The Important Concepts

The next step in figuring out how to build our bridge was looking at the different forces that act on a bridge at  various times and places on the structure. Ironically, many of the forces are rather simple ones that most everybody knows, it's just that they're specifically taken advantage of in the construction of a bridge.

Compression & Tension

Compression is the force that pushes two objects together. It can easily and simply be demonstrated by pressing the palms of your hands together. The harder one pushes, the more compression forces there are between the two hands. On the other hand (pun fully intended), tension is a force that is opposite to compression. Instead of the force that pushes two objects together, it is the force seen when an object is stretched in opposite directions. A very simple example that relates to bridges can be seen above. When an object is placed on top of a bridge, the weight it exerts downwards caused compression on the top of the deck, while causing tension on the bottom of the deck. When building a bridge, utilizing both of these forces becomes key in making sure that a bridge doesn't collapse as soon as weight is put on it. 

Weight & Equilibrium

Weight is yet another concept that is extremely basic, yet is important to the building of a bridge. Weight is a force dependent upon Newton's Law of Universal Gravitation, as well as partially being related to Newton's Third Law, which states that every action has an opposite and equal reaction. Essentially, gravity is responsible for giving objects weight, which is shown by the equation for weight, w=mg where w is weight, m is mass, and g is the acceleration due to gravity (9.80 m/s^2 on Earth). This equation was derived from Newton's Second Law, which states that Force = Mass x Acceleration. The effect of weight on bridges is rather self-explanatory; the more weight that's on a bridge, the more force that is needed to counteract that weight. Though there are many different forces that act on an object to achieve equilibrium, we can get a general sense of equilibrium through weight. For instance, if a man is sitting in a chair, the system is in equilibrium. If the man weights approximately 50 N, then according to Newton's Third Law, the chair is pushing back with a normal force of 50 N as a result. The system extends even further into successive layers, as the ground that the chair is sitting on is pressing up on the chair with a force of 50 N, and the building is pressing up on the floor with a force of 50 N, and so on. According to Newton's First Law, which states that  an object at rest will stay at rest unless acted on by an unbalanced force, the chair will stay at rest unless someone were to, say, push the chair from behind. 

Torque

Torque is a force that provides a twisting motion to an object. That being said, it's important to prevent such a twisting on a bridge because it can lead to the bridge collapsing from the forces that exerted. To look at torque from an analytical perspective, it can be defined by the equation T=FL, where F is the force exerted and L is the lever arm. The lever arm can further be broken down into the equation L=rsin(theta), where r is the radius and theta is the degree measure formed by the line of action and the object being pushed. Torque became a major part of our bridge design, as you'll be able to see in the next post.

Vector Addition

When all is said and done, vector addition is the end all be all for determining the force and direction of any combined force. Basically, by using the magnitude and direction of two forces pushing on the same object, one can determine the resulting magnitude and force. Not only that, the resultant can be determined either graphically or algebraically. It's hard to put it into words exactly, but the graphical method is done by using the two forces to form a parallelogram, and using the diagonal of that parallelogram as the resultant vector. That kind of addition can be experimented with here. The alternate method, through algebra, is generally more common because of its accuracy compared to the graphical method. Again, it's a bit hard to explain, in words, but basically one must multiply the magnitude by the cosine of the degree measure for the horizontal factor of both, and then multiply the magnitude by the sine of the degree measure for the vertical factor. You then must add up the vertical and horizontal quantities, square the results, and take the square root of the squared results added together. This will give you the magnitude. The second part is finding the direction, in which case you use the inverse tangent of the vertical quantity over the horizontal quantity. In the case of the resultant being in the 2nd or 3rd quadrant, you then have to add 180 degrees, or if it is in the 4th quadrant, you have to add 360 degrees.