The curved and flat plates of width 6-m are connected at A, B and C. They are submerged in water at the depth h = 7-m. The distance d =4-m and the radius R = 2-m. Find the resultant force [kN] in the hinge at B. h В A d

The curved and flat plates of width 6-m are connected at A, B and C. They are submerged in water at the depth h = 7-m. The distance d =4-m and the radius R = 2-m. Find the resultant force [kN] in the hinge at B. h В A d

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.121P: One side of the container has a 03-m square door that is hinged at its top edge. If the container is...

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

The curved and flat plates of width 6-m are connected at A, B
and C. They are submerged in water at the depth h=7-m. The
distance d =4-m and the radius R= 2-m. Find the resultant
force [kN] in the hinge at B.
h
В
R
A
d

Expert Solution

Step 1 Calculate the resultant force at B

First we have to calculate the force on the member AB. We have

$T h e h o r i z o n t a l f o r c e F_{H} = ρ A g \bar{x} = 1000 \times 9.81 \times 6 \times 2 \times (7 + \frac{2}{2}) = 941.76 k N; T h e v e r t i c a l f o r c e F_{V} = 1000 \times 9.81 \times (π \times 2^{2} \times 6 + 6 \times 7 \times 2) = 1563.7 kN; So the net force is acting on AB is = \sqrt{{F_{H}}^{2} + {F_{V}}^{2}} = \sqrt{941 . 76^{2} + 1563 . 7^{2}} = 1825.4 kN;$

The inclination of force on AB is = $θ_{A B} = \tan^{- 1} (\frac{F_{V}}{F_{H}}) = \tan^{- 1} (\frac{1825.4}{941.76}) = 62.7 °$

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