Beam (structure)

“ It will therefore be useful for us to examine the strength of a beam when its load is applied otherwise than at the centre. [Pg 199]
406. We shall employ, in the first place, a beam 40" span, 0"·5 broad, and 1" deep; and we shall break it by applying a load simultaneously at two points, as may be most conveniently done by the contrivance shown in the diagram, Fig. 53. a b is the beam resting on two supports; c and d are the points of trisection of the span; from whence loops descend, which carry an iron bar p q; at the centre r of which a weight w is suspended. ”

“ We [Pg 222] have shown that when a beam of wood is supporting a weight, the fibres at the bottom of the beam are extended, the tendency being to tear them (Art. 376) . The fibres on the top of the beam are compressed, while the centre of the beam is in its natural state. The condition of strain in a cast iron beam is precisely similar; the bottom portions are in a state of extension, while the top is compressed. If therefore a beam be very thin, the material at the lower part may not be sufficient to withstand the forces of extension, and fracture is produced. ”

“ In most balances the beam rests on steel knife edges; but a maker who has lately obtained celebrity makes his supports of pure rock crystal. The steel edges can be seen with the naked eye; the quartz edges cannot be seen even with a magnifying glass. One writer on this subject thinks that with these perfect crystal edges, with an inflexible girder beam, a short beam giving quick vibrations, and a sensitiveness that can be increased by screwing up the centre of gravity, there can hardly be a practical limit to the smallness of the weight that will turn the beam. ”

“ The strength of a beam 40" × 0"·5 × 1" is four times as great as the strength of 40" × 0"·5 × 0"·5, though the quantity of wood is only twice as great in one as in the other. In general we may state that if a beam were bisected by a longitudinal cut, the strength of the beam would be halved when the cut was horizontal, and unaltered when the cut was vertical; thus, for example, two beams of experiment No. 4, placed one on the top of the other, would break with about 40 lbs., whereas if the same rods were in one piece, the breaking load would be nearly 80 lbs. ”

“ Now, the strength of a beam varies as the square of the depth of the beam, and it is obvious that in the case of a circular steel tube the material is evenly distributed about the neutral axis, and therefore its strength in both horizontal and vertical directions is equal ”

“ Paragraph 18 - If the supports, when the beam sits on pegs in the wall, are not one tefach wide and three long, some say that they must be strong enough to support the beam and a half brick and some say that they only need to be strong enough to support the beam. ”

“ A pillar supporting a weight is under compression. At c the weight tends to bend the beam. The upper part is under tension, the lower part under compression. This is known as beam action, and depends on whether the beam is supported at one end, as shown, or on both ends. ”

“ Other beams ran lengthwise of the body, placed straight, obliquely, diagonally, and in every direction calculated to strengthen and stiffen, and all bound together with rods and bars and bolts. One great beam, reaching from rear part through the body to centre of his forehead, is calculated to sustain fully a ton’s weight, if at any time his great head should need such support. ”

“ A light beam, A B, having two square inches of pith, C, at one end, is balanced on a very fine fibre of glass, D D', stretched horizontally in a tube; one end of the fibre being connected with a torsion handle, E, passing through the tube, and indicating angular movements on a graduated circle. The beam is cemented to the torsion fibre, and the whole is inclosed in glass, and connected with the mercury pump by a spiral tube, F, and exhausted as perfectly as possible. G is a spiral spring, to keep the fibre in a uniform state of tension, H is a piece of cocoon silk. ”

“ Each end of the beam is sprung obliquely upwards and towards the middle, so as to form a spring through which a pushing screw passes, which serves to vary the distance of the point of support from the fulcrum, and, at the same time, by its oblique action to raise or depress it, so as to furnish a means of bringing the points of support and the fulcrum into a right line. ”

“ Thus we see that the resistance of a beam to a cross strain, as well as to tension and compression, is affected by the incompressibility and inextensibility of the material.
The formula for the dimensions of any beam to support a strain transversely is
S = the ultimate strength in lbs. ”

“ When the weight reaches 140 lbs. the deflection at first indicated is 2"·37; but gradually the cross lines are seen to descend in the field of the telescope, showing that the beam is yielding and finally it breaks across. This experiment teaches us that a beam is at first deflected by an amount proportional to the weight it supports; but that when two-thirds of the breaking weight is reached, the beam is deflected more rapidly.
366. It is a question of the utmost importance to ascertain the greatest load a beam can sustain without injury to its strength. ”

“ Thus, if a beam which is one foot broad and one foot deep support a given weight, then a beam of the same depth and two feet broad will support double the weight; but if a beam be one foot broad and two feet deep it will support four times as much as a beam one foot broad and one foot deep. If a beam one foot square support a given weight, then a beam two feet square will support eight times as much. Also a cylinder of two inches in diameter will support eight times as much as a cylinder one inch in diameter. The appended table gives data bearing on the subject. ”

“ If we decompose the light vector into two components, of which one has the direction of the beam, while the other is perpendicular to it, then the latter can be arbitrarily rotated around the beam, and in every direction, the ratio is determined between the two. ”

“ This is one of the first principles in the resistance of material, that the strength of a beam varies directly as the width—that is, if we make the beam twice as wide, it will hold twice as much; and that the strength varies as the square of the depth that is, if we make it twice as deep, it will hold up four times as much. ”

“ If the beam is not made perfectly (for example, it is bent or it is made out of a weaker material like straw) we can pretend that it is straight and made out of metal, and would therefore be able to hold an ariah. ”

“ The side of the beam, supposing it square, was found by multiplying the diameter of the cylinder by the length of the stroke, and extracting the cube root of the quotient, which will be the depth or thickness of the beam. This rule allows a beam 16 feet long to bend 1/8th of an inch, and a beam 32 feet long to bend 1/4 of an inch. For cast iron beams the square of the diameter of the cylinder, multiplied by the length between the centres, is equal to the square of the depth, multiplied by the thickness. ”

“ He brought up the blaster, aimed and squeezed the trigger. There was a faint bluish glow at the muzzle, and a blast of energy tore through the brush, smashing the molecular structure of everything that stood in the way. There was an involuntary shout of alarm from the direction of the road; at least one of the policemen had escaped the blast. Hradzka holstered his weapon and crept away for some distance, keeping under cover, then turned and waited for some sign of the presence of his enemies. For some time nothing happened; he decided to turn hunter against the men who were hunting him. ”

“ If the beam be sufficiently loaded, the centre of gravity will at length be raised to the fulcrum S, and the beam will rest indifferently in any position. If more weight be then added, the centre of gravity will be raised above the fulcrum, and the beam will turn over. ”

“ The beam, or that part of the plough which carries the coulter, and furnishes the point of draft, should be as near that of resistance as possible; because the more these are approached, the less is the moving power required. Even the shape of the beam is not a matter of indifference. ”

“ If you stand a plank upon its edge, supported at each end so as to form a beam, its strength will vary as its width and as the square of its height. If then you double its width you only double its strength, but if you double its height you multiply its strength four times. ”

“ To keep the beam truly in its place, which is very necessary, as all the bearings are flat, the recesses for the ends of the studs are formed so as to draw the beam without strain into its true position every time that it is thrown out of gear by the sliding frame. The end knife-edges are adjusted and tightly jammed into exact position by means of wedge pieces and set screws, and the beam is furnished with delicate adjusting weights at its top. ”

“ Give us the real dope on how you're going to do it.”
“Well, with what I picked up from the Lassans, I think I know. They know all about light and mechanics, but they're rotten chemists, and don't realize how good a thing they've got in lots of ways. Now look—if you throw a beam of radiations from a cathode tube into finely divided material you break up some of the atoms. Well, all we have to do is get an extra-powerful cathode tube, break up a lot of atoms, and then deliver the positive charges from them onto whatever we're going for. That would be your gravity beam.” ”

“ The amount of strain caused by any weight applied in a transverse direction, to a beam supported at both ends, is as the breadth, as the length inversely, and as the 125square of the depth. Whatever depression takes place, tends to shorten the upper, and to extend the under-side; whence the fibres of the top part suffer compression, and those of the bottom extension. The amounts of compression and extension must of course be equal, and therefore if any material resists these two strains in a different degree, the number of fibres opposing each will also be different. ”

“ The collapse of a beam by a transverse strain commences by fracture of the fibres on the lower surface, followed by a rupture of all fibres up to a considerable depth. Here we see that by a transverse force the fibres in a beam of 48" × 1" × 1" have been broken by a strain of 140 lbs. (Art. 366) ; but we have already stated (Art. 353) that to tear such a rod across by a direct pull at each end a force of about four tons is necessary. ”

“ A.--The web of a cast-iron beam or girder serves merely to connect the upper and lower edges or flanges rigidly together, so as to enable the extending and compressing strains to be counteracted in an effectual manner by the metal of those flanges. It is only necessary, therefore, to make the flanges of sufficient strength to resist effectually the crushing and tensile strains to which they are exposed, and to make the web of the beam of sufficient strength to prevent a distortion of its shape from taking place. ”

“ This subject is to be studied by examining the effect of different deflections upon the fibres of a beam. A beam is always deflected [Pg 183] whatever be the load it supports; thus by looking through the telescope of the cathetometer I can detect an increase of deflection when a single pound is placed in the tray: hence whenever a beam is loaded we must have some deflection. An experiment will show what amount of deflection may be experienced without producing any permanently injurious effect. ”

“ Before the final determination of an exact weight the beam should always be lifted from the knife-edges and again lowered into place, as it frequently happens that the scale pans are, in spite of the pan-arrests, slightly twisted by the impact of the weights, the beam being thereby virtually lengthened or shortened. ”

“ When a beam passes obliquely from one transparent medium to another of different density, as from air to water or glass, its direction is changed and it is said to be refracted. This is illustrated in a very simple manner by Fig. 3, in which a ray of the sun, entering through an aperture in a dark room and received on the surface of water in a glass vessel, is seen to be broken as it were at the surface and bent downward. ”

“ Returning to Fig. 62, we see the reason why the rectangle e d c f should have one or both of its diagonals introduced. A load placed, for example, at d would tend to depress the piece d e, and thus deform the rectangle, but when the diagonals are introduced this deformation is impossible.
444. Hence one of these frames is almost as strong as a beam supported at the points c and d, and therefore, from the principles of Art. 388, its strength is three times as great as that of an unsupported beam. ”

“ In delicate weighings by a chemical balance it is requisite to ascertain exactly the point at which the beam comes to rest, and when standard weights are being compared the position of the beam is ascertained by a carefully divided scale viewed through a microscope. But when the beam is just coming to rest, friction, small impediments or other accidental causes may readily obstruct it, because it is near the point at which the force of stability becomes infinitely small. ”

“ Balances are of various forms; in that most commonly used a horizontal beam rests so as to turn easily upon a fulcrum in the middle. From the extremities of the beam, called the centres of suspension, hang the scales; and a slender metal pointer between them, and in front of the fulcrum, indicates when the beam is level. The characteristics of a good balance are: (1) that the beam should rest in a horizontal position when the scales are either empty or loaded with equal weights ”