Answered: D 30° B 60° 45° A

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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Question

The system lamp has a mass M and is supported by the six strings shown. The length of the chords and the horizontal distance ED are constant, point E remains fixed but the vertical distance ED can vary.

a) If in the position shown the chord BC is horizontal, calculate the angle ? to maintain equilibrium, consider the mass M = 10 kg.

b) Explain what happens to the magnitude of the stresses when point D moves.

Expert Solution

Step 1 When chord BC is horizontal then

$C o n d i d e r j o i n t A i n e q u i l i b r i u m F_{x} = 0; F_{A B} \cos (60 °) = F_{A C} \cos (45 °) F_{A B} = F_{A C} \times \sqrt{2} F_{Y} = 0; F_{A B} \sin (60 °) + F_{A C} \sin (45 °) = 10 B y s o l v i n g b o t h e q^{n} F_{A C} = \frac{10 \sqrt{2}}{(\sqrt{3} + 1)} a n d F_{A B} = \frac{20}{(\sqrt{3} + 1)} B y \cos i d e r i n g j o i n t B i n e q u i l i b r i u m F_{x} = 0; F_{A B} \cos (60 °) + F_{B C} = F_{E B} \cos (30 °) - - - - - - 1 A N D F_{Y} = 0; F_{A B} \sin (60 °) = F_{E B} \sin (30 °) \Rightarrow F_{E B} = \frac{20 \sqrt{3}}{(\sqrt{3} + 1)} B Y e q 1 F_{B C} = \frac{20}{(\sqrt{3} + 1)}$

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