Compressive Force on Aqueduct Pillars as a Barge Passes: 04-BS-7, December 2014, Q11

Question 11 — Compressive Force on Aqueduct Pillars as a Barge Passes (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Barge length × width	15 m × 3 m
Barge draught	1.2 m
Canal width × depth	5 m × 2 m

Find. The change in compressive force transmitted to the aqueduct pillars while the barge is on the span.

Fig. Q11 — the aqueduct trough (supported on pillars) carries the canal across a valley; the loaded barge floats within it.

Approach. By Archimedes' principle, a floating barge displaces a volume of water whose weight exactly equals the barge's own weight. The total weight the aqueduct structure must support (water + barge together) therefore INCREASES by exactly the barge's weight when it is on the span — regardless of how the local water level adjusts.

Displaced volume. $$V_{disp} = L\times W\times \text{draught} = 15\times3\times1.2 = \boxed{54\text{ m}^3}$$
Weight of displaced water = weight of the barge (Archimedes). This is exactly the increase in total load on the pillars while the barge is present: $$\Delta F = \rho_{water}\,g\,V_{disp} = 1000\times9.81\times54 = \boxed{529.7\text{ kN increase}}$$

Quantity	Result
Displaced volume	54 m³
Increase in compressive force on pillars	529.7 kN

This is the classic "boat-in-a-supported-trough" load result: the barge's own weight is fully transmitted to the water via buoyant pressure, and the water's weight is fully carried by the structure, so the total support reaction rises by exactly the barge's weight — independent of whether the water level rises, spills over, or stays essentially constant, and independent of the canal's own width or depth (which only govern whether the barge physically fits, not the load outcome).

Common misconception	Correct reasoning
"The load is unchanged — the barge just displaces its own weight of water"	That phrase describes what happens to the WATER LEVEL, not the total force on the supporting structure, which genuinely increases by the barge's weight.

Topic: Archimedes' principle applied to a body of water resting on a supporting structure.

Key relations: buoyant weight = weight of displaced fluid = ρgV_disp; total support reaction = weight of all water present + weight of any floating body.

Why this works: the trough must support the full weight of everything it contains; adding a floating barge adds the barge's weight to that total (transmitted through the water to the structure), an increase exactly equal to the barge's weight regardless of the canal's own dimensions.

Common pitfall: confusing "displacement conserves water level in a large open body" with "the load on a SUPPORTED trough is unchanged" — these are different statements; the latter is false.

Source: White, Fluid Mechanics, 8th ed., §2.8 (buoyancy, Archimedes' principle).

Question 11 of 13: Compressive Force on Aqueduct Pillars as a Barge Passes

Question 11 — Compressive Force on Aqueduct Pillars as a Barge Passes (5 marks)