Advanced Bridge Building You are designing a new cable suspension bridge and the
ID: 1471451 • Letter: A
Question
Advanced Bridge Building You are designing a new cable suspension bridge and the central span is to be made out of steel. The bridge will be built in an area that has annual temperatures ranging from a low of-10 C to a high of 35 C. The central span will be 450 m long. The steel beams for the span have the following properties: a density of 7890 kg/m3, Young's modulus of 20 Times 10^10N/m2, shear modulus of 8.4 Times 10^10 N/m2, bulk modulus of 6 Times 10l0N/m2, cross-section of 1.0 nr, and a linear thermal expansion coefficient of 11 Times 10^-6 C-1. What design considerations should you take into account when designing the bridge structure, suspension cables and the deck? Be as specific as possible addressing all of the relevant physics we have covered in class.Explanation / Answer
The most important aspects of the design are the thermal expansion and linear expansion of roadway and cables.
We calculate the thermal expansion of steel. D=Delta (variation)
DL = L DT DL= 11 10-6 450 (35- (-10))=0.22275 10-2 m
We calculate the expansion of the cable due to the weight of bridge
F/A= Y DL/L Y Young modul
DL = L F/A Y F=W = mg = m/V V= A L
DL = L ( LA) g /AY = L2 g/Y
. g= 9.8 m/s2 @ 10 m/s2
DL =(450)2 7890 10/ 20 1010 = 0.0799 m
Shown that the thermal expansion is the most important parameter in the calculation.
We calculate the deformation of the road due to the weight, displacement is equal to the amount stretched by cable
DL = 0.0799 m
F/A = S DL/h F/A= 8.4 1010 0.0799/1 = 6.7 109 N/m2
When comparing the number with the tabulated value of the shear force of steel (4 108 N/m2) we see that the bridge should be supported by multiple cable to reduce this value and avoid the collapse.
In resume the most important parameters are:
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