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The angle of oblique plane formula calculates the angle θ when a member is subjected to axial loading. It relates the normal stress on an oblique plane to the stress along the y-direction using trigonometric relationships.
The calculator uses the formula:
Where:
Explanation: The formula uses the inverse cosine function to determine the angle based on the ratio of normal stress to axial stress, divided by 2 to get the correct oblique plane angle.
Details: Calculating the angle of oblique plane is crucial for understanding stress distribution in materials under axial loading, analyzing failure planes, and designing structural components to withstand specific stress conditions.
Tips: Enter normal stress on oblique plane and stress along y-direction in Pascals. Both values must be positive, and normal stress cannot exceed stress along y-direction.
Q1: What is the range of valid angles?
A: The angle θ ranges from 0° to 90°, where 0° represents a plane parallel to the axis and 90° represents a plane perpendicular to the axis.
Q2: Why divide the arccos result by 2?
A: The division by 2 accounts for the geometric relationship between the oblique plane angle and the stress components in axial loading scenarios.
Q3: What units should be used for stress values?
A: Pascals (Pa) are the standard SI units, but any consistent pressure units can be used as long as both inputs are in the same units.
Q4: When is this formula applicable?
A: This formula applies to members subjected to pure axial loading where stress distribution follows the assumed trigonometric relationships.
Q5: What if normal stress equals stress along y-direction?
A: When σθ = σy, the angle θ becomes 0°, indicating the oblique plane is parallel to the axis of loading.