Problem 1 Determine the force in member BC, FC, and GC.2000 Ib1000 Ib1500 lbB12H.1000 lb

Answered: Problem 1 Determine the force in member…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Problem 1 Determine the force in member BC, FC, and GC.
2000 Ib
1000 Ib
1500 lb
B
12
H.
1000 lb

Expert Solution

Step 1

Draw the free body diagram of the given truss:

Consider the equilibrium of moments about point A:

$\begin{array}{rcl} - (E_{y}) (36 i n) + (1500 l b) (9 i n) + (3000 l b) (18 i n) + (1000 l b) (27 i n) & = & 0 \\ E_{y} & = & 2625 l b \end{array}$

Consider the equilibrium of vertical forces:

$\begin{array}{rcl} A_{y} + E_{y} - (1500 l b) - (3000 l b) - (1000 l b) & = & 0 \\ A_{y} + (2625 l b) - (1500 l b) - (3000 l b) - (1000 l b) & = & 0 \\ A_{y} & = & 2875 l b \end{array}$

Consider the equilibrium of horizontal forces:

$A_{x} = 0$

Step 2

Consider the equilibrium of joint A:

Consider the equilibrium of vertical forces:

$\begin{array}{rcl} A_{y} - F_{A B} \sin 41.63 ° & = & 0 \\ (2875 l b) - F_{A B} \sin 41.63 ° & = & 0 \\ F_{A B} & = & 4327.75 l b \end{array}$

Consider the equilibrium of horizontal forces:

$\begin{array}{rcl} F_{A B} \cos 41.63 ° - F_{A F} & = & 0 \\ (4327.75 l b) \cos 41.63 ° - F_{A F} & = & 0 \\ F_{A F} & = & 3234.78 l b \end{array}$

Step 3

Consider equilibrium of joint B:

Consider the equilibrium of horizontal forces:

$\begin{array}{rcl} - F_{A B} \sin 48.37 ° + F_{B C} \cos 23.96 ° & = & 0 \\ - (4327.75 l b) \sin 48.37 ° + F_{B C} \cos 23.96 ° & = & 0 \\ F_{B C} = 3539.81 l b \end{array}$

Consider the equilibrium of vertical forces:

$\begin{array}{rcl} (- 1500 l b) + F_{A B} \cos 48.37 ° + F_{F B} - F_{B C} \sin 23.96 ° & = & 0 \\ (- 1500 l b) + (4327.75 l b) \cos 48.37 ° + F_{F B} - (3539.81 l b) \sin 23.96 ° & = & 0 \\ F_{F B} & = & 1859.78 l b \end{array}$

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