Balance is a very important word in nature.

^{Landscape of Panorama Miami Florida}
As you may remember from Sir Isaac Newton's gravitational law, every object of mass exerts a force on every other object of mass that is close to it. With all these forces of attraction all over the place, it seems sensible to expect objects to be in constant motion in response to these forces, right? While discussing with a friend of mine, the concept of unbalanced forces kept coming up aboutNewton's First Law of Motion. In case you don't remember, that law states:

When you think about it, this law is pretty common sense. I mean, there are forces (frictional forces, gravitational forces, reaction forces) all over the place so if nothing changes, then these forces must be balanced somehow. If something changes, then the force is unbalanced, and the changes that occur must be in the direction of the net force. Okay, so maybe I jumped right into the middle of this discussion. Let us back it up a little.

Balanced and Unbalanced Forces

An easy way to visualise balanced forces is to think of children playing thug-of-war. The idea is to see which team would produce a greater force. Initially, when both teams begin to pull on each other, the two teams are in equilibrium meaning that the force both sides are equal and opposite. Equal but opposite forces are balanced forces. If however, the force on one end becomes greater than the force on the other end, the team producing the less force would have to move in the direction of the team that produced the greater force. Therefore, the weaker team would move in the direction of the net force and the force in this system is said to be unbalanced. According to Newton's first law, an unbalanced force must produce an acceleration. In the image to the right, an unbalanced force could exist if the man was standing in quicksand. The reason that a man standing on quicksand would sink is that the force of gravity does not have any sense whatsoever. That force has no idea that the man thought he was standing on sand and expects not to sink. No, the force of gravity is the same whether the man stands on a concrete floor or a quicksand. In the case of the man standing on quicksand, the force of gravity will remain constant and thus sink the man until he reaches a stronger surface that is capable of producing enough force to counter the force of gravity. Of course, this is why houses must be built on solid ground with good foundations.

Building Structures and Translational Equilibrium

Structures are built to serve different purposes, ranging from buildings that are constructed to protect people and their properties from outside environmental conditions to bridges that are built to support vehicles and people. In each case, the structure must be strong enough to carry its weight and external forces that it must bear when it is in use or due to natural disasters such as earthquake, flood or wind. An understanding of the forces which such buildings must resist without causing deformity of the structure is key to determining the strength of the materials to be used in construction and other design considerations.

As I discussed in the above picture, the acceleration of a body in uniform motion or at rest is zero because no net external force is acting on it. When a body satisfies this condition, the body is said to be in Translational Equilibrium. In the case of a building or a bridge, for the structures to be in translational equilibrium, the load or forces acting on the structures must be balanced by the reaction forces at the foundations and supports. In the image shown to the left, it can be seen that the forces which act on a body are not always vertical or horizontal. The forces usually act at an angle and must, therefore, be resolved into their vertical and horizontal components to analyse the effect of each of these forces properly. In the case of the body shown, representing the reaction force of the plane into the horizontal and vertical components, resolving the force, F into vertical and horizontal components, adding the three forces and equating them to zero would enable us find the value of the force, F, which is necessary to maintain the translational equilibrium of the body.

As shown in the calculation, the force, F must be at least 50N or else the body would slide right downwards. An exact force of 50N would ensure translational equilibrium. However, if the force exceeds 50N, the body would slide up in the direction of F. In other words, if translational equilibrium were not satisfied, the structure would fail and therefore accelerate in the direction of the net force. Because gravity is constant, this acceleration is usually in the direction of acceleration due to gravity.

How Gravity Works Against Structures

Some of the fears of builders and architects include:

• fears that the whole building might gradually sink into the ground (much like a man standing on a quicksand). To solve this problems, buildings (especially tall ones) are erected on solid, compressed ground or rocks.
• fears that the building may not stand upright (that is, that the building might be inclined at an angle other than right angles). This is the case for the Leaning Tower of Pisa.

• there is also fear that the building may collapse under its weight due to tension and compression forces.

Underlying each of these points of failure in a building structure is the action of gravity on structures. Ordinarily, the force of gravity acts straight down such that a building that can carry its weight should not fall. However, the weight of any structure is known to be concentrated in the middle of the structure, called centre of mass. For an upright structure, the centre of mass is in the middle, but if the structure is tilted to one side, the centre of mass shifts away from the centre and the force of gravity can have a turning effect. This turning effect is called a moment that is capable of making the structure to topple over.

To reinforce the Leaning Tower, some modifications were made on the building a couple of decades ago when lead counterweights were added at the base to keep the building stable. Now, after ensuring that a building does not topple over by erecting it upright, the builder must provide that the building can carry its weight.

Weight Support in Buildings

To ensure that buildings do not collapse under their weight, the foundations are made of stronger, heavier materials that the stories. An effective way of doing this is through the use of steel pillars and reinforced concrete. Also, lightweight materials such as cardboard and fibres are used in the interior of the building where strength is not required to ensure that the building does not carry more load than is required.

Conclusion

Apart from toppling over due to the moment of force of gravity, buildings also have to cope with tension and compression. That's not all: building must carry another load apart from the weight of the materials used to erect the building. The tallest skyscraper must house people, furniture, office equipment, generators and even a helipad. The simplest bridge must carry motor vehicles, human beings and animals. This means that every static structure also has to cope with varying loads. Working out the maximum size of these loads and the strength of materials that can be used in a particular design to provide greater resistance to the inevitable load are crucial parts of the design process.

Finally

What do you think may be the possible forces at work in the Leaning Tower and why hasn't the damn thing toppled over?

References

1. Wikipedia | The Leaning Tower of Pisa
2. The Slideplayer | Rotational Force
3. Explain That Stuff | How Buildings Work
4. Jaconline | Design Changes
5. The Physics Classroom | Balanced and Unbalanced Forces

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