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TABLE IV. SPRUCE BEAMS.

Table of safe quiescent loads for horizontal rectangular beams, supported at both ends, load uniformly distributed. For concentrated load at centre divide by two. For permanent loads (such as masonry) reduce by 10 per cent.

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Loads above and to the right of heavy line will crack plastered ceilings.

TABLE V.

WHITE-PINE (OR COMMON SOFT PINE) BEAMS.

Table of safe quiescent loads for horizontal rectangular beams, supported at both ends, load uniformly distributed. For concentrated load at centre divide by two. For permanent loads (such as masonry) reduce by 10 per cent.

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Loads above and to the right of heavy line will crack plastered ceilings.

The foregoing tables for strength of beams are computed from the data given in this chapter, taking the strength of the wood as given in the table for co-efficients.

These tables are as accurate as can be computed with our present knowledge; and, as the co-efficients are based upon experiments on full-sized timbers, it would seem as though the tables should be almost absolutely correct.

STONE BEAMS. — The same formulas apply to stone as to wooden beams, only the values of the co-efficient A are only from one-sixth to one-tenth of breaking loads. Sandstone beams should never be subjected to any very heavy loads; but, where used as lintels, the stone should be relieved by iron beans or brick arches back of the stone.

Solid Built Beams.

[From Wheeler's "Civil Engineering."]

A solid beam is oftentimes required of greater breadth or thickness than that of any single piece of timber. To provide such a beam, it is necessary to use a combination of pieces, consisting of several layers of timber laid in juxtaposition, and firmly fastened together by bolts, straps, or other means, so that the whole shall act as a single piece. This is termed a solid built beam.

When two pieces of timber are built into one beam having twice the depth of either, keys of hard wood are used to resist the shearing-strain along the joint, as shown in Fig. 9.

Tredgold gives the rule, that the breadth of the key should be twice its depth, and the sum of the depths should be equal to once and a third the total depth of the beam.

It has been recommended to have the bolts and the keys on the right of the centre make an angle of forty-five degrees with the axis of the beam, and those on the left to make the supplement of this angle.

The keys are sometimes made of two wedge-shaped pieces, for the purpose of making them fit the notches more snugly, and, in case of shrinkage in the timber, to allow of easy re-adjustment.

When the depth of the beam is required to be less than the sum of the depths of the two pieces, they are often built into one by indenting them, the projections of the one fitting accurately into the notches made in the other, and the two firmly fastened together by bolts or straps. The built beam shown in Fig. 10 illustrates this method. In this particular example the beam tapers slightly from the middle to the ends; so that the iron bands may be slipped on over the ends, and driven tight with mallets.

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When a beam is built of several pieces in length as well as in depth, they should break joints with each other. The layers below the neutral axis should be lengthened by the scarf or fish joints used for resisting tension; and the upper ones should have the ends abut against each other, using plain butt joints.

Fig. 10.

Represets a solid built beam, the top part being of two pieces, b, b, which abut against a
broad flat iron bolt, a, termed a "king bolt"

Many builders prefer using a built beam of selected timber to a single solid one, on account of the great difficulty of getting the latter, when very large, free from defects: moreover, the strength of the former is to be relied upon, although it cannot be stronger than the corresponding solid one, if perfectly sound.

CHAPTER XVI.

STIFFNESS AND DEFLECTION OF BEAMS.

IN Chaps. XIV. and XV. we have considered the strength of beams to resist breaking only; but in all first-class buildings it is desired that those beams which show, or which support a ceiling, should not only have sufficient strength to carry the load with safety, but should do so without bending enough to present a bad appearance to the eye, or to crack the ceiling: hence, in calculating the dimensions of such beams, we should not only calculate them with regard to their resistance to breaking, but also to bending. Unfortunately, we have at present no method of combining the two calculations in one operation. A beam apportioned by the rules for strength will not bend so as to strain the fibres beyond their elastic limit, but will, in many cases, bend more than a due regard for appearance will justify.

The amount which a beam bends under a given load is called its deflection, and its resistance to bending is called its stiffness: hence the stiffness is inversely as the deflection.

The rules for the stiffness of beams are derived from those for the deflection of beams; and the latter are derived partly from mathematical reasoning, and partly from experiments.

We can find the deflection at the centre, of any beam not strained beyond the elastic limit, by the following formula:

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By making the proper substitutions in Formula 1, we derive the

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