A Treatise On Statics: Containing the Fundamental Principles of ...
A Treatise On Statics: Containing the Fundamental Principles of ...
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If the triangle be replaced by a polygon of any number of sides, prove that the equivalent of the forces is a couple whose moment is proportional to the square root of the area of the (similar) polygon enclosed by their lines of action.
9. A triangular plate, ABO (fig. 1 17), is acted upon at each angle by forces, along the two sides containing it, represented in magnitudes and lines of action by the distances between the angle and the feet of the perpendiculars let fall from the other two angl...es on these sides. Find the line of action of the resultant force.
Let the perpendiculars let fall on the three sides, a, 6, c, from any point, P, f* 7 on the resultant be x, y, z, respectively, ^^* ' ' and let A^B'jC/ he the feet of the perpendiculars. Then the force in AB in the sense AB is Ad^BC, or 6 cos il— a cos -5. Hence the moment of this force about P is z {p cos A^a cos B\ and since the sum of the moments of all the forces (estimated in cyclical order) round P is = (Art. 76), we have a;(ccosJ?
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To quickly assess the difficulty of the text, read a short excerpt:
If the triangle be replaced by a polygon of any number of sides, prove that the equivalent of the forces is a couple whose moment is proportional to the square root of the area of the (similar) polygon enclosed by their lines of action.
9. A triangular plate, ABO (fig. 1 17), is acted upon at each angle by forces, along the two sides containing it, represented in magnitudes and lines of action by the distances between the angle and the feet of the perpendiculars let fall from the other two angl...es on these sides. Find the line of action of the resultant force.
Let the perpendiculars let fall on the three sides, a, 6, c, from any point, P, f* 7 on the resultant be x, y, z, respectively, ^^* ' ' and let A^B'jC/ he the feet of the perpendiculars. Then the force in AB in the sense AB is Ad^BC, or 6 cos il— a cos -5. Hence the moment of this force about P is z {p cos A^a cos B\ and since the sum of the moments of all the forces (estimated in cyclical order) round P is = (Art. 76), we have a;(ccosJ?
What to read after A Treatise On Statics: Containing the Fundamental Principles of ...?
You can find similar books in the "Read Also" column, or choose other free books by George Minchin Minchin to read onlineMoreLess
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