Explanation Calculation: Remove the roller support B and treat reaction ( R B ) as redundant. Show the replace loading in beam in below Figure 1. Calculate the moment ( M 1 ) in beam due reaction at A as below: M 1 = R B × L = R B L Calculate the M 1 E I value: Substitute R B L for M 1 . M 1 E I = R B L E I Show the M 1 E I diagram in below Figure 2. Calculate the area ( A 1 ) using the relation: A 1 = 1 2 L ( M 1 E I ) Substitute R B L E I for ( M 1 E I ) . A 1 = 1 2 L R B L E I = R B L 2 2 E I Calculate the moment ( M 2 ) in beam due UDL: M 2 = − w 0 × L × L 2 = − w 0 L 2 2 Calculate the M 2 E I value: Substitute ( − w 0 L 2 2 ) for M 2 . M 2 E I = ( − w 0 L 2 2 ) E I = − w 0 L 2 2 E I Show the M 2 E I diagram in below Figure 3. Calculate the area ( A 2 ) using the relation: A 2 = 1 3 L ( M 2 E I ) Substitute − w 0 L 2 2 E I for ( M 2 E I ) . A 2 = 1 3 L ( − w 0 L 2 2 E I ) = − w 0 L 3 6 E I Calculate the moment ( M 3 ) in beam due UVL: M 3 = ( 1 2 × − w 0 × L ) × ( 1 3 L ) = w 0 L 2 6 Calculate the M 3 E I value; Substitute w 0 L 2 6 for M 2

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ISBN: 8220100257063

Author: BEER

Publisher: YUZU

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Chapter 9.6, Problem 149P

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The reaction (RB) at the roller support.

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Chapter 9.6, Problem 148P

Chapter 9.6, Problem 150P

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Chapter 9 Solutions

EBK MECHANICS OF MATERIALS

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The reaction ( R B ) at the roller support.

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

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The reaction (RB) at the roller support.

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