1.The beam shown has a mass of 120 kg. Determine the reactions at pinned support

Question

1.The beam shown has a mass of 120 kg. Determine the reactions at

pinned support A and smooth surface B.

2. The lever ABC is loaded and supported as shown. Determine

the force exerted on the lever by link CD, and determine the reactions

at pinned support A.

3. The man has a mass of 75 kg, and the beam has a mass of 40

kg. The beam is in equilibrium with the man standing at the

end and pulling on the cable. Determine the force exerted on

the cable by the man and the reactions at pinned support C.

4. A frame is supported and loaded as shown. Determine the

reactions at pinned support A and rollersupport E. (Hint: Use a FBD

of the frame as one whole body.)

Explanation / Answer

it is chegg rule to ask only one question in one post. So, I am answering only first question .

horizontal Distance of B from A :

H = 4*cos(30)

Vertical distance :

V = 4*sin(30)

Now, taking moment about point A :

Let reaction force at B is Bx and By and it will act perpendicular to the surface .

Now :

By*sin(30)*4*sin(30)+Bx*sin(60)*4*sin(30)+120*9.8*2*sin(30)+1600*sin(30)*3*sin(30) = By*cos(30)*4*cos(30)+By*cos(60)*4*cos(30)+1600*cos(30)*3*cos(30)

2*By=-1224

By = -612 N

Taking moment about A :

A*4*sin(30)-120*9.8*2*sin(30)-1600*cos(30)*1*sin(30)+1600*sin(30)*1*cos(30) =0

A = 899.769 N

Now, balancing force in X-direction :

Bx*sin(60)-612*sin(30)+1600*sin(30)-899.769 = 0

Bx = 468.542 N

REaction force at A :

A = 899.769 N

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