Answered: The figure below shows a rectangular…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The figure below shows a rectangular gate holding sea water behind it (sg = 1.08). If the water is 18.00 ft deep, (Part a) compute the magnitude (in lb) and (Part b) determine the location of the resultant force on the gate. (Report the location to three decimal places).

Expert Solution

Introduction

Objectives:

Determine the magnitude of the hydrostatic force acting on the gate
Determine the location of the resultant hydrostatic force on the gate

Given:

Specific gravity of seawater (sg) = 1.08

Depth of water (D) = 18 ft

Depth of top of the gate from free surface (H) = 11 ft

Height of the gate (h) = 7 ft

Width of the gate (b) = 4 ft

The magnitude of the resultant force on the gate (F_R) can be expressed as:

$F_{R} = γ_{s e a w a t e r} h A$

here,

$γ_{s e a w a t e r}$ : specific unit of seawater

$h$ : depth of centroid of the gate from free surface $= (H + \frac{h}{2})$

$A$ : surface area of the gate

The location of the resultant from the free surface (h*) can be expressed as:

$h * = \frac{I_{G}}{A h} + h$

here,

$I_{G}$ : moment of inertia of the gate $= \frac{b \times h^{3}}{12}$

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