October 2011

Problem 001-mm | Method of Members

Problem 001-mm
The structure shown in Fig F-001(MM) is pinned together at points A, B, and C and held in equilibrium by the cable CD. A load of 12,000 lb is acting at the midpoint of member AB, and a load of 8000 lb is applied at point C. Determine the reaction at A, the internal force in member BC, and the tension on cable CD.
 

Structure with cable and three-force member

 

Problem 002-mm | Method of Members

Problem 002-mm
Members AB and BC shown in Fig. F-002(MM) are pinned together at point B, and are pinned to the floor at points A and C. The structure supports a pulley at point B with which, a person is hoisting a 2.0 kN load. Member BC has a weight of 1.6 kN, which may be considered to act at its center, while AB is made of strong-light material and has negligible weight. Determine the value of the external support reactions at A and C.
 

002-mm-three-hinged-structure.gif

 

Problem 003-mm | Method of Members

Problem 003-mm
For the structure shown in Fig. (MM)-P003 below, determine the reactions at A and D and the internal force in member CF.
 

Cantilever frame

 

Problem 004-mm | Method of Members

Problem 004-mm
For the structure shown in Fig. FR-004(MM), members AD, DC, and ABC are assumed to be solid rigid members; member ED is a cable. For this structure, determine the reaction at A, the tension on cable ED, and the force in member DC.
 

Triangular frame supported by cable

 

Problem 005-mm | Method of Members

Problem 005-cb
For the cabled structure in Fig. 005(FR-CB), member ABC which is assumed to be rigid is pinned at A and held in equilibrium by cable CD. For this structure, determine the reaction at A and the tension in the cable.
 

005-mm-cable-boom-structure.gif

 

Problem 006-fr | Analysis of Simple Frame

Problem 006-fr
In the structure shown in Fig. P-006(FR-H), all members are assumed to be solid rigid members. The system is pinned to the wall at point A and supported by a roller at point E. Calculate the force on member BD and the reactions at A and E.
 

Simple Frame (Inverted L-frame)

 

Problem 007-cb | Analysis of Cabled Frame

Problem 007-cb
In the structure shown in Fig. CB-007(FR), members BCE, and CD are assumed to be solid rigid members. Members AE and DE are cables. For this structure, determine the
reaction at B.
 

Structure supported by cable

 

Friction

Friction is the contact resistance exerted by one body when the second body moves or tends to move past the first body. Friction is a retarding force that always acts opposite to the motion or to the tendency to move.
 

Problem 506 | Friction

Problem 506
A 400 lb block is resting on a rough horizontal surface for which the coefficient of friction is 0.40. Determine the force P required to cause motion to impend if applied to the block (a) horizontally or (b) downward at 30° with the horizontal. (c) What minimum force is required to start motion?
 

Problem 507 | Friction

Problem 507
The 2225-N block shown in Fig. P-507 is in contact with 45° incline. The coefficient of static friction is 0.25. Compute the value of the horizontal force P necessary to (a) just start the block up the incline or (b) just prevent motion down the incline. (c) If P = 1780 N, what is the amount and direction of the friction force?
 

Block on an incline pushed by horizontal force

 

Problem 508 | Friction

Problem 508
The 200-lb block shown in Fig. P-508 has impending motion up the plane caused by the horizontal force of 400 lb. Determine the coefficient of static friction between the contact surfaces.
 

508-inclined-plane-friction_0.gif

 

Problem 509 | Friction

Problem 509
The blocks shown in Fig. P-509 are connected by flexible, inextensible cords passing over frictionless pulleys. At A the coefficients of friction are μs = 0.30 and μk = 0.20 while at B they are μs = 0.40 and μk = 0.30. Compute the magnitude and direction of the friction force acting on each block.
 

Two blocks on two inclined planes connected by cords

 

Problem 510 | Friction

Problem 510
What weight W is necessary to start the system of blocks shown in Fig. P-510 moving to the right? The coefficient of friction is 0.10 and the pulleys are assumed to be frictionless.
 

Weight of a hanging block

 

Problem 511 | Friction

Problem 511
Find the least value of P required to cause the system of blocks shown in Fig. P-511 to have impending motion to the left. The coefficient of friction under each block is 0.20.
 

Two blocks connected by a cord

 

Problem 512 | Friction

Problem 512
A homogeneous block of weight W rests upon the incline shown in Fig. P-512. If the coefficient of friction is 0.30, determine the greatest height h at which a force P parallel to the incline may be applied so that the block will slide up the incline without tipping over.
 

Tall block on an inclined plane

 

Problem 513 | Friction

Problem 513
In Fig. P-512, the homogeneous block weighs 300 kg and the coefficient of friction is 0.45. If h = 50 cm, determine the force P to cause motion to impend.
 

Tall block on an inclined plane

 

Problem 514 | Friction

Problem 514
The 10-kN cylinder shown in Fig. P-514 is held at rest on the 30° incline by a weight P suspended from a cord wrapped around the cylinder. If slipping impends, determine P and the coefficient of friction.
 

Cylinder sliding down the plane

 

Problem 515 | Friction

Problem 515
Block A in Fig. P-515 weighs 120 lb, block B weighs 200 lb, and the cord is parallel to the incline. If the coefficient of friction for all surfaces in contact is 0.25, determine the angle θ of the incline of which motion of B impends.
 

Two blocks with one on top of the other

 

Problem 516 | Friction

Problem 516
Referring to Fig. P-515 if the coefficient of friction is 0.60 and θ = 30°, what force P applied to B acting down and parallel to the incline will start motion? What is the tension in the cord attached to A?
 

Two blocks with one on top of the other