Explanation Calculation: Remove the roller support A and treat reaction ( R A ) as redundant. Calculate the moment ( M 1 ) in beam due reaction at A : M 1 = R A × L = R A L Calculate the M 1 E I value: Substitute R A L for M 1 . M 1 E I = R A L E I Show the M 1 E I diagram in below Figure 1. Calculate the area ( A 1 ) using the relation: A 1 = 1 2 L ( M 1 E I ) Substitute R A L E I for ( M 1 E I ) . A 1 = 1 2 L R A L E I = R A L 2 2 E I Calculate the moment ( M 2 ) in beam due point load: M 2 = − P L 2 = − P L 2 Calculate the M 2 E I value: Substitute ( − P L 2 ) for M 2 . M 2 E I = ( − P L 2 ) E I = − P L 2 E I Show the M 2 E I diagram in below Figure 2. Calculate the area ( A 2 ) using the relation: A 2 = 1 2 L C B ( M 2 E I ) Substitute ( − P L 2 E I ) for ( M 2 E I ) and L 2 for L C B

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 9.6, Problem 147P

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The reaction (RA) at the roller support.

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Chapter 9.6, Problem 146P

Chapter 9.6, Problem 148P

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Chapter 9 Solutions

Mechanics of Materials, 7th Edition

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The reaction ( R A ) at the roller support.

Solution Summary: The author calculates the moment (R_A) in beam due reaction at A using the relation:

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The reaction (RA) at the roller support.

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