Graphic and Analytic Statics in Their Practical Application to the Treatment of Stresses in Roofs, Solid Girders, Lattice ... and Other FrameworksCrosby Lockwood and Company, 1887 - 401 стор. |
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Graphic and Analytic Statics in Their Practical Application to the Treatment ... Robert Hudson Graham Попередній перегляд недоступний - 2016 |
Загальні терміни та фрази
abscissa angle b₁ beam bending bending moment centre of gravity co-ordinates constant construct corresponding cos.² cosec couple cross-section curve determined direction draw a line drawn dx dy elasticity elemental area ellipse of inertia equal equation equilibrium expressed force-line frame girder Hence horizontal integration intercept intersect joint length limits line of action line of loads M₁ moment of inertia moments 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 represented required to find respectively resultant force resultant stress S₁ shearing force shew shewn sin.² supposed system of forces tension triangle vertical line weight x₁ Y₁
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Сторінка iii - 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.
Сторінка 165 - Example : — Let it be required to find the centre of gravity of a conical or pyramidal solid, such as that shewn in Fig. 105. Assume the axis of, x, to pass through the vertex, 0, and the centre of the base, B, and let the plane. of the base be inclined to this axis at angle, 0.
Сторінка 149 - GRAVITY. 149 duced in a certain ratio. —. — -' — r. beyond the sides of an equiangular polygon, 1, 2, 3, 4, . . 7, 8. Let a series of equally heavy particles be placed at the points, B, and let it be required to find the centre of gravity of the system of particles so distributed. Take the axis of, x, parallel to any one of the perpendiculars drawn from, A, upon the sides, as for example to that drawn perpendicularly to the side, 8. Let the radius-vector, 0 A, of the point, A, equal, c ; and...
Сторінка 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.
Сторінка 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 ; rig....
Сторінка 169 - Shew that the centre of gravity of a wire bent into a triangular shape coincides with the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the original triangle. 7. If the centre of gravity of a triangle be equidistant from two angular points of the triangle, the triangle must be isosceles.
Сторінка 242 - ... constant. 12. Shew by the graphic method, that if the sum of the moments of a series of forces, acting in one plane on a particle retains the same value for two points in the plane, the straight line, joining these two points, must be parallel to the line of action of the resultant force. 13. Let, ABC, be a triangle, D, E, F, the middle points of the sides opposite to A, B, and C, respectively; shew, by aid of the polar and force polygons, that forces, represented in magnitude and direction,...
Сторінка 96 - ... 40 per cent of the breaking load, and about 60 per cent of the load usually called the limit of elasticity. It will be seen (See Figs.
Сторінка 194 - 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
Сторінка 240 - ... against the efforts of the men, in a downward direction, at an angle of 15° to the horizon, and intercepting the axis of the tree at a point, 30 ft. above its base ; — find the moment about the root, 0, due to the wind and combined strength of the men. Moment = 3720 foot-lbs. 6. Assuming...