Question

P3 F E 3) Determine the force in members BC, BE, and EF of the truss and state if these members are in tension or compression. Set P = 6 kN, P2= 9 KN, and Ps= 12 kN. 3 m A Draw and label a complete FBD of the section you choose to B c analyze. 3 m 3 m 3 m P2

The question lists the wrong members, there is no BE. Determine the force in BC, CF, and EF.

Answer 1

Fer E P3 truss F E 12 KN 3 m Fur 31 D 0 B С D 3 m 3 m 3 m to B FBC C Ay PL 3 m 3 m 6kN P2 9 KN ī Dy P, 9 KN

For the entire truss (left FBD), take moment about pin-A:

$\sum M_A = 0$

Dy(9) - 6(3) - 9(6) – 12(3) = 0

$\Rightarrow D_y = 12\;\;kN$

Take a section passing through EF, CF and BC as shown in the right FBD above.

Take moment about C for the section;

$\sum M_C = 0$

$\Rightarrow F_{EF}(3)+D_y(3) = 0$

$\Rightarrow F_{EF} = -D_y$

$\Rightarrow F_{EF} = -12\;\;kN$

...(Answer)

Take moment about F for the section;

$\sum M_F = 0$

$\Rightarrow D_y (6) - 9(3) - F_{BC}(3) = 0$

$\Rightarrow 12(6) - 9(3) - F_{BC}(3) = 0$

$\Rightarrow F_{BC} = 15\;\;kN$

...(Answer)

Angle is given as;

$\theta = tan^{-1}(3/3) = 45^o$

Take moment about D;

$\sum M_D = 0$

$\Rightarrow F_{EF}(3)+9(3) - (F_{CF}sin\theta)(3) = 0$

$\Rightarrow (-12)(3)+9(3) - (F_{CF}sin45^o)(3) = 0$

$\Rightarrow F_{CF} = -4.243\;\;kN$

...(Answer)