First moment of area
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The first moment of area, also known as the first moment of inertia, is usually denoted by the symbol Q and is a property of a shape that is used to predict its resistance to shear stress.
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[edit] Definition
- Qx - the first moment of area about the axis x
- dA - an elemental area
- y - the perpendicular distance to the element dA from the axis x
[edit] Units
The SI unit for first moment of area is metre to the third power (m3). In the American Engineering and Gravitational systems the unit is foot to the third power (ft3).
[edit] Shear Stress in a Semi-monocoque Structure
The equation for shear flow in a particular web section of the cross-section of a semi-monocoque structure is:
- q - the shear flow through a particular web section of the cross-section
- Vy - the shear force perpendicular to the neutral axis x through the entire cross-section
- Qx - the first moment of area about the neutral axis x for a particular web section of the cross-section
- Ix - the second moment of area about the neutral axis x for the entire cross-section
Shear stress may now be calculated using the following equation:
- Τ - the shear stress through a particular web section of the cross-section
- q - the shear flow through a particular web section of the cross-section
- t - the (average) thickness of a particular web section of the cross-section
