Engineering Mechanics: Statics and Dynamics, 14th Edition
Authors: Russell C. Hibbeler
ISBN-13: 978-0133915426
See our solution for Question 35P from Chapter 6 from Hibbeler's Engineering Mechanics.
Problem 35P
Step-by-Step Solution
We are given the force ${F_1} = 4\,{\rm{kN}}$ acting at point $E$ and the force ${F_2} = 8\,{\rm{kN}}$ acting at point $F$, the distance between $E$ and $D$ is $a = 1.5\,{\rm{m}}$, the distance between $C$ and $D$ is $b = 2\,{\rm{m}}$, and the distance between $B$ and $C$ is $c = 2\,{\rm{m}}$.
We are asked to determine the force in members $EF$, $CF$, and $BC$, and state if the members are in tension or compression.
Step 2
First draw the free body diagram for the given system at section $aa$.
Figure-(1)
Step 3
The negative value of force represents compression and the positive value of force represents tension.
Find the force in member $EF$ taking moment at point $C$ equal to zero using the following relation.
\[{F_{EF}}\left( a \right) - {F_1}\left( b \right) = 0\]Substitute the known values in the above expression.
\[\begin{array}{c} {F_{EF}}\left( {1.5\,{\rm{m}}} \right) - \left( {4\,{\rm{kN}}} \right)\left( {2\,{\rm{m}}} \right) = 0\\ {F_{EF}} = 5.33\,{\rm{kN}}\,\,\left( {\rm{T}} \right) \end{array}\]Step 4
Find the force in member $BC$ adding all the forces acting along $y$-axis equal to zero using the following relation.
\[ - {F_{BC}} - {F_{EF}} = 0\]Substitute the known values in the above expression.
\[\begin{array}{c} - {F_{BC}} - 5.33\,{\rm{kN}} = 0\\ {F_{BC}} = - 5.33\,{\rm{kN}}\\ {F_{BC}} = 5.33\,{\rm{kN}}\,\,\left( {\rm{C}} \right) \end{array}\]Step 5
Find the force in member $CF$ adding all the forces acting along $x$-axis equal to zero using the following relation.
\[{F_1} + {F_2} - {F_{CF}} = 0\]Substitute the known values in the above expression.
\[\begin{array}{c} 4\,{\rm{kN}} + 8\,{\rm{kN}} - {F_{CF}} = 0\\ {F_{CF}} = 12\,{\rm{kN}}\,\left( {\rm{T}} \right) \end{array}\]