the
* Example: The following are costs of one pier and
one super-struchure span of multiple span to bridge
for rarious
Span lengts. The cost of supeo Stouchese
the costs of sailings, & flooring system-
Calculate the economic span.
span excludes.
12
8
7ooo
15
245oo
16000
Spon in metres.
Euper smuchise cost (RS)
cub Struchise cost (Rs)
1700
22200
23200
23000
2360o
Answers
Answer:
A bridge has two abutments, one or more spans in the superstructure, and one fewer piers than spans. So, if the bridge has n spans, it will have n-1 piers and 2 abutments. Let the cost of one span to the cost of one pier be R.
R=s/p then. or s=pR
Where s is the cost of one span and p is the cost of one pier. If A is the cost of one abutment, then C = 2A+ns+(n-1)p = 2A+npR+(n-1)p
For C to be as low as possible, dC/dn=0.
→0+pR+p=0
→p(R+1)=0
Because the cost of pier p will not be zero,
R+1=0
→R=-1
Because R is the cost ratio, the negative sign must be avoided.
This means that s/p=1.
→s=p
That means if the cost of one span and one pier is same then the bridge has minimum cost, hence economical.
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