# Elements or Carpentry

## ac, ad, strains, beam, ba, fig and beams

Page: 1 2 3 4

Nedesinee -we know that the weighed would- just balance 'an equal weight g, pulling directly upwards 'by the intervention of the pulley G ; we see just balances the weights and c, acting in the directions AB, AC, we must infer, that the knot A is affected in the same manner by those two weights or by the single weight e. ; and therefore that two pressures, acting in the directions, and with the intensities, AB, AC, are equivalent to a single pre: Sums having the direction and proportion e AD. In like manner, the pressures AB, AK, are equivalent to:AR, which is equal and opposite to AC. Also AK and AC are equivalent to AI, which -is equal and opposite to AB.

We shall consider this combination of -pressures a•little more particularly.

Suppose an upright beam BA (fig. 3.) pushed in the direction of its length by a load B, and abutting on the ends of beams AC, AD, which are firm ly resisted at their extreme 'points C and D, -which rest 'on two - blocks, but are nowise joined to them : •hese-two beams can resist• no' way -but in' the diree ;done CA, DA nod -therefore 'the' erelleatt which i they sustain from-the beam BA are n the AC; AD. We with -to' know much each mi 'rains e Produce BA to 11, taking AE from a -of- equal pasts, to represent the number of tom or 'pounds by-which BA is pressed. Draw SF and 13G -parallel 'to -AD and AC ; then AF, measured on the same scale, will -give us' the number of -which AC•ia strained or crushed, and 'AG will e the strain on AD.

-It deserves particadar remark that the length of AC or AD has no influence on the Wain, arising -from the thrust of BA, while the-directions remain the same. The effects, however, of this strain are modified by the length of :the piece on which it is exerted. This strain compresses-the- beam, and will 'therefore compress a beam of double •-length twice 'as much. -This may change the form of the assent.

•blage. If -AC, for example, be very much shorter than AD, it -will be much lees compressed: the line CA will tuns about the centre C, while DA will hardly change its position ; and the angle CAD will grow mere open, the foist A sinking down. The artist will find it. of great consequence to pay a very minute attention to this circumstance, and to be able to see clearly the change of shape which necessarily results from these mutual strains. He will mein

this the cause of failure in many-very great works.— By thus ehanging-shape, strains are often produced in places where there were none befbre, and fre quently of the tending to break the beams across.

dotted lines of this figure show another*. Lion of the beam AIY. This makes a prodigious change; not only in the strain on AD', but also in that on AC. Both of them are much increased; AG is &tweet doubled, and AF is 6our times greater than befdre. This addition was made to the figure, to show what• strains may be produced by a very moderate 'force AE, when it is melted on a very obtuse angle.

The 4th and 5th figures will smile the most min enacted reader in conceiving how the very same strains AF, A G,-are laid on these beams, bye weight simply hanging from- a billet resting on A, pressing on AD, and also 'earring a little oa AC; or by an upright piece AE, joggled on the twobeanu AC, AD, and performing the office of•an ordinary king. post. The reader will thus learn to call off his a. tention from the •which the strains are pre -duced, and learn to consider them abstractedly mere ly as strains, in whatever situation he finds them, and from whatever cause arise.

We presume that every reader will perceive, that the proportions •of these strains will be precisely the liame if every thing be inverted, and each beam be drawn 'or the opposite direction. In the -same way that we have substituted a Tope and weight in fig. 4. or a 'king-post in fig. 5. for the loaded beam BA of fig. .8. we might have substi tuted the framing of fig. 6. which is a very used practice. • In this framing,• the batten DA is stretch ed by a force AG, and the piece AC is compress ed by a force AF. • It is evident, that we may em ploy a rope, dr an iron rod.tooked.on at Di in place of hattensIM, And the *t ho lame as before.

This seemingly simple.inatteris still fall of imams. .tirin; and we hope that. the well-infornsed reader.will .pardonthough.we dwell a little. longer en it. for the sake the young artist.

By changing the form of this filming, as in fig. 7. . we produce thesame strains as.in• the disposition re •.reseatedhy the dotted lines in 4. 8. The strains on both the battens .AD,, AC, are. now greatly in , creased.

Page: 1 2 3 4