Many have argued the Golen Gate Bridge was impractical to build in the engineering perspective. The decision to go ahead with the construction was even placed in the hands of hundreds of thousands of San Francisco residents. They voted through the project and it just started like this. Even then, the strong winds that pass through the Golden Gate Strait posed challenges, but they theorized that a long span suspension bridge could cross the Gate from the Pacific Ocean to the San Francisco Bay. However, a suspension structure of this length had never been tried before. Despite a series of obstacles throughout the project, the Golden Gate Bridge remains, even today, the quintessence of a suspension bridge. So how did the Golden Gate Bridge go from impossible to an engineering classic? In order to answer this, we must take a look at the physics knowledge that can explain how the bridge was made possible and how it was made strong.
Golden Gate Bridge
Statics is the science that deals with forces that balance each other to keep objects in a state of rest. And when all the forces acting upon an object are balanced, the object is in equilibrium. In other words, in such a system the net horizontal force is 0 N as well as the net vertical force. According to Newton’s second law, only when there is a net force acting on a mass is acceleration produced (Fnet=ma); and in the case of equilibrium, the absence of a net force indicates the non-existence of acceleration. That means the object is at rest or moving with constant velocity. Examples of equilibrium include a mug sitting on a table (at rest), buildings (at rest), and a skydiver in action (moving with uniform motion), with the first two in static equilibrium. However, when only ΣFx=0 and ΣFy=0 are met, static equilibrium isn’t guaranteed; the second condition must be applied to guarantee static equilibrium: ΣT=0 Nm, net Torque is zero Newton meters. For this physics investigative adventure, we will devote ourselves in the study of static equilibrium, which is the kind of equilibrium where objects are at rest (i.e. they are not moving up/down/left/right, nor rotating in any direction) and the kind of equilibrium the concept of suspension bridge is based on. In other words, it’s the principle of static equilibrium that made possible suspension bridges with a span of that of the Golden Gate Bridge.
How do suspension bridges work?
A sketch of forces
In a suspension bridge, the weight of the bridge deck and vehicles is transferred up through the suspender rods to the main suspension cable, which in turn transfers the force to the two bridge towers and the anchor blocks. The forces from the suspender rods (vertical cables) produce tension in the main suspension cable—that is, force which attempts to stretch or lengthen the cable. Where the main suspension cable meets the towers, it runs through a smooth saddle, which enables it to transfer forces into the tower. In simple terms, the two tension forces from the main cable pull horizontally against each other, while at the same time pushing down on the tower, which, in turn, must push back up against these downward forces. We can therefore say that the tension from the cable produce a compressive force in the tower—that is, a force which tends to shorten or compress the tower. The tower must then be designed to support these compressive forces without crushing or buckling (bending).
Suspension bridges vs. Static equilibrium
1) 1st condition of static equilibrium: ΣFx=0 and ΣFy=0
The horizontal forces include the tensions between the anchor blocks and the towers, the tensions between the two towers, and the friction force from soil or rock against the anchor block. The left and right forces have to balance each other to make the bridge stable, not swaying from one end to the other. It works like this: as we can see in both the sketch above and the diagram, when tensions from the main cables on both sides of the tower pull on the tower, they pull horizontally against each other, thus cancelling some of the force, while directing the other part of the force down to the tower. At the end of the bridge, tension is also transferred to the anchor block, but is then balanced by the gravitational force on the mass and frictional force.
The vertical forces include the weight of the deck and traffic, the tension in the suspender rods, the downward forces exerted on the towers by the main cables and the upward force the towers push back up against the compressive forces. Again, these forces must equilibrated, up versus down. It works like this: the weight of the bridge deck along with the loads of traffic is transferred up the suspender rods to the main cables (Wdeck=Tsuspenders, or mg-T=0). Then, as mentioned, a portion of the tension from the main cables pushes down the towers to relieve the force, hence the tower must be able to exert an upward force to counteract that compressive force. Otherwise, the tower, the main support for the bridge, is going to bend.
2) 2nd condition of static equilibrium: ΣT=0 (2nd condition must be applied because even when two forces acting on a bar have a net force of zero, the forces can cause the object to spin, i.e. not static. Eg. Meter stick)
The vertical forces include the weight of the deck and traffic, the tension in the suspender rods, the downward forces exerted on the towers by the main cables and the upward force the towers push back up against the compressive forces. Again, these forces must equilibrated, up versus down. It works like this: the weight of the bridge deck along with the loads of traffic is transferred up the suspender rods to the main cables (Wdeck=Tsuspenders, or mg-T=0). Then, as mentioned, a portion of the tension from the main cables pushes down the towers to relieve the force, hence the tower must be able to exert an upward force to counteract that compressive force. Otherwise, the tower, the main support for the bridge, is going to bend.
2) 2nd condition of static equilibrium: ΣT=0 (2nd condition must be applied because even when two forces acting on a bar have a net force of zero, the forces can cause the object to spin, i.e. not static. Eg. Meter stick)
ΣTcw= ΣTccw. If we take one of the blue points as the pivot point, the total torque trying to rotate the bridge clockwise must equal the total torque trying to rotate it counterclockwise (yes, it sounds bizarre to spin a bridge). Let’s say the middle point is the pivot, then the counterclockwise torques (produced by the weight on the left side of the bridge and the tension in suspenders pulling up on the right side) have to balance the clockwise torques (produced by the weight on the right side of the bridge and the tension in suspenders pulling up on the left side).
How was the Golden Gate Bridge made strong?
After knowing how a suspension bridge over a nearly 2-km span is in fact practical, we shall investigate how to build the Golden Gate strong and able to stand for hundreds and even thousands of years. There are a few important factors that contribute to the achieving of this goal:
1) Stable towers: In order to bear the compressive force given by the main cables from both sides, the towers need to be extremely solid and stable at the base. It turned out that one of the towers of the Golden Gate Bridge had to be built in the ocean although towers are usually built near the shore. To build the base for that tower, bridge builders actually needed to work underwater—30 meters below the ocean surface. They made a huge box that reached from the surface down to the ocean floor. Then they pumped the seawater out so that they could construct a strong concrete base for the tower. In fact, the sturdier the tower base is made, the greater amount of force it can hold, therefore the more traffic load can travel through.
2) Gigantic cables: Another challenge was making the cables (suspenders and main cables) strong enough for the heavy deck to hang safely. It weighs over 150 000 tonnes! Engineers needed cables that were over 90 centimeters thick to hold that weight. So they accomplished that thickness by bundling up small wires and twisting them, which were then bundled and twisted together again and again. It took 130 000 kilometers of wire to do the job! By increasing the thickness and strength of the cables, the range of tension they can withstand is greatly increased, thus a heavier mass on the bridge deck is permissible.
3) Heavy anchor blocks: The concrete blocks at both ends of the Golden Gate Bridge are to resists the tensile pull from the main suspension cable, through its mass primarily and some friction force against the anchorage surface. In most suspension bridges, the anchorage is a reinforced concrete block cast against and firmly connected to underlying rock. Inside the anchor block, the stranded suspension cable is unwound and splayed out to provide a more substantial connection between the concrete and the cable. This way, the block encounters the tension from the cable more easily and can act upon the force more easily and directly. By increasing the mass of the anchor block, the tension from the cable is allowed a greater magnitude, maximizing the weight of the traffic on the deck.
1) Stable towers: In order to bear the compressive force given by the main cables from both sides, the towers need to be extremely solid and stable at the base. It turned out that one of the towers of the Golden Gate Bridge had to be built in the ocean although towers are usually built near the shore. To build the base for that tower, bridge builders actually needed to work underwater—30 meters below the ocean surface. They made a huge box that reached from the surface down to the ocean floor. Then they pumped the seawater out so that they could construct a strong concrete base for the tower. In fact, the sturdier the tower base is made, the greater amount of force it can hold, therefore the more traffic load can travel through.
2) Gigantic cables: Another challenge was making the cables (suspenders and main cables) strong enough for the heavy deck to hang safely. It weighs over 150 000 tonnes! Engineers needed cables that were over 90 centimeters thick to hold that weight. So they accomplished that thickness by bundling up small wires and twisting them, which were then bundled and twisted together again and again. It took 130 000 kilometers of wire to do the job! By increasing the thickness and strength of the cables, the range of tension they can withstand is greatly increased, thus a heavier mass on the bridge deck is permissible.
3) Heavy anchor blocks: The concrete blocks at both ends of the Golden Gate Bridge are to resists the tensile pull from the main suspension cable, through its mass primarily and some friction force against the anchorage surface. In most suspension bridges, the anchorage is a reinforced concrete block cast against and firmly connected to underlying rock. Inside the anchor block, the stranded suspension cable is unwound and splayed out to provide a more substantial connection between the concrete and the cable. This way, the block encounters the tension from the cable more easily and can act upon the force more easily and directly. By increasing the mass of the anchor block, the tension from the cable is allowed a greater magnitude, maximizing the weight of the traffic on the deck.
Conclusion:
Challenges were faced, solutions were sought, massive materials used, and millions spent. This is how the Golden Gate Bridge came to be, from the impossible to today’s classic among suspension bridges. It has proved the powerfulness of static equilibrium--how it can be applied to enhance the field of engineering and our lives.