I believe there is no better way to understand the relationship between tension and compression than to analyze how a suspension bridge works. Perhaps there is no better suspension bridge to analyze than the Golden Gate Bridge in San Francisco, CA. There are plenty of books and manuals that define...
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I believe there is no better way to understand the relationship between tension and compression than to analyze how a suspension bridge works. Perhaps there is no better suspension bridge to analyze than the Golden Gate Bridge in San Francisco, CA.
There are plenty of books and manuals that define tension and compression, but do firefighters truly understand the tension/compression relationship and why structural engineers choose either tension or compression to move stress from one structural component to the next? This article will describe how the Golden Gate Bridge uses tension and compression to transfer live and dead loads — cars, trucks, concrete, steel, rain, wind, people and concrete — to the bottom of San Francisco Bay as compression. We begin with some Golden Gate Bridge background, followed with a photographic tour that will describe how the bridge uses tension and compression to resist gravity.
The Golden Gate Bridge
Engineered by Joseph B. Strauss, Golden Gate Bridge construction started in 1933 and was completed in 1937 at a cost of $27 million — five months late and $1.3 million under budget. (Strauss said, "It took two decades and 200 million words to convince people that the bridge was feasible.") Eleven workers were killed during construction; at least 1,200 people have jumped from the bridge. From abutment to abutment, the Golden Gate Bridge stretches 1.7 miles (8,981 feet). The total length of the suspended span sections is 1.2 miles (6,450 feet). The middle span suspended between the towers stretches 4,200 feet. The length of one side span is 1,125 feet. The highest clearance above the water is 220 feet. The height of the towers above the water is 746 feet. The height of the towers above the roadway is 500 feet. The width of the bridge is 90 feet. The width of the roadway between curbs is 62 feet. The sidewalk is 10 feet wide. Each leg of each tower base measures 33 by 54 feet.
As of 1986, the total combined dead load of the Golden Gate (bridge, anchorages and approaches) was 887,000 tons. The live-load capacity was calculated to be 4,000 pounds per lineal foot. The bridge deck (roadway, sidewalks and curbs) weighs 3,830 pounds per lineal foot. The concrete paving weighs 6,470 pounds per lineal foot. The bridge deck is suspended by a series of vertical cables.
To prevent aeroelastic flutter (dynamic oscillations), the bridge deck was stiffened by using a series of steel trusses that weigh 33,000 pounds per lineal foot. (The open-web trusses also let wind pass through.) For example, the design wind pressures were 30 pounds per square foot on the bridge deck and suspension cables, and 50 pounds per square foot on the towers. Additional rigidity is provided by diagonal bracing between the parallel chord trusses; the diagonal bracing adds 600 pounds per lineal foot.
The bridge has two main cables that pass over the tips of the two main towers and are secured at each end by gigantic on-shore anchorages. The total weight of each on-shore anchorage is 60,000 tons. The south anchorage is on the San Francisco shore; across the bay, the north anchorage is on the Marin County shore near Sausalito. More than one million tons of concrete was used to complete the anchorages.
The main cables rest atop the columns of each main tower in huge steel castings called saddles. The diameter of one main cable is 36 and 3/8ths inches. The length of one main cable is 7,650 feet. Each main cable is comprised of 80,000 miles of galvanized steel wires. Each main cable contains 61 bundles, or strands, of galvanized steel wire. The 61 bundled strands are comprised of 27,572 wires; the diameter of each wire is 0.192 inches. The spinning of the main cable wires took six months and nine days to complete. The (tested) tensile strength of the main cables in 235,000 pounds per square inch; the yield strength of the main cables is 182,600 pounds per square inch. The bridge deck and roadway are suspended by 250 pairs of vertical suspension cables (referred to as stringers or hangers). The diameter of each vertical cable measures two and 11/16th inches. Including the vertical cables and connection hardware, both main cables weigh 24,000 tons.
To support the two main cables, the bridge has two main towers. As mentioned, each tower rises 746 feet above the water. The towers consist of two laterally braced columns. The weight of both main towers is 44,000 tons. The load delivered to each tower by the (horizontal, curved) main cables is 61,500 tons. Some 153,500 cubic yards of concrete was poured for the piers which support the towers.
Tension and Compression Analysis
So, how does the Golden Gate Bridge deliver all this dead load (and live load) to the earth as compression? From here on, I will use images to help explain how the whole thing works.
Matters of Size
Examine Photo 4 and notice how much larger the towers are than the cables. The reason for this is that the cables are loaded entirely in tension and the tower columns are loaded entirely in compression. Resisting compression requires the rigid, unyielding mass of the columns; resisting tension allows for reduced mass and increased flexibility, including significant stretching and pronounced bending.
The photo reveals a clue to understanding the relationship between tension and compression. The dead load and live load that the main cables deliver to the tower columns is the exact same dead load and live load delivered to the bottom of San Francisco Bay. Granted, the towers also deliver their own weight to the bottom of the bay, but once the tension arrives at the top of the columns, there is a "moment" when the tension changes to compression and the flexibility must change to rigidity and the tower mass (dead load) must increase substantially.
Recall that both main cables are 36 inches in diameter and weigh 24,000 tons; the base of each main tower measures 33 by 54 feet and weigh 44,000 tons. The weight of the towers is nearly twice the weight of the main cables, yet the main cables are a fraction of the size. Tension reduces dead load; reducing dead load makes developers happy; making developers happy generates revenue; revenue makes fire departments happy.
Tension Becomes Compression
How does the tension in the main cables magically change to compression? Tension from the main cables arrives axially at the column saddles; that is, the tension arrives from both sides of the towers uniformly. Should the main cable fail on one side of a tower, the cable attached on the opposite side would exert a lateral (eccentric) force that would pull the tower out of plumb and likely drop the bridge deck into the bay.
Fortunately, the load arrives at the saddles axially so that the tension in the main cables pulls down on the tower columns. This downward pull — not push — on the columns generates compression; since the columns are restrained at the bottom by concrete piers in the water, the downward pull has a shortening effect; thus, the columns are in compression. The towers are rigid and resist the downward pull thus compression is generated.
Why does this happen? It happens because the cables are flexible and can elongate. The vertical cables pull down along the length of the main cables, creating a bowl-shaped curve. Most of the pull on the main cables is generated below the tops of the towers. Visualize polishing the toe of a boot with a cloth; as you rapidly pull the cloth back and forth, your hands would be below your boot so that you pull the cloth into tension. Even though the cloth is pulled into 100% tension and is moving from side to side (dynamic), the resulting stress on the boot is compression. Cables get longer when loaded (tension); columns get shorter when loaded (compression).
This "moment" of tension-compression transformation happens because the main cables are uniformly pulled downward into a bowl-shape referred to as a parabolic curve. Since the main cables are restrained at the top of the columns the result is compression. The tower columns send the compression to the bottom of San Francisco Bay. Same load, different stress.
The tension/compression phenomenon atop the towers is similar to the compressive force generated at the anchors of a post-tension floor assembly. After being jacked (stretched), the tension is slowly released until wedges at the anchor bite the strands. If not restrained by the anchors, the strands would return to their original length. Although the cables within the floor will forever remain in tension, the urge to return to their original length generates compression at the anchors.
The Long Center Span
The entire 4,280-foot center span bridge deck and roadway is supported by the vertical cables. Each of the 250 pairs of vertical cables is loaded entirely in tension. The vertical cables deliver their bridge deck load and live load to the two main cables as tension.
The Bridge Deck
The main cables collect the tension from each vertical cable and send the tension left and right to the tower columns. Recall that all tension must somehow and someplace change to compression. As was previously discussed, this change does not occur until the main cables deliver the accumulated tension to the towers.
The bridge deck is stiffened by parallel chord trussing; further rigidity is provided by cross bracing between the trusses and under the roadway.
Tacoma Narrows Bridge
Lacking stiffening trusses and cross-bracing, a moderate wind would destroy the bridge. This lesson was learned in November 1940 in Washington State. Four months after opening, the Tacoma Narrows Bridge failed, collapsing during a storm featuring 40-mph winds. At the time, the Tacoma Narrows Bridge was the third-longest bridge in the world. Two suspension bridges now span the Tacoma Narrows.
Main Cable Anchors
Each main cable of the Golden Gate Bridge is anchored on the San Francisco shore and across the bay on the Marin County shore. The anchors are huge. Recall that the total weight of each on-shore anchorage is 60,000 tons. The anchors restrain the end of each main cable so that the cables stretch; without the anchors, the cables could not be stretched into tension. As in any structural system, the connections are critical. In the case of a structure that relies a lot on pure tension, each piece becomes critical. Imagine what would happen if one of the main cable/anchor connections failed…Imagine what would happen if one tower column buckled…
It is my desire that this article will provide a catalyst for fire station discussion. Should you possess a strong building construction background, I hope this article provides a good review of the tension/compression relationship.
Building construction is the anatomy and physiology of the square-foot (structural) fireground. Just as a competent surgeon must possess a strong foundation of human anatomy and physiology knowledge, a competent fire officer must possess a strong foundation of building anatomy and physiology knowledge. Golden Gate Bridge anatomy includes the towers, cables, concrete, steel and trusses; Golden Gate Bridge physiology includes the tension, compression, torsion and shear that move throughout and reshape the anatomy.
Next: The Wonderful World of Beams and Columns
MARK EMERY, EFO, is a shift battalion chief with the Woodinville, WA, Fire & Life Safety District. He is a graduate of the National Fire Academy's Executive Fire Officer program and an NFA instructor specialist. Emery received a bachelor of arts degree from California State University at Long Beach and is a partner with Fire Command Seattle LLC in King County, WA. He may be contacted at firstname.lastname@example.org or access his website www.competentcommand.com.