Determine the normal force, shear force, and moment at point C.
Prob. F7-1
The normal force, shear force, and moment at point C.
Answer to Problem 1FP
The normal force at point C,
The shear force at point C,
The moment at point C,
Explanation of Solution
Assumption:
- Consider the state of the member as tension, where the force is pulling the member, and as compression, where the force is pushing the member.
- The normal force is positive if it creates tension; a positive shear force acting on the segment causes it to rotate clockwise, and a positive bending moment acting on the segment will cause it to bend and concave upwards. Loadings that are opposite to these are considered negative.
- Consider the force indicating the right side as positive and the left side as negative, in the horizontal components of forces.
- Consider the force indicating upside as positive and downside as negative, in the vertical components of forces.
- Consider the clockwise movement as negative and the anti-clockwise movement as positive, wherever applicable.
- The method of sections can be used to determine the internal loadings.
Determine the reactions:
Entire beam:
Show the free body diagram of the entire beam as in Figure (1).
Using Figure (1),
Moment at point A:
Determine the vertical reaction at point B by taking the moment about point A.
Solve Equation (I).
Determine the forces and moment:
Segment CB:
Show the free body diagram of the segment CB as in Figure (2).
Using Figure (2),
Along the vertical direction:
Determine the shear force at point C by resolving the vertical component of forces.
Along the horizontal direction:
Determine the normal force at point C by resolving the horizontal component of forces.
Moment about point C:
Determine the moment at point C by taking the moment about point C.
Conclusion:
Substitute 13.75 kN for
Thus, the shear force at point C,
Refer to Equation (III).
Thus, the normal force at point C,
Substitute 13.75 kN for
Thus, the moment at point C,
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Chapter 7 Solutions
EBK ENGINEERING MECHANICS
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