THIS chapter will give merely the information called for by the Syllabus for the Advanced Course. The subject is fully gone into in Part IV.

The headings in this chapter, marked A to F, are quoted from the Syllabus (see p. vii.), and mention the points required to be understood in the Advanced Course.

Stress And Strain

When a load or any force acts upon a structure or piece of material, it produces a change of form which is called the strain. . The internal forces called out in the material to resist this strain are called the stress.

Thus a load hanging from a bar of iron lengthens it, causing a strain, and calls out in it the resistance of the fibres -which are under a tensile stress.

These two terms are sometimes used indiscriminately, but it is more accurate to make the above distinction between them.

A. " The Nature of the Stresses to which the different Parts of Simple Structures are subjected."

These stresses are as follows: -

Tension is the stress produced by pulling; it elongates the body upon which it acts, and tends to cause rupture by tearing it asunder.

Thus if a rope or a bar of iron is subjected to a sufficient pulling or tensile stress it will break or tear across.

Compression is the stress produced by pressure ; it shortens the body to which it is applied and tends to cause rupture by crushing.

Thus a block of stone bearing a weight is under compression, and if the weight is sufficient it will be crushed.

Transverse Stress is one caused by bending the body on which it acts, and it tends to break it across.

Thus the weight in Fig. 422 bends the beam as shown, until, if the weight is sufficiently increased, the beam will break across as in Fig. 423.

Stress And Strain 200328

Fig. 422.

Stress And Strain 200329

Fig. 423.

Shearing Stress is that produced when one part of a body is forcibly pressed or pulled so as to tend to make it slide over another part.

Thus when two plates riveted together as in Fig. 424 are separated by pulling (or pushing) in opposite directions one plate slides upon the other and the rivet is sheared as in Fig. 425.

Stress And Strain 200330

Fig. 424.

Stress And Strain 200331

Fig. 425.

Bearing Stress is that which occurs when one body presses against another so as to tend to produce indentation or cutting.

Stress And Strain 200332

Fig. 426.

Stress And Strain 200333

Fig. 427.

In Fig. 426 the plates a and b being pulled in opposite directions, the rivet c being of harder iron than the plate has borne upon it, making the hole larger, as shown at d, Fig. 427.

Load

The load or weight upon a beam may be either concentrated at the centre as in Fig. 428, or uniformly distributed over the whole beam as in Fig. 429.

Load 200334

Fig. 428.

Load 200335

Fig. 429.

There may be concentrated loads at any point or points in the length of the beam, as in Figs. 430 and 431;1 or the load may be uniformly distributed over a portion only of the beam, as in Fig. 432.

Load 200336

Pig. 430.

Load 200337

Fig. 431.

Load 200338

Fig. 432.

Weight Of Beam

In addition to the external loads represented in the figures by W and w, the weight of the beam or girder itself must, when it is large and heavy, be considered.

A Dead Load is one which is very gradually and steadily applied, and which remains steady.

Thus water poured gradually into a tank, supported by a girder, would be a dead load, and so would the tank and the weight of the girder itself.

A Live Load is one which is suddenly applied, as in the case of trains coming suddenly upon a bridge. It is generally taken as equivalent in effect to double its amount of dead load. Thus a live load of 10 tons would produce the same amount of stress as a dead load of 20 tons.

A Mixed Load, consisting partly of live load and partly of dead load, may be reduced to an equivalent amount of dead load by doubling the live load and adding it to the dead load.

Thus, if a structure weighs 500 tons (dead load), and is subject to a live load of 900 tons, the equivalent deadload would be500 + (2 x 900) = 2300 tons.

The Breaking Load for any structure or piece of material is that dead load which will just produce fracture in the structure or material.

The Working or Safe Load is the greatest dead load which the structure or material can safely be permitted to bear in practice.

1 The small italic letters in Fig. 431 may be ignored for the present. They are explained in Part IV. The numbers in Fig. 432 are explained at p. 267.

The Breaking Stress is that caused by the breaking load; it is sometimes called the ultimate stress.

The Working Stress is that caused by the working or safe load: it is sometimes called the Limiting or Safe Stress.

It is evident that structures intended to stand must not be subjected to breaking loads or breaking stresses, but only to safe loads and working stresses (see Table, p. 252).

The Factor of Safety is the ratio in which the breaking load or stress exceeds the working load or stress.

That is, it is the figure by which the breaking load or stress is divided to obtain the working load or stress.

Thus if the breaking tensile stress of a bar of iron is 20 tons per square inch, and it is subjected to a working stress of only 5 tons, the factor of safety is 20/5 = 4.

B. "Beams supported at Ends, fixed at one or both Ends, or continuous," and Cantilevers "to know which Parts of the Beam are in Compression and which in Tension."

Supported Beams. Beam Supported At Both Ends With A Breaking Load In The Centre

A rectangular wooden beam, supported at the ends, when subjected to a concentrated load greater than it can bear breaks as shown in Fig. 433.

Supported Beams Beam Supported At Both Ends With A 200339

Fig. 433.

The beam bends, sinking most just under the weight, and the fibres of the upper portion of the beam are crushed, and those of the lower portion torn asunder, as shown on a larger scale in Fig. 434.

Supported Beams Beam Supported At Both Ends With A 200340

Fig. 434.

Beam Supported At Both Ends And With A Uniformly Distributed Load

A load uniformly distributed over the beam would produce rupture in the same way, but that the form of the beam before rupture would be slightly different.

A Beam supported at both Ends and subject to a Safe Load - that is, one much smaller than is required to break it will bend to a certain extent, and the fibres of the upper part of the beam will be in compression, and those of the lower part in tension, as shown in Fig. 435. There is a layer between the upper and the lower fibres, in which there is neither compression nor tension, which is called the neutral layer.

Beam Supported At Both Ends And With A Uniformly D 200341

Fig. 435.

A Cantilever, however it may be loaded, has the upper fibres in tension and the lower in compression, as shown in Fig. 436.

Beam Supported At Both Ends And With A Uniformly D 200342

Fig. 436.