Graphic and Analytic Statics in Theory and Comparison: Their Practical Application to the Treatment of Stresses in Roofs, Solid Girders, Lattice, Bowstring and Suspension Bridges, Braced Iron Arches and Piers, and Other Frameworks: to which is Added a Chapter on Wind Pressures "Containing Diagrams and Plates to Scale, with Numerous Examples, Many Taken from Existing Structures"Crosby Lockwood and Company, 1883 - 374 páginas |
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Términos y frases comunes
abscissa angle b₁ beam bending bending moment centre of gravity co-ordinates constant construction corresponding cos.² couple cross-section curve deflection determined direction draw a line drawn dx dy ellipse of inertia equal equation equilibrium expressed force-line girder Hence horizontal inch integration intercept intersect length limits line of action line of loads M₁ maximum moment of inertia moments neutral axis nucleus objective path ordinate P₁ parallel forces parallel to bar perpendicular distance plane of section point of application polar line polar polygon pole polygon of forces principal axes R₁ R₂ radius of gyration reactions reciprocal figure relatively represent required to find respectively resultant force S₁ shearing force shearing stress shew ß₁ supposed system of forces tension tons triangle truss uniform load vertical line W₁ weight wherefore x₁ y₁
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Página i - GRAPHIC AND ANALYTIC STATICS. In their Practical Application to the Treatment of Stresses in Roofs, Solid Girders, Lattice, Bowstring, and Suspension Bridges, Braced Iron Arches and Piers, and other Frameworks. By R. HUDSON GRAHAM, CE Containing Diagrams and Plates to Scale. With numerous Examples, many taken from existing Structures. Specially arranged for Class-work in Colleges and Universities. Second Edition, Revised and Enlarged.
Página 165 - For example, let it be supposed that the centre of gravity of a sector of a circular disc has been found (Case IX. Article 44), and let it be required to find the centre of gravity of a sector of an elliptic disc. In fig. 99, let A B' A B' be the ellipse, AOA = 2 a, and B' O B' = 2 5, its axes, and C' O D' the sector whose centre of gravity is required.
Página 139 - Gravity is a term defined by the help of a special volume-unit of force ; as for example by the number of pounds contained in a certain fixed volume of water. Equal volumes of other materials are then compared in weight with water, and tables are formed giving the comparative weights or specific gravities of different substances. 3. CENTRES OF GRAVITY. — The centre of gravity of a body is a point traversed by the resultant of the weights of its separate particles, considered as so many parallel...
Página 4 - ... various positions in the plane, there can be constructed a series of similar polar polygons, all related to the same pole, and having their sides respectively parallel to each other. All polar polygons, whether drawn for the same or different poles, possess in common the singular property of indicating a point on the line of action of the resultant of the given system of forces. For instance, if a system of forces be applied to any structure in the objective paths, 1, 2, 3, and 4, Fig. 2 ; Fig...
Página 268 - Neglecting orders of infinitesimals higher than the second, and equating to zero the sum of the moments of all the forces acting on the elemental prism, which exists in a state of equilibrium, we find, bf.
Página 169 - Shew that the centre of gravity of any open triangular truss, of equal scantlings, coincides with the centre of the circle, inscribed in the triangle formed by joining the middle points of the side rafters and tie-rod of the given truss. 6. Given an angle-iron of the dimensions, 6...
Página 222 - Ft. xt. y^., vanishes, that is the chosen axes will be conjugate. In order therefore to construct the central ellipse it is only necessary to find the radii of gyration relatively to the axes, 0 A and 0 x. Let, h, be the length of the perpendicular, let fall from, A,onBC ; — then the square of the radius of gyration with respect to the axis, BC, will be, [p.
Página 194 - ... the product, xdxdy. Let a second system of rectangular axes, x x', y' y, Fig. 1 16, traversing as before the centre of gravity of the system, make an angle, yOy
Página 242 - ... number of common points cannot exceed mn. (See Theory of Equations, Chapter XX.) 64. We will exemplify the articles of this chapter by applying them to prove some properties of a triangle. The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. Let ABC be a triangle, D, E, F the middle points of the sides ; take A for the origin, AB for the direction of the axis of x, and a line through A perpendicular to AB for the axis of y. Let AB = a, and...
Página 39 - ACB, fig. 64, and measure the distances between the points where it cuts the lines of action. Then each force will be proportional to the distance between the lines of action of the other two. The direction of the middle force C is contrary to that of the other two forces, A and B.