Researches in Graphical StaticsD. Van Nostrand, 1878 - 114 pàgines |
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Frases i termes més freqüents
actual angle of friction applied forces applied weights arch rib assumed bending mo bending moments bisect bridge brium polygon cable cause center of gravity center vertical compression cone construction convenient cross section crown determine direction draw drawn earth effect ellipse equal equation equili equilibrating polygon exert force polygon frame pencil given GRAPHICAL STATICS hence hoop tension horizontal thrust inertia intensity intersection joints live load load line Louis Arch lune manner maximum ment meridian method moment of inertia negative loading neutral axis obliquity obtain ordinates parallel piers plane pole distance polygon e positive load principal stresses prism problem proportional quantities radius ratio represent resistance respectively resultant stress right shearing stress scale segments side span stiffening truss straight girder stress solids suppose surface sustained tangent tangential components thickness third closing line tion treated triangle vertical resistances weight line zontal
Passatges populars
Pàgina 65 - ... be represented in magnitude and direction by the sides of a closed polygon taken in order, they are in equilibrium. The simplest case is that of two equal and opposite forces, represented by (say) AB and BA. The next is that of the ' triangle of forces/ which asserts that three forces represented by AB, BC, CA are in equilibrium f.
Pàgina 46 - If the forces which balance each other in or upon a given body or structure be distinguished into two systems called respectively active and passive, which stand to each other in the relation of cause and effect, then will the passive forces be the least which are capable of balancing the active forces consistently with the physical condition of the body or structure.
Pàgina 65 - ... their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through the point of intersection of the two sides representing the forces.
Pàgina 56 - To FIND THE CONTENTS OF A SPHERE. A sphere may be regarded as composed of pyramids whose bases form the surface of the sphere and whose height is the radius. Hence, To find the contents of a sphere, Multiply the number of units in the convex surface by the number of units in J of the radius, or in % of the diameter. 606. EXAMPLES. 1. How many cubic feet of air may be contained in a room 20 ft. long, 16 ft. 6 in. wide, and 12 ft. high ? Ans. 3,960 cu. ft.
Pàgina 98 - ... closing lines coincide and their areas partially cover each other, the ordinates intercepted between these two polygons are proportional to the real bending moments acting in the arch.
Pàgina 12 - If in any arch the equilibrium polygon (due to the weights) be constructed which has the same horizontal thrust as the arch actually exerts ; and if its closing line be drawn from consideration of the conditions imposed by the supports, etc. ; and if, furthermore, the neutral surface curve of the arch itself be regarded as another equilibrium polygon due to some systems of loading not given, and its closing line be also found from the same considerations respecting supports, etc. ; then when these...
Pàgina 110 - Fig. 6, let xx and yy be two planes at right angles to each other, on which the stress is...
Pàgina 41 - ... p is the length of the perpendicular from the origin to the line and a is the angle between the perpendicular and the positive direction of the jc-axis.
Pàgina 66 - ... relations among the magnitudes of the forces so as to produce equilibrium will be indeterminate, determinate, or impossible, according as the construction of the reciprocal figure is so. Reciprocal figures are mechanically reciprocal ; that is, either may be taken as representing a system of points, and the other as representing the magnitudes of the forces acting between them. In figures like 1, 2 and II., 3 and III., in which the equation e=2s-2 is true, the forces are determinate in their...
Pàgina 57 - ... arch; as appears from the same reasons which were stated in connection with arches of masonry. And, further, the hoop compression will vanish at that level of the dome where the equilibrium curve, in departing from the crown, first becomes more nearly vertical than the tangent of the meridian section...