Knowing that the radius of each pulley is 120 mm and neglecting friction, determine the internal forces at (a) point C, (b) point J that is 100 mm to the left of C.
Fig. P7.15 and P7.16
(a)
The internal forces exerted at the point
Answer to Problem 7.15P
The internal forces of shearing force is
Explanation of Solution
Sketch the free body diagram for the internal forces acting on the frame and pulley system as shown in the Figure 1.
Write the equation of the axial force exerted at the axial point
Here, the force exerted on the frame at the point
Write the equation of the moment of couple formed in the bending moment of the frame and pulley system supported at the point
Here, the axial force exerted on the pulley at point
Write the equation of the axial force exerted at the axial point of the frame from y direction (Refer fig 1).
Here, the axial force exerted on the pulley at point
Sketch the free body diagram for the cable as shown in the Figure 2.
The slope of the cable (Refer fig 2):
The angle formed in the slope of the cable:
Rewrite the above relation to find the angle.
Write the equation of the axial force exerted at the axial point
Here, the angle between the pulley
Sketch the free body diagram for the cable for the point
Write the equation of the axial force exerted at the point
Here, shearing force acting on the semicircular rod is
At the pulley
Write the equation of the moment of couple formed in the bending moment supported at the point
Here, the moment of couple exerted at the point
Conclusion:
Substitute
Solve the above equation for
Substitute
Substitute
Substitute
Substitute
The above equation can be written as,
Therefore, the internal forces of shearing force is
(b)
The internal forces exerted at the point
Answer to Problem 7.15P
The internal forces of shearing force is
Explanation of Solution
Sketch the free body diagram for the cable for the point
Write the equation of the axial force exerted at the axial point
Here, the force exerted on the frame at the point
Write the equation of the axial force exerted at the axial point of the frame from y direction (Refer fig 4).
Here, the axial force exerted on the pulley at point
Write the equation of the moment of couple formed in the bending moment supported at the point
Here, the moment of couple exerted at the point
Conclusion:
Substitute
Substitute
Substitute
The above equation can be written as,
Therefore, the internal forces of shearing force is
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