Reactions at a Built-ln Support The object in Fig. 5.14 has a built-ih support and is subjected to two forces and a couple. What are the reactions at the support?

Question

Reactions at a Built-ln Support

The object in Fig. 5.14 has a built-ih support and is subjected to two forces and a couple. What are the reactions at the support?

Accepted Answer

Draw the Free-Body Diagram We isolate the object from its support and show the reactions at the built-in support (Fig. a). There are three unknown reactions: two force components [latex]A_{x}[/latex] , and [latex]A_{y}[/latex] and a couple [latex]M_{A}[/latex]. (Remember that we can choose the directions of these arrows arbitrarily.) We also resolve the 100-lb force into its components.

Apply the Equilibrium Equations Summing the moments about point A, the equilibrium equations are

[latex]\sum{ F_{x}} = A_{x} + 100 \cos 30º = 0 .[/latex]

[latex]\sum{ F_{y}} = A_{y} - 200 +100 \sin 30º = 0 .[/latex]

[latex]\sum{ M_{(point A)}} = M_{A} + 300 - (200)(2) - (100\cos 30º)(2) +(100 \sin 30º)(4) = 0 .[/latex]

Solving these equations, we obtain the reactions [latex] A_{x} = -86.6 lb, A_{y} = 150.0 lb, and M_{A} = 73.2 ft-lb.[/latex]

Discussion

Notice that the 300-ft-lb couple and the couple [latex] M_{A} [/latex] exerted by the built-in support don't appear in the first two equilibrium equations because a couple exerts no net force. Also, since the moment due to a couple is the same about any point, the moment about point A due to the 300-ft-lb counterclockwise couple is 300 ft-lb counterclockwise.

Question 5.2: Reactions at a Built-ln Support The object in Fig. 5.14 has ...

Related Answered Questions

Reactions at Properly Aligned Hinges The plate in Fig. 5.34 is supported by hinges at A and B and the cable CE. The properly aligned hinges do not exert couples on the plate, and the hinge at A does not exert a force on the plate in the direction of the hinge axis. Determine the reactions at the ...

Verified Answer:

Verified Answer:

Design for Human Factors Figure 5.17 shows an airport luggage carrier and its free-body diagram when it is held in equilibrium in the tilted position. If the luggage carrier supports a weight W = 50 lb, the angle α = 30°, a = 8 in., b = 16 in., and d = 48 in., what force F must the user exert? ...

Verified Answer:

Verified Answer:

Verified Answer:

Determining Reactions in Three Dimensions The bar AB in Fig. 5.32 is supported by the cables BC and BD and a ball and socket support at A. Cable BC is parallel to the z axis, and cable BD is parallel to the x axis. The 200-N weight of the bar acts at its midpoint. What are the tensions in the ...

Verified Answer:

Verified Answer:

Reactions on a Car’s Tires The 2800-lb car in Fig. 5.15 is stationary. Determine the normal forces exerted on the front and rear tires by the road. ...

Verified Answer:

Reactions at Pin and Roller Supports The beam in Fig. 5.13 has pin and roller supports and is subjected to a 2-kN force. What are the reactions at the supports? ...

Verified Answer:

Proper and Improper Supports State whether each L-shaped bar in Fig. 5.24 is properly or improperly supported. If a bar is properly supported, determine the reactions at its supports. ...

Verified Answer: