated Load of Reaction

Concentrated Load of Reaction is the reaction force that is assumed to act at a single point on the structure.

Symbol: R

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Concentrated Load of Reaction

Yield Stress of Steel

Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

Symbol: F_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Stress of Steel

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 in Webs under Concentrated Loads category

Go Stress when Concentrated Load is Applied Close to Beam End

f a = \frac{R}{t w \cdot (N + 2.5 \cdot k)}

Go Stress for Concentrated Load Applied at Distance Larger than Depth of Beam

f a = \frac{R}{t w \cdot (N + 5 \cdot k)}

Go Length of Bearing when Load applied at Distance Larger than Depth of Beam

N = (\frac{R}{f a \cdot t w}) - 5 \cdot k

Go Web Thickness for Given Stress

t w = \frac{R}{f a \cdot (N + 5 \cdot k)}

How to Evaluate Beam Depth for given Column Load?

Beam Depth for given Column Load evaluator uses Depth of Section = (Bearing or Plate Length*(3*(Web Thickness/Flange Thickness)^1.5))/((Concentrated Load of Reaction/((67.5*Web Thickness^(3/2))*sqrt(Yield Stress of Steel*Flange Thickness))-1)) to evaluate the Depth of Section, The Beam Depth for given Column Load formula is defined as the parameters, bearing length, web and flange thickness, and the yield stress of web and column load used for finding the depth of a beam. Depth of Section is denoted by D symbol.

How to evaluate Beam Depth for given Column Load using this online evaluator? To use this online evaluator for Beam Depth for given Column Load, enter Bearing or Plate Length (N), Web Thickness (t_w), Flange Thickness (t_f), Concentrated Load of Reaction (R) & Yield Stress of Steel (F_y) and hit the calculate button.

FAQs on Beam Depth for given Column Load

What is the formula to find Beam Depth for given Column Load?

The formula of Beam Depth for given Column Load is expressed as Depth of Section = (Bearing or Plate Length*(3*(Web Thickness/Flange Thickness)^1.5))/((Concentrated Load of Reaction/((67.5*Web Thickness^(3/2))*sqrt(Yield Stress of Steel*Flange Thickness))-1)). Here is an example- 147932.2 = (0.16*(3*(0.1/0.015)^1.5))/((235000/((67.5*0.1^(3/2))*sqrt(250000000*0.015))-1)).

How to calculate Beam Depth for given Column Load?

With Bearing or Plate Length (N), Web Thickness (t_w), Flange Thickness (t_f), Concentrated Load of Reaction (R) & Yield Stress of Steel (F_y) we can find Beam Depth for given Column Load using the formula - Depth of Section = (Bearing or Plate Length*(3*(Web Thickness/Flange Thickness)^1.5))/((Concentrated Load of Reaction/((67.5*Web Thickness^(3/2))*sqrt(Yield Stress of Steel*Flange Thickness))-1)). This formula also uses Square Root Function function(s).

Can the Beam Depth for given Column Load be negative?

No, the Beam Depth for given Column Load, measured in Length cannot be negative.

Which unit is used to measure Beam Depth for given Column Load?

Beam Depth for given Column Load is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Beam Depth for given Column Load can be measured.

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Beam Depth for given Column Load Formula

Beam Depth for given Column Load Example

Beam Depth for given Column Load Solution

Beam Depth for given Column Load Formula Elements

Other formulas in Webs under Concentrated Loads category

How to Evaluate Beam Depth for given Column Load?

FAQs on Beam Depth for given Column Load

Variable Name