Tutorial Chapter 3: Statics of Rigid Body

Resultants of a Force and Couple System

1. List the characteristics of force by the aid of appropriate diagram.

2. Explain the conditions to preserve the static equilibrium for a rigid body.

3. Define the moment of a force about a point for two-dimensional objects. Describe the moment equation by the help of sketch.

4. The two forces and a moment are applied to an angle bracket as shown in Figure 1. Determine:

a. The resultant of this system of forcesb. The distance from the resultant force to the point A

[ans: a) FR =154.9 N, θ= 18.83° b) d = 0.179 m ]

Figure 1

5. A beam is loaded as shown in Figure 2. Neglecting the reactions at supports, determine the equivalent force couple system at point A.

Figure 2

[ans: a) FR =-150 N, MA = 250 N.m ]

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Tutorial Chapter 3: Statics of Rigid Body

6. A post AB is subjected with three forces as shown in Figure 3.a. Determine the resultant force and couple moment that is acting at point A.b. If those three forces are replace with the resultant force obtained from part a),

determine the distance of this resultant force from point A along AB

[ans: a) FR =15.62 kN, θ =39.8°, MA = 22 kN.m , b) d = 1.833 m from point A]

Figure 3

7. Three forces are acting on a post as shown in Figure 4. Replace the forces by a single resultant force and determine the point of application of the resultant force that is measured from point A.

Figure 4

[ans: a) FR =1.676 kN, θ =28.5°, MA = -2.167 kN.m , b) d = 1.471 m from point A]

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Tutorial Chapter 3: Statics of Rigid Body

8. Replace the two forces in Figure 5 by an equivalent resultant force and couple moment at point O if given F= 30 N.

Figure 5

[ans: FR =127.12 N, θ =73.55°, MO = 27.23 N.m]

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Tutorial Chapter 3: Statics of Rigid Body

Reactions at Supports and Connections // Equilibrium of a 2-Force and 3-Force Body

1. Explain the concepts of equilibrium of two-force member and three-force member. Sketch appropriate diagrams.

2. Figure 6 shows a light rod AB, hinge at A and B and attached at B to a short link BD. Draw the free body diagram of the two-force and three-force members if the system is in static equilibrium.

Figure 6

3. A horizontal beam is supported by a hinge and pulley and is loaded as shown in Figure 7. Neglecting the weight of the beam and the friction of the pulley, determine the tension in cable ADEB and the component of the reaction at C.

Figure 7

[ans: TADEB =156.17 N, CX = 266.23N, Cy= -9.744 N]

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Tutorial Chapter 3: Statics of Rigid Body

4. A beam shown in Figure 8 is supported by a pin at A and a roller at B. Determine the reaction forces at the pin A and the roller B.

Figure 8

[ans: By =5 k N, AX = 0 N, Ay= 13 kN]

5. A beam is loaded as shown in Figure 10. Neglecting the thickness of the beam, calculate the horizontal and vertical component of reactions at supports A and B.

Figure 9

[ans: By =348.1 N, AX = 230.77 N, Ay= - 51.95 N]

6. Three loads and a 8 kN tension are applied to a beam as shown in Figure 10. The beam is supported by a pin at A and roller at B.

a. Draw the free body diagram of the beam.b. By neglecting the thickness of the beam, determine the reactions at A and B.

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Tutorial Chapter 3: Statics of Rigid Body

Figure 10

[ans: By =84.051 kN, AX = -5.657kN, Ay= - 3.394kN]

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