Allowable Unit Stress at Angle to Grain Calculator

✖Allowable Unit Stress Parallel to Grain is maximum stress per unit area when parallel to the grain.ⓘ Allowable Unit Stress Parallel to Grain [c]			+10% -10%
✖Allowable Unit Stress Perpendicular to Grain is maximum stress per unit area when perpendicular to grain.ⓘ Allowable Unit Stress Perpendicular to Grain [c_⟂]			+10% -10%
✖Angle between Load and Grain is the angle between direction of load and direction of grain.ⓘ Angle between Load and Grain [θ]			+10% -10%

✖Allowable Unit Stress at Angle to Grain is maximum stress per unit area when at some angle to grain.ⓘ Allowable Unit Stress at Angle to Grain [c']

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Formula

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Allowable Unit Stress at Angle to Grain

Formula

`"c'" = ("c"*"c"_{"⟂"})/("c"*(sin("θ")^2)+"c"_{"⟂"}*(cos("θ")^2))`

Example

`"1.806513MPa"=("2.0001MPa"*"1.4MPa")/("2.0001MPa"*(sin("30°")^2)+"1.4MPa"*(cos("30°")^2))`

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Allowable Unit Stress at Angle to Grain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Allowable Unit Stress at Angle to Grain = (Allowable Unit Stress Parallel to Grain*Allowable Unit Stress Perpendicular to Grain)/(Allowable Unit Stress Parallel to Grain*(sin(Angle between Load and Grain)^2)+Allowable Unit Stress Perpendicular to Grain*(cos(Angle between Load and Grain)^2))
c' = (c*c_⟂)/(c*(sin(θ)^2)+c_⟂*(cos(θ)^2))
This formula uses 2 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Allowable Unit Stress at Angle to Grain - (Measured in Pascal) - Allowable Unit Stress at Angle to Grain is maximum stress per unit area when at some angle to grain.
Allowable Unit Stress Parallel to Grain - (Measured in Pascal) - Allowable Unit Stress Parallel to Grain is maximum stress per unit area when parallel to the grain.
Allowable Unit Stress Perpendicular to Grain - (Measured in Pascal) - Allowable Unit Stress Perpendicular to Grain is maximum stress per unit area when perpendicular to grain.
Angle between Load and Grain - (Measured in Radian) - Angle between Load and Grain is the angle between direction of load and direction of grain.

STEP 1: Convert Input(s) to Base Unit

Allowable Unit Stress Parallel to Grain: 2.0001 Megapascal --> 2000100 Pascal (Check conversion here)
Allowable Unit Stress Perpendicular to Grain: 1.4 Megapascal --> 1400000 Pascal (Check conversion here)
Angle between Load and Grain: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c' = (c*c_⟂)/(c*(sin(θ)^2)+c_⟂*(cos(θ)^2)) --> (2000100*1400000)/(2000100*(sin(0.5235987755982)^2)+1400000*(cos(0.5235987755982)^2))

Evaluating ... ...

c' = 1806512.79818067

STEP 3: Convert Result to Output's Unit

1806512.79818067 Pascal -->1.80651279818067 Megapascal (Check conversion here)

FINAL ANSWER

1.80651279818067 ≈ 1.806513 Megapascal <-- Allowable Unit Stress at Angle to Grain

(Calculation completed in 00.004 seconds)

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Credits

Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 200+ more calculators!

Verified by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has verified this Calculator and 50+ more calculators!

< 6 Columns Calculators

Allowable Unit Stress at Angle to Grain

Go Allowable Unit Stress at Angle to Grain = (Allowable Unit Stress Parallel to Grain*Allowable Unit Stress Perpendicular to Grain)/(Allowable Unit Stress Parallel to Grain*(sin(Angle between Load and Grain)^2)+Allowable Unit Stress Perpendicular to Grain*(cos(Angle between Load and Grain)^2))

Allowable Unit Stress on Timber Columns for Single Member

Go Allowable Unit Stress = (3.619*Modulus of Elasticity)/((Unsupported Length of Column/Radius of Gyration)^2)

Elasticity Modulus using Allowable Unit Stress of Circular Timber Columns

Go Modulus of Elasticity = (Allowable Unit Stress*((Unsupported Length of Column/Least Dimension)^2))/0.22

Allowable Unit Stress on Timber Columns of Circular Cross Section

Go Allowable Unit Stress = (0.22*Modulus of Elasticity)/((Unsupported Length of Column/Least Dimension)^2)

Elasticity Modulus given Allowable Unit Stress of Square or Rectangular Timber Columns

Go Modulus of Elasticity = (Allowable Unit Stress*((Unsupported Length of Column/Least Dimension)^2))/0.3

Allowable Unit Stress on Timber Columns of Square or Rectangular Cross Section

Go Allowable Unit Stress = (0.3*Modulus of Elasticity)/((Unsupported Length of Column/Least Dimension)^2)

Allowable Unit Stress at Angle to Grain Formula

What is Allowable Unit Stress?

Allowable Unit Stress or allowable unit strength is the maximum stress per unit area (tensile, compressive or bending) that is allowed to be applied on a structural material.

How to Calculate Allowable Unit Stress at Angle to Grain?

Allowable Unit Stress at Angle to Grain calculator uses Allowable Unit Stress at Angle to Grain = (Allowable Unit Stress Parallel to Grain*Allowable Unit Stress Perpendicular to Grain)/(Allowable Unit Stress Parallel to Grain*(sin(Angle between Load and Grain)^2)+Allowable Unit Stress Perpendicular to Grain*(cos(Angle between Load and Grain)^2)) to calculate the Allowable Unit Stress at Angle to Grain, The Allowable Unit Stress at Angle to Grain formula calculates the maximum stress or strength or load allowed per unit area when the load is at angle to the grain. Allowable Unit Stress at Angle to Grain is denoted by c' symbol.

How to calculate Allowable Unit Stress at Angle to Grain using this online calculator? To use this online calculator for Allowable Unit Stress at Angle to Grain, enter Allowable Unit Stress Parallel to Grain (c), Allowable Unit Stress Perpendicular to Grain (c_⟂) & Angle between Load and Grain (θ) and hit the calculate button. Here is how the Allowable Unit Stress at Angle to Grain calculation can be explained with given input values -> 1.8E-6 = (2000100*1400000)/(2000100*(sin(0.5235987755982)^2)+1400000*(cos(0.5235987755982)^2)).

FAQ

What is Allowable Unit Stress at Angle to Grain?

The Allowable Unit Stress at Angle to Grain formula calculates the maximum stress or strength or load allowed per unit area when the load is at angle to the grain and is represented as c' = (c*c_⟂)/(c*(sin(θ)^2)+c_⟂*(cos(θ)^2)) or Allowable Unit Stress at Angle to Grain = (Allowable Unit Stress Parallel to Grain*Allowable Unit Stress Perpendicular to Grain)/(Allowable Unit Stress Parallel to Grain*(sin(Angle between Load and Grain)^2)+Allowable Unit Stress Perpendicular to Grain*(cos(Angle between Load and Grain)^2)). Allowable Unit Stress Parallel to Grain is maximum stress per unit area when parallel to the grain, Allowable Unit Stress Perpendicular to Grain is maximum stress per unit area when perpendicular to grain & Angle between Load and Grain is the angle between direction of load and direction of grain.

How to calculate Allowable Unit Stress at Angle to Grain?

The Allowable Unit Stress at Angle to Grain formula calculates the maximum stress or strength or load allowed per unit area when the load is at angle to the grain is calculated using Allowable Unit Stress at Angle to Grain = (Allowable Unit Stress Parallel to Grain*Allowable Unit Stress Perpendicular to Grain)/(Allowable Unit Stress Parallel to Grain*(sin(Angle between Load and Grain)^2)+Allowable Unit Stress Perpendicular to Grain*(cos(Angle between Load and Grain)^2)). To calculate Allowable Unit Stress at Angle to Grain, you need Allowable Unit Stress Parallel to Grain (c), Allowable Unit Stress Perpendicular to Grain (c_⟂) & Angle between Load and Grain (θ). With our tool, you need to enter the respective value for Allowable Unit Stress Parallel to Grain, Allowable Unit Stress Perpendicular to Grain & Angle between Load and Grain and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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