Explanation Draw the free body diagram of the beam as Figure (1). Refer Figure (1). Calculate the equivalent force at end A ( R ) using the relation: Consider the vertical equilibrium condition. ∑ F y = 0 − 300 − 200 + R = 0 R = 500 N ( ↓ ) Calculate the moment about A ( M ) using the relation: ∑ M A = M 500 + 200 − ( 300 × 3 ) = M M = − 200 N ⋅ m ( clockwise ) Refer to the Problem 3.100. (a) Draw the free body diagram of the beam ( a ) as Figure (2). Refer Figure (2). Calculate the equivalent force at end A ( R a ) using the relation: Consider the vertical equilibrium condition. ∑ F y = 0 − 300 − 200 + R a = 0 R a = 500 N ( ↓ ) Calculate the moment about A ( M a ) using the relation: ∑ M A = M a − 400 − ( 200 × 3 ) = M a M a = − 1000 N ⋅ m ( clockwise ) (b) Draw the free body diagram of the beam ( b ) as Figure (3). Refer Figure (3). Calculate the equivalent force at end A ( R b ) using the relation: Consider the vertical equilibrium condition. ∑ F y = 0 300 + 200 + R b = 0 R b = − 500 N ( ↑ ) Calculate the moment about A ( M b ) using the relation: ∑ M A = M b − 400 + ( 300 × 3 ) = M b M b = 500 N ⋅ m ( anti-clockwise ) (c) Draw the free body diagram of the beam ( c ) as Figure (4). Refer Figure (4). Calculate the equivalent force at end A ( R c ) using the relation: Consider the vertical equilibrium condition. ∑ F y = 0 − 300 − 200 + R c = 0 R c = − 500 N ( ↓ ) Calculate the moment about A ( M c ) using the relation: ∑ M A = M c 400 − ( 300 × 3 ) = M c M c = − 500 N ⋅ m ( clockwise ) (d) Draw the free body diagram of the beam ( d ) as Figure (5). Refer Figure (5). Calculate the equivalent force at end A ( R d ) using the relation: Consider the vertical equilibrium condition. ∑ F y = 0 − 500 = R d R d = − 500 N ( ↓ ) Calculate the moment about A ( M d ) using the relation: ∑ M A = M d 400 − ( 500 × 3 ) = M d M d = − 1100 N ⋅ m ( clockwise ) (e) Draw the free body diagram of the beam ( e ) as Figure (6)

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

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Chapter 3.4, Problem 3.102P

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The equivalent loading of the given beam compared with Problem 3.100.

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Chapter 3.4, Problem 3.101P

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Vector Mechanics for Engineers: Statics and Dynamics

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