The span of the bridge is said to be economical when1. the cost of sup

1.	The span of the bridge is said to be economical when1. the cost of supporting system of one span is equal to cost of one pier.2. the cost of supporting system of one span is equal to cost of one abutment.3. the cost of pier is equal to half the cost of abutment.4. the cost of supporting system of one span is equal to half the cost of pier
Answer» Correct Answer - Option 1 : the cost of supporting system of one span is equal to cost of one pier. Concept: The span of the bridge for which the total cost of the bridge is minimum is called economic span. Let, the ratio of cost of one span ‘S’ to cost of one pier ‘P’ be R (i.e. R = S /P). Then, The overall cost of the considered bridge be – C = nS + (n - 1) × P Putting S = RP C = n (RP) + (n-1)P Where, n – Number of spans (n - 1) – Number of piers For C to be minimum, dC / dn = 0, ⟹ PR + (-1) × P =0 ⟹ R = 1 Hence, S = P Hence, Economical span is one for which the cost of one span is equal to one pier. In other words, Economical span is defined as that span for which the total cost of the substructure is equal to the total cost of superstructure.

The span of the bridge is said to be economical when1. the cost of supporting system of one span is equal to cost of one pier.2. the cost of supporting system of one span is equal to cost of one abutment.3. the cost of pier is equal to half the cost of abutment.4. the cost of supporting system of one span is equal to half the cost of pier

Answer» Correct Answer - Option 1 : the cost of supporting system of one span is equal to cost of one pier.

Concept:

The span of the bridge for which the total cost of the bridge is minimum is called economic span.

Let, the ratio of cost of one span ‘S’ to cost of one pier ‘P’ be R (i.e. R = S /P).

Then,

The overall cost of the considered bridge be –

C = nS + (n - 1) × P

Putting S = RP

C = n (RP) + (n-1)P

Where,

n – Number of spans

(n - 1) – Number of piers

For C to be minimum,

dC / dn = 0,

⟹ PR + (-1) × P =0

⟹ R = 1

Hence,

S = P

Hence,

Economical span is one for which the cost of one span is equal to one pier.

In other words, Economical span is defined as that span for which the total cost of the substructure is equal to the total cost of superstructure.