Final answer:
Living bridges can span up to 50 meters or more, but the references provided focus on thermal expansion and oscillations in traditional bridges, not living bridges.
Step-by-step explanation:
The question on the span of larger living bridges seems to point towards a real-world application rather than a theoretical or mathematical context; however, the provided reference information does not contain specific details about living bridges. Living bridges, made from the roots of trees, primarily found in the northeastern Indian state of Meghalaya, can span up to 50 meters or more. These bridges are formed by guiding the pliable roots of the Ficus elastica tree across rivers or ravines, and they strengthen over time. The reference info given talks about the thermal expansion of bridges and the concept of scale in diagrams but doesn't directly provide the answer to the initial question.
Concerning the expansion joints in bridges, they are crucial for accommodating changes in length due to temperature fluctuations. For example, the Golden Gate Bridge can experience a change in length when the temperature varies between –15°C and 40°C. These joints allow the bridge to expand and contract without causing damage.
Engineering applications such as measuring the force needed for bridge oscillations are important for maintaining the structural integrity of bridges. For instance, a suspension bridge that oscillates with a certain force constant requires a specific amount of energy to maintain its amplitude of oscillation.