- Surface forces and mass forces
- Simple forces and compound forces
- Shear stress
- Stress and strain
- Shear modulus
- References
The shear force is a compound force that is characterized by being parallel to the surface on which it is exerted and tends to divide the body, displacing the sections resulting from the cut.
It is schematically represented in figure 1, in which a cutting force applied to two different points of a wooden pencil is shown. The shear force in turn requires two parallel and opposite forces, which depending on their intensity, are capable of deforming the pencil or definitely fracturing it.
Figure 1. the shear force applied with the hands causes the pencil to break. Source: Pixabay.
So even though we talk about the shear force in the singular, in reality two forces are applied, since the shear force is a compound force. These forces consist of two forces (or more, in complex cases) applied at different points on an object.
Two forces of the same magnitude and opposite direction, but with parallel lines of action, constitute a pair of forces. The pairs do not provide translation to the objects, since their resultant is zero, but they do provide a net torque.
With a pair, objects such as the steering wheel of a vehicle are rotated, or they can be deformed and broken, as in the case of the pencil and the wooden board shown in Figure 2.
Figure 2. Shear force divides a wooden bar into two sections. Note that the forces are tangential to the cross section of the log. Source: F. Zapata.
Surface forces and mass forces
Compound forces are part of the so-called surface forces, precisely because they are applied on the surface of bodies and are not related in any way to their mass. To clarify the point, let's compare these two forces that frequently act on objects: weight and friction force.
The magnitude of the weight is P = mg and since it depends on the mass of the body, it is not a surface force. It is a mass force, and weight is the most characteristic example.
Now, friction depends on the nature of the contact surfaces and not on the mass of the body on which it acts, therefore it is a good example of surface forces that frequently appear.
Simple forces and compound forces
Surface forces can be simple or compound. We have already seen an example of a compound force in the shear force, and for its part, friction is represented as a simple force, since a single arrow is enough to represent it in the isolated body diagram of the object.
Simple forces are responsible for printing changes to the movement of a body, for example we know that the kinetic friction force between a moving object and the surface on which it moves, results in a reduction in speed.
On the contrary, compound forces tend to deform bodies and in the case of shears or shears, the end result can be a cut. Other surface forces such as tension or compression lengthen or compress the body on which they act.
Each time the tomato is cut to prepare the sauce or a scissors is used to section a sheet of paper, the principles described apply. Cutting tools usually have two sharp metal blades to apply shear force on the cross section of the object to be chopped.
Figure 3. Shear force in action: one of the forces is applied by the knife blade, the other is the normal one exerted by the cutting board. Source: Food photo created by katemangostar - freepik.es
Shear stress
The effects of the shear force depend on the magnitude of the force and the area on which it acts, that is why in engineering the concept of shear stress is widely used, which takes into account both force and area.
This stress has other meanings such as shear stress or shear stress and in civil constructions it is extremely important to consider it, since many failures in structures come from the action of shear forces.
Its usefulness is immediately understood when considering the following situation: suppose that you have two bars of the same material but different thickness that are subjected to increasing forces until they break.
It is evident that to break the thicker bar, greater force must be applied, however the effort is the same for any bar that has the same composition. Tests like this are frequent in engineering, given the importance of selecting the right material for the projected structure to function optimally.
Stress and strain
Mathematically, if the shear stress is denoted as τ, the magnitude of the applied force as F and the area over which it acts as A, we have the average shear stress:
Being the quotient between force and area, the unit of effort in the International System is the newton / m 2, called Pascal and abbreviated as Pa. In the English system the pound-force / foot 2 and the pound-force / inch 2.
However, in many cases the object subjected to the shear stress is deformed and then recovers its original shape without actually breaking, once the stress has ceased to act. Suppose the deformation consists of a change in length.
In this case the stress and strain are proportional, therefore the following can be considered:
The symbol ∝ means "proportional to" and as for the unit deformation, it is defined as the quotient between the change in length, which will be called ΔL and the original length, called L o. In this way:
Shear modulus
Being a quotient between two lengths, the strain has no units, but when placing the equality symbol, the constant of proportionality must provide them. Calling G to said constant:
G is called the shear modulus or shear modulus. It has Pascal units in the International System and its value depends on the nature of the material. Such values can be determined in the laboratory by testing the action of different forces on samples of varied composition.
When it is required to determine the magnitude of the shear force from the previous equation, simply substitute the definition of stress:
Shear forces are very frequent and their effects must be taken into account in many aspects of science and technology. In constructions, they appear in the support points of the beams, they can arise during an accident and break a bone and their presence is capable of altering the operation of machinery.
They act on a large scale on the earth's crust causing rock fractures and geological accidents, thanks to tectonic activity. Therefore they are also responsible for continually shaping the planet.
References
- Beer, F. 2010. Mechanics of materials. 5th. Edition. McGraw Hill. 7 - 9.
- Fitzgerald, 1996. Mechanics of Materials. Alpha Omega. 21-23.
- Giancoli, D. 2006. Physics: Principles with Applications. 6 t th Ed. Prentice Hall. 238-242.
- Hibbeler, RC 2006. Mechanics of materials. 6th. Edition. Pearson Education. 22 -25
- Valera Negrete, J. 2005. Notes on General Physics. UNAM. 87-98.
- Wikipedia. Shear Stress. Recovered from: en.wikipedia.org.