What Are the Tensions in Each Cable of a Suspension Bridge?

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SUMMARY

The discussion focuses on calculating the tensions in the cables of a suspension bridge, specifically in the context of a problem involving a uniform rectangular roadway supported by vertical cables. The tension in cable CD is established as Mg/4, where M is the mass of the roadway and g is the acceleration due to gravity. Participants suggest using equilibrium equations to derive the tensions in segments AB, BC, DE, and EF, while addressing the missing height information for points B and E. The consensus is that the problem can be solved with the provided data, despite initial confusion regarding the relevance of certain dimensions.

PREREQUISITES
  • Understanding of static equilibrium in structures
  • Knowledge of tension forces in cables
  • Familiarity with trigonometric functions and their application in physics
  • Ability to solve systems of equations
NEXT STEPS
  • Study the principles of static equilibrium in civil engineering structures
  • Learn how to derive tension in cables using vector analysis
  • Explore the application of trigonometry in calculating angles and forces in structures
  • Investigate common mistakes in tension calculations for suspension bridges
USEFUL FOR

Civil engineers, structural analysts, and students studying mechanics of materials or structural engineering will benefit from this discussion, particularly those focusing on cable-stayed and suspension bridge design.

  • #31
insightful said:
I'd love to see how the textbook got their answers. Doubling doesn't appear to explain my discrepancy.
True.
The textbook answer looks ridiculous to me. Since ##\frac{\sqrt{5}}{2}>1.1## it is saying, via its value for AB and EF, that each of the four pylons is resisting a force equal to more than the entire weight of the bridge.
 
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  • #32
insightful said:
Yes, it would be fun to see if they match mine [(mg/4)sqrt(2) for AB and EF, and (mg/8)sqrt(5) for BC and DE].
These are also the answers I arrived at. (No saying I haven't blundered somewhere, though.)[/color][/size][/color]
 

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