(a) Explanation Calculation: The length of beam is 4 m . Let the force and moment of couple acting in upward direction and moment of couple in anticlockwise direction are taken as positive and downward force and moment of couple in clockwise direction are taken as negative quantities. Write the expression to calculate the force part of force couple system. R = ∑ F Here, R is the vector sum of all forces acting on the beam and F denotes any individual force. Write the expression to calculate ∑ F . ∑ F = F A + F B Here, F A is the force applied at end A and F B is the force applied at end B. Rewrite the expression for R by substituting the above relation for ∑ F . R = F A + F B Write the expression to calculate the couple part of force couple system. M A R = ∑ ( r × F ) Here, M A R is the moment resultant of beam about point A and r is the length of beam which lies perpendicular to forces. Write the expression to calculate ∑ ( r × F ) . ∑ ( r × F ) = M A + M B + ( 0 m × F A ) + ( r × F B ) = M A + M B + ( r × F B ) Here, M A is the moment at end A and M B is the moment at end B. Rewrite the expression for M A R by substituting the above relation. M A R = M A + M B + ( r × F B ) Calculate the resultant force ( R ) . Substitute − 200 N for F A and − 400 N for F B . R = − 200 N+ ( − 400 N ) = − 600 N Calculate the moment resultant of beam about point A ( M A R ) . Substitute − 400 N ⋅ m for M A , 2800 N ⋅ m for M B , − 400 N for F B and 4 m for r . M A R = − 400 N ⋅ m + 2800 N ⋅ m+ ( 4 m × − 400 N ) = 800 N ⋅ m Calculate the force couple system of each loading given in Fig. P3.101. Refer figure 3.101(a). Calculate the resultant force ( R ) . Substitute − 400 N for F A and − 200 N for F B . R = − 400 N+ ( − 200 N ) = − 600 N Calculate the moment resultant of beam about point A ( M A R ) . Substitute 0 N ⋅ m for M A , 1800 N ⋅ m for M B , − 400 N for F B and 4 m for r . M A R = 0 N ⋅ m + 1800 N ⋅ m+ ( 4 m × − 200 N ) = 1000 N ⋅ m Refer figure 3.101(b). Calculate the resultant force ( R ) . Substitute − 600 N for F A and 0 N for F B . R = − 600 N+ 0 N = − 600 N Calculate the moment resultant of beam about point A ( M A R ) . Substitute 0 N ⋅ m for M A , − 900 N ⋅ m for M B , 0 N for F B and 4 m for r . M A R = 0 N ⋅ m + ( − 900 N ⋅ m ) + ( 4 m × 0 N ) = − 900 N ⋅ m Refer figure 3.101(c). Calculate the resultant force ( R ) . Substitute 300 N for F A and − 900 N for F B . R = 300 N+ ( − 600 N ) = − 6 00 N Calculate the moment resultant of beam about point A ( M A R ) . Substitute 0 N ⋅ m for M A , 4500 N ⋅ m for M B , − 900 N for F B and 4 m for r . M A R = 0 N ⋅ m + 4500 N ⋅ m+ ( 4 m × − 900 N ) = 900 N ⋅ m Refer figure 3.101(d). Calculate the resultant force ( R ) . Substitute − 400 N for F A and 800 N for F B . R = − 400 N+ 800 N =400 N Calculate the moment resultant of beam about point A ( M A R )

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Chapter 3.4, Problem 3.102P

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Identify the equivalent loading of figure P3.102 from any of the loadings from figure P3.101.

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Chapter 3.4, Problem 3.101P

Chapter 3.4, Problem 3.103P

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Identify the equivalent loading of figure P3.102 from any of the loadings from figure P3.101.

Solution Summary: The author identifies the equivalent loading of Figure P3.102 from any of the loadings from figure P3.101. Write the expression to calculate the force part of force couple system.

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Identify the equivalent loading of figure P3.102 from any of the loadings from figure P3.101.

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