Question

The St. Francis Dam was original designed at a height of 175 ft. However, during the construction phase, the height of the dam was increased by 10 ft to 185 ft to provide the additional reservoir storage capacity. What would be the increase in the overturning moment (lb-ft/ft) about the toe (point O) of the dam caused by the water pressure due to height increase

Answer 1

This question is incomplete, the missing diagram is uploaded along this answer below;

Answer:

the increase in the overturning moment is 10.1 × 10⁶ lb.ft/ft

Option c) 10.1 × 10⁶ lb.ft/ft id the correct answer

Step-by-step explanation:

Given the data in the question and illustrated in the image below;

Hydrostatic force on Dam ( per unit length )

P =
`(1)/(2)` rH.H =
`(1)/(2)`rH² lb/ft

Now, Overturning moment;

M = R × P = H/3 ×
`(1)/(2)`rH² =
`(1)/(6)`rH³ lb.ft/ft

so when H = 175 ft

M₁ =
`(1)/(6)`r × ( 175 )³ =
`(1)/(6)` × 62.4 × ( 175 )³

M₁ = 55737500

Also, When H = 185 ft

M₂ =
`(1)/(6)`r × ( 185 )³ =
`(1)/(6)` × 62.4 × ( 185 )³

M₂ = 65848900

∴ Increase in overturning moment will be;

⇒ M₂ - M₁ = 65848900 - 55737500

⇒ 10111400 ≈ 10.1 × 10⁶ lb.ft/ft

Therefore, the increase in the overturning moment is 10.1 × 10⁶ lb.ft/ft

Option c) 10.1 × 10⁶ lb.ft/ft id the correct answer