The frame shown supports part of the roof of a small building. Knowing that the tension in the cable is 150 kN, determine the reaction at the fixed end E.

Question

Accepted Answer

Free-Body Diagram. A free-body diagram of the frame and of the cable BDF is drawn. The reaction at the fixed end E is represented by the force components [latex]{E}_{x}\operatorname{and}\ {E}_{y}[/latex] and the couple [latex]{M}_{E}[/latex]. The other forces acting on the free body are the four 20-kN loads and the 150-kN force exerted at end F of the cable.

Equilibrium Equations. Noting that [latex]DF~=~2\overline{(4.5~m)^2~ + ~(6~m)^2} ~=~7.5~m,[/latex] we write

[latex]\stackrel{+}{ o}\Sigma F_{x}\;=\;0\mathrm{:}\qquad\qquad\qquad E_{x}+{\frac{4.5}{7.5}}(150\,\mathrm{kN})\,=\,0 \ \ \qquad\qquad\qquad\qquad\qquad\qquad E_{x}=-90.0\,\mathrm{kN}\qquad\qquad\mathrm{E}_{x}=90.0\mathrm{kN}\,Z[/latex]

[latex]+\uparrow\Sigma F_{y}\,=\,0\mathrm{:}\qquad\qquad\qquad E_{y}-4(20\,\mathrm{kN})\,-\,\frac6{7.5}(150\,\mathrm{kN})\,=\,0 \ \ \qquad\qquad\qquad\qquad\qquad\qquad E_{y}=\ +200\mathrm{~kN}\qquad\qquad\ \ \ E_{y}=\ 200\mathrm{~kN}~X[/latex]

[latex]+{\mathrm l{{\Sigma}}M_{E}=0}\mathrm{:}\qquad\qquad\qquad (20\mathrm{~kN})(7.2\mathrm{~m})\,+\,(20\mathrm{~kN})(5.4\mathrm{~m})\,+\,(20\mathrm{~kN})(3.6\mathrm{~m}) \ \ \qquad\qquad\qquad +~(20~\mathrm{kN})(1.8~\mathrm{m})-\frac{6}{7.5}(150~\mathrm{kN})(4.5~\mathrm{m})\,+\,M_{E}\,=\,0 \ \ \qquad\qquad\qquad\qquad\qquad\qquad M_{E}=+180.0\,\,\mathrm{kN}\cdot\,\mathrm{m}\qquad\mathrm{M}_{E}=\,180.0\,\,\mathrm{kN}\cdot\,\mathrm{m}\,\,1[/latex]

Question 4.4: The frame shown supports part of the roof of a small buildin......

Related Answered Questions

A 400-lb weight is attached at A to the lever shown. The constant of the spring BC is k = 250 lb/in., and the spring is unstretched when u = 0. Determine the position of equilibrium. ...

Verified Answer:

Verified Answer:

Three loads are applied to a beam as shown. The beam is supported by a roller at A and by a pin at B. Neglecting the weight of the beam, determine the reactions at A and B when P = 15 kips. ...

Verified Answer:

A 450-lb load hangs from the corner C of a rigid piece of pipe ABCD which has been bent as shown. The pipe is supported by the ball-and-socket joints A and D, which are fastened, respectively, to the floor and to a vertical wall, and by a cable attached at the midpoint E of the portion BC of the ...

Verified Answer:

Verified Answer:

A uniform pipe cover of radius r = 240 mm and mass 30 kg is held in a horizontal position by the cable CD. Assuming that the bearing at B does not exert any axial thrust, determine the tension in the cable and the reactions at A and B. ...

Verified Answer:

A 5 × 8-ft sign of uniform density weighs 270 lb and is supported by a ball-and-socket joint at A and by two cables. Determine the tension in each cable and the reaction at A. ...

Verified Answer:

A man raises a 10-kg joist, of length 4 m, by pulling on a rope. Find the tension T in the rope and the reaction at A. ...

Verified Answer:

A fixed crane has a mass of 1000 kg and is used to lift a 2400-kg crate. It is held in place by a pin at A and a rocker at B. The center of gravity of the crane is located at G. Determine the components of the reactions at A and B. ...

Verified Answer: