problem 4-a 45 o o d c a b the semicircular rod abcd is maintained in equilibrium by the small...

Problem 4-a

45o45o

OD

C

A

B

The semicircular rod ABCD ismaintained in equilibrium bythe small wheel at D and therollers at B and C. Knowingthat = 45o, determine thereactions at B , C , and D.

P

45o45o

OD

C

A

B

1. Draw a free-body diagram of the body. This diagram shows the body and all the forces acting on it.

P Solving Problems on Your Own


Problem 4-a

45o45o

OD

C

A

B

2. Write equilibrium equations and solve for the unknowns. For two-dimensional structure the three equations might be:

Fx = 0 Fy = 0 MO = 0where O is an arbitrary point in the plane of the structureor Fx = 0 MA = 0 MB = 0where point B is such that line AB is not parallel to the y axisor MA = 0 MB = 0 MC = 0where the points A, B , and C do not lie in a straight line.

P Solving Problems on Your Own


Problem 4-a

45o45o

OD

C

A

B

Problem 4-a Solution

Draw a free-body diagramof the body.

45o45o

OD

C

A

B

P sin

P cos

D

C

R

B

C/ 2

C/ 2B/ 2

B/ 2

P

P


45o45o

OD

C

A

B

P sin

P cos

D

C

R

B

C/ 2

C/ 2B/ 2

B/ 2

Write three equilibriumequations and solvefor the unknowns.

+ MO = 0: (P sin) R _ D (R) = 0 D = P sin

+Fx = 0: P cos + B/ 2 _ C / 2 = 0 (2)

+Fy = 0: _P sin + B/ 2 + C / 2 _ P sin = 0

_2P sin + B/ 2 + C / 2 = 0 (3)

P


45o45o

OD

C

A

B

P sin

P cos

D

C

R

B

C/ 2

C/ 2B/ 2

B/ 2

(2) + (3) P(cos _ 2sin) + 2 B/ 2 = 0

B = (2sin _ cos) P (4)

(2) _ (3) P(cos + 2sin) _ 2 C/ 2 = 0

C = (2sin + cos) P (5)

22

22

P


45o45o

OD

C

A

B

P sin

P cos

D

C

R

B

C/ 2

C/ 2B/ 2

B/ 2For = 45o

sin = cos = 1/ 2

EQ. (4) : B = ( _ ) P = P ; B = P 45o

EQ. (5) : C = ( _ ) P = P ; C = P 45o

EQ. (1) : D = P/ 2 D = P/ 2

32

P

22 2

2 2

1

22 2

2 2

1 32

12

12

problem 4-a 45 o o d c a b the semicircular rod abcd is maintained in equilibrium by the small...

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