Strength of Materials - The Bennett College

Whenever a force or a number of forces act on a rigid body the general effect is to put the body in what is called a state of stress. By this is meant that there is a tendency for one part of the body to move relatively to another as a result of the force or forces acting on the body. For example, a colliery winding rope is said to be in a state of stress because the force acting along the rope, due to the weight of the cage, tends to separate the lower portion of the rope from the upper.

As another example we may take the case of an engine crank shaft. Here again, the shaft is in a state of stress because the thrust along the connecting rod, acting at the crank pin, turns the shaft and tends to separate one section of the shaft from another by twisting the one relatively to the other.

Stresses are of different kinds. When the forces act in one straight line in opposite directions, away from each other, as represented by Fig. I, the stress is known as a tensile stress. Thus the colliery winding rope above referred Fig. I to is subjected to a tensile stress due to the forces acting on it, viz. the weight of the cage and the force or reaction resisting this weight; these forces act in the same straight line but in opposite directions, away from each other. The student is of course aware that wherever there is an action there is an equal and opposite reaction.
This is Newton's Third Law of Motion. If the forces act in one straight line but in opposite directions, towards each other, as represented by Fig. 2, the stress produced is known as a compressive stress.

A vertical column supporting a roof, for example, is subjected to a stress of this nature, the load resting on the column acting downwards, and the reaction due to the load acting in the same straight line but in the opposite direction, i.e. upwards.

The piston rod of a steam engine is in tension one stroke and in compression the other.

Another kind of stress is that known as shear stress. This kind of stress is produced when the forces applied act parallel to each other in opposite directions, as indicated in Fig. 3, The general effect of forces acting on a body in this manner is to cause one portion of the body to slide relatively to another. Metal plates cut in a shearing machine are exposed to shear stress, one portion of plate being separated from another in consequence of two forces acting in opposite directions parallel to each other, one on each blade of the machine.

An ordinary line shaft on which are secured driving pulleys is exposed to shear stress, but as the force applied tends to twist the shaft, the stress is more often spoken of as a twisting or torsional stress.

One other kind of stress sometimes referred to is that termed a bending stress. Thus a beam supporting a load in the manner indicated by Fig. 4 is subjected to bending. As a matter of fact, however, although the beam is subjected to  bending, the resulting stresses resolve themselves into tensile, compressive, and shear stresses, all three actually existing, as will be shown later, in the beam.

It must be understood that the stresses Fig. 4 we shall be called upon to consider are the result of forces acting external to the body; such stresses are usually known as external stresses. It sometimes happens that stresses exist in a body although the body is not exposed to any external forces. Such stresses are termed initial or internal stresses, and are usually the result of defects in manufacture, such as uneven cooling of metal castings. These initial stresses cannot as a rule be estimated.

Whenever a body is put in a state of stress it undergoes a change of form or shape. This change of form is termed strain. A body which was absolutely rigid would of course remain unstrained, no matter how intense was the stress, but no such bodies actually exist. If a body be of a soft and yielding nature, such as india rubber, the amount of strain for a given stress may be considerable, but if the body be very hard, such as tool steel, it will be strained very little even when exposed to great stress.

The nature of the strain in a body depends on the kind of stress to which the body is exposed. Thus if the stress be a tensile stress, i.e. the result of a simple longitudinal pull, the strain consists of a lengthening of the body concerned, together with a reduction of the lateral dimensions. A bar of india rubber, for example, when pulled in the direction of its length, and thus exposed to tensile stress, stretches a certain amount, at the same time undergoing contraction in both directions at right angles to the length, and so undergoes a change of form, or is strained.

When a body is exposed to compressive stress, the result of a push or thrust, the strain consists of a shortening of the body, and at the same time the dimensions of the body at right angles to the length, i.e. the breadth and width, increase.

Thus a tensile stress produces an extension or lengthening of a body, with a decrease of lateral dimensions, whilst a compressive stress produces a contraction or shortening of the body, with an increase of lateral dimensions.

In the case of a simple shear stress the strain consists of a distortion or sliding of one portion of the body relatively to another.

When the stress is torsional, as in the case of a line shaft having driving pulleys keyed upon it, the strain may be described as being in the nature of a twist.

With regard to a body subjected to bending, as for example a beam, the effect of the bending is to deflect the beam, so that the strain is in the nature of a deflection.

Measurement of Simple Tensile and Compressive Stresses. So far we have dealt only with the meaning of the term stress. We must now consider how the stress in a body exposed to external forces is measured.

When a body is in a state of stress we understand that there is a mutual action between two parts of the body, each part exerting a force upon the other, and thus tending to cause the separation of the one from the other.

Now it is of little use to the designer of a machine or structure to know merely that any particular member of the machine or structure is in a state of stress, as this affords him no indication as to whether or not that member is strong enough to fulfil its function. What he actually wishes to know is the intensity of the stress. The engineer usually measures stress in pounds or tons per square inch or per square foot of sectional area. Consider the case of two solid round cast-iron pillars of different diameters, each supporting a certain load. We may assume one column to be of large diameter and the other of small diameter, the former being intended to carry a very heavy load and the latter a comparatively light load. Suppose now we wished to determine which of the two columns was the better able to support the load upon it. (We must assume the columns to be short so that the question of buckling does not enter into the calculation.

Ultimate or Breaking Stress. Having determined the stress in any particular case, the student will naturally wish to know of what use this is in determining whether or not the member concerned is sufficiently strong to sustain safely the load imposed upon it, and this we may now proceed to explain.

Every metal used in the construction of machinery has been carefully tested with the object of determining the stress which would cause it to rupture. This stress is termed the ultimate stress or the breaking stress. Mild steel, for example, has an ultimate stress of about 30 tons per square inch in tension, which means that a bar of mild steel one square inch in sectional area would just fail under a tensile load of 30 tons. A mild steel bar of 2 square inches sectional area would break with a load of twice 30 tons, or 60 tons.