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Rod AB is fixed to a smooth collar D, which slides freely along the vertical guide. Determine the internal normal force, shear force, and moment at point C, which is located just to the left of the 60-lb concentrated load.

60 lb -15 lb/ft F30° |C 3 ft 1.5 ft- Prob. 7-20

Image Transcription

60 lb -15 lb/ft F30° |C 3 ft 1.5 ft- Prob. 7-20

Answer
Step 1

Consider the free body diagram of the member AB as shown below.

Civil Engineering homework question answer, step 1, image 1

Consider the moment equilibrium about point B.

Civil Engineering homework question answer, step 1, image 2

Consider the moment equilibrium at point A.

Civil Engineering homework question answer, step 1, image 3

 

 

Step 2

Consider the portion BC as shown below.

Civil Engineering homework question answer, step 2, image 1

Here, NC is the normal force at point C, VC is the shear force at point C and MC is the moment at point C.

Consider the summation of forces in the horizontal direction.

Civil Engineering homework question answer, step 2, image 2

Consider the summation of forces in the vertical direction.

Civil Engineering homework question answer, step 2, image 3

Consider the equilibrium moment about point C.

Civil Engineering homework question answer, step 2, image 4

Therefore, at point C the normal force is 54.13 lb towards right, the shear force is 22.5 lb in the downward direction and the moment is 135 lb-ft in the clockwise direction.

 

 

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