April 2011

Problem 258
Replace the system of forces shown in Fig. P-258 by an equivalent force through O and a couple acting through A and B. Solve if the forces of the couple are (a) horizontal and (b) vertical.
 

Problem 257
Replace the system of forces acting on the frame in Fig. P-257 by a resultant R at A and a couple acting horizontally through B and C.
 

Problem 256
A vertical shaft AB is 5 ft long and bolted to a rigid support at its lower end A. At its upper end B is attached a horizontal bar BC which is 2 ft long. At the end of C is applied a force P = 180 lb. Force P is perpendicular to the plane containing points A, B, and C. Determine the twisting effect of P on the shaft AB and the bending effect at point A.
 

Problem 255
A short compression member carries an eccentric load P = 200 lb situated 2 in. from the axis of the member, as shown in Fig. P-225. In strength of materials it is learned that the internal stresses are determined from the equivalent axial load and couple into which P may be resolved. Determine the equivalent axial load and couple.
 

Problem 253
In Fig. P-253 a system of forces reduces to downward vertical force 400 lb through A plus a counterclockwise couple of 800 lb·ft. Determine the single force that will produce an equivalent effect.
 

Problem 252
A force system consists of a clockwise couple of 480 N·m plus a 240 N force directed up to the right through the origin of X and Y axes at θ_x = 30°. Replace the given system by an equivalent single force and compute the intercepts its line of action with the X and Y axes.
 

Problem 251
A vertical force P at A and another vertical force F at B in Fig. P-251 produce a resultant of 100 lb down at D and a counterclockwise couple C of 200 lb·ft. Find the magnitude and direction of forces P and F.
 

Problem 250
The cantilever truss shown in Fig. P-250 carries a vertical load of 10.8 kN. The truss is supported by bearing at A and B which exert the forces A_v, A_h, and B_h. The four forces shown constitute two couples which must have opposite moment effects to prevent movement of the truss. Determine the magnitude of the supporting forces.
 

Problem 249
Fig. P-249 represents the top view of a speed reducer which is geared for a four to one reduction in speed. The torque input at the horizontal shaft C is 100 lb·ft. The torque output at the horizontal shaft D, because of the speed reduction, is 400 lb·ft. Compute the torque reaction at the mounting bolts A and B holding the reducer to the floor. Hint: The torque reaction is caused by the unbalanced torque, which is a couple.
 

Problem 248
To close a gate valve it is necessary to exert two forces of 60 lb at opposite sides of a handwheel 3 ft in diameter. Through an accident the wheel is broken and the valve must be closed by a thrusting bar through a slot in the valve stem and exerting a force 4 ft out from the center. Determine the force required and draw a free-body diagram of the bar.