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Allowable Unit Stress at Angle to Grain Formula

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Allowable Unit Stress at Angle to Grain is maximum stress per unit area when at some angle to grain. Check FAQs

c' = \frac{c \cdot c ⟂}{c \cdot ({\sin (θ)}^{2}) + c ⟂ \cdot ({\cos (θ)}^{2})}

c' - Allowable Unit Stress at Angle to Grain?c - Allowable Unit Stress Parallel to Grain?c_⟂ - Allowable Unit Stress Perpendicular to Grain?θ - Angle between Load and Grain?

Allowable Unit Stress at Angle to Grain Example

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Here is how the Allowable Unit Stress at Angle to Grain equation looks like with Values.

Here is how the Allowable Unit Stress at Angle to Grain equation looks like with Units.

Here is how the Allowable Unit Stress at Angle to Grain equation looks like.

1.8065 = \frac{2.0001 \cdot 1.4}{2.0001 \cdot ({\sin (30)}^{2}) + 1.4 \cdot ({\cos (30)}^{2})}

1.8065MPa = \frac{2.0001MPa \cdot 1.4MPa}{2.0001MPa \cdot ({\sin (30°)}^{2}) + 1.4MPa \cdot ({\cos (30°)}^{2})}

1.8065 = \frac{2.0001 \cdot 1.4}{2.0001 \cdot ({\sin (30)}^{2}) + 1.4 \cdot ({\cos (30)}^{2})}

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Allowable Unit Stress at Angle to Grain Solution

Follow our step by step solution on how to calculate Allowable Unit Stress at Angle to Grain?

FIRST Step Consider the formula

c' = \frac{c \cdot c ⟂}{c \cdot ({\sin (θ)}^{2}) + c ⟂ \cdot ({\cos (θ)}^{2})}

Next Step Substitute values of Variables

∴

c' = \frac{2.0001MPa \cdot 1.4MPa}{2.0001MPa \cdot ({\sin (30°)}^{2}) + 1.4MPa \cdot ({\cos (30°)}^{2})}

Next Step Convert Units

∴

c' = \frac{2E+6Pa \cdot 1.4E+6Pa}{2E+6Pa \cdot ({\sin (0.5236rad)}^{2}) + 1.4E+6Pa \cdot ({\cos (0.5236rad)}^{2})}

Next Step Prepare to Evaluate

∴

c' = \frac{2E+6 \cdot 1.4E+6}{2E+6 \cdot ({\sin (0.5236)}^{2}) + 1.4E+6 \cdot ({\cos (0.5236)}^{2})}

Next Step Evaluate

∴

c' = 1806512.79818067Pa

Next Step Convert to Output's Unit

∴

c' = 1.80651279818067MPa

LAST Step Rounding Answer

∴

c' = 1.8065MPa

Allowable Unit Stress at Angle to Grain Formula Elements

Variables

Functions

Allowable Unit Stress at Angle to Grain

Allowable Unit Stress at Angle to Grain is maximum stress per unit area when at some angle to grain.

Symbol: c'

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Unit Stress at Angle to Grain

Allowable Unit Stress Parallel to Grain

Allowable Unit Stress Parallel to Grain is maximum stress per unit area when parallel to the grain.

Symbol: c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Unit Stress Parallel to Grain

Allowable Unit Stress Perpendicular to Grain

Allowable Unit Stress Perpendicular to Grain is maximum stress per unit area when perpendicular to grain.

Symbol: c_⟂

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Unit Stress Perpendicular to Grain

Angle between Load and Grain

Angle between Load and Grain is the angle between direction of load and direction of grain.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle between Load and Grain

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Columns category

Go Allowable Unit Stress on Timber Columns for Single Member

P|A = \frac{3.619 \cdot E}{{(\frac{L}{k G})}^{2}}

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

P|A = \frac{0.3 \cdot E}{{(\frac{L}{d})}^{2}}

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

E = \frac{P|A \cdot ({(\frac{L}{d})}^{2})}{0.3}

Go Allowable Unit Stress on Timber Columns of Circular Cross Section

P|A = \frac{0.22 \cdot E}{{(\frac{L}{d})}^{2}}

How to Evaluate Allowable Unit Stress at Angle to Grain?

Allowable Unit Stress at Angle to Grain evaluator 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 evaluate 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 evaluate Allowable Unit Stress at Angle to Grain using this online evaluator? To use this online evaluator 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.

FAQs on Allowable Unit Stress at Angle to Grain

What is the formula to find Allowable Unit Stress at Angle to Grain?

The formula of Allowable Unit Stress at Angle to Grain is expressed as 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)). Here is an example- 1.8E-6 = (2000100*1400000)/(2000100*(sin(0.5235987755982)^2)+1400000*(cos(0.5235987755982)^2)).

How to calculate Allowable Unit Stress at Angle to Grain?

With Allowable Unit Stress Parallel to Grain (c), Allowable Unit Stress Perpendicular to Grain (c_⟂) & Angle between Load and Grain (θ) we can find Allowable Unit Stress at Angle to Grain using the formula - 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)). This formula also uses Sine (sin), Cosine (cos) function(s).

Can the Allowable Unit Stress at Angle to Grain be negative?

No, the Allowable Unit Stress at Angle to Grain, measured in Pressure cannot be negative.

Which unit is used to measure Allowable Unit Stress at Angle to Grain?

Allowable Unit Stress at Angle to Grain is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Allowable Unit Stress at Angle to Grain can be measured.

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Allowable Unit Stress at Angle to Grain Formula

Allowable Unit Stress at Angle to Grain Example

Allowable Unit Stress at Angle to Grain Solution

Allowable Unit Stress at Angle to Grain Formula Elements

Other formulas in Columns category

How to Evaluate Allowable Unit Stress at Angle to Grain?

FAQs on Allowable Unit Stress at Angle to Grain

Variable Name