Explanation Calculation: Let ( R B ) be the redundant reaction. Show the free body diagram of the beam as in Figure 1. Calculate the moment due to the reaction at B : M 1 = R B × L A B Here, L A B is length of the beam. Substitute 12 ft for L A B . M 1 = R B × 12 = 12 R B Calculate the M 1 E I value: Substitute 12 R B for M 1 . ( M 1 E I ) = 12 R B 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 A B ) ( M 1 E I ) Substitute 12 ft for L A B and 12 R B for ( M 1 E I ) . A 1 = 1 2 ( 12 ) ( 12 R B ) = 72 R B Calculate the moment ( M 2 ) due the point load at E : M 2 = − 10 × ( L A D + L D E ) Substitute 4.5 ft for L A D and 3 ft for L D E . M 2 = − 10 × ( 4.5 + 3 ) = − 75 kips ⋅ ft Calculate the ( M 2 E I ) value: Substitute − 75 kips ⋅ ft for M 2 . ( M 2 E I ) = − 75 E I Show the ( M 2 E I ) diagram in below Figure 3. Calculate the area ( A 2 ) using the relation: A 2 = 1 2 ( L A B + L B C ) ( M 2 E I ) Substitute 4.5 ft for L A D , 3 ft for L D E , and − 75 E I for ( M 2 E I ) . A 2 = 1 2 ( 4.5 + 3 ) ( − 75 E I ) = − 281.25 kips ⋅ ft 2 Calculate the moment ( M 3 ) due the point load at D as below: M 3 = − 30 × ( L A D ) Substitute 4.5 ft for L A D . M 3 = − 30 × ( 4.5 ) = − 135 kips ⋅ ft Calculate the ( M 3 E I ) value: Substitute − 135 kips ⋅ ft for M 3 . ( M 2 E I ) = − 135 E I Show the ( M 3 E I ) diagram in below Figure 4. Calculate the area ( A 3 ) using the relation: A 3 = 1 2 ( L A D ) ( M 3 E I ) Substitute 4.5 ft for L A D and − 135 E I for ( M 2 E I ) . A 3 = 1 2 ( 4.5 ) ( − 135 E I ) = − 303.75 kips ⋅ ft 2 Refer Appendix C, “Properties of rolled steel shape (U.S. Customary units)” for moment of inertia of section W 14 × 38 and the value is 385 in . 4 . Take young’s modulus of steel ( E ) as 29 × 10 6 psi . Calculate the value ( EI ): Substitute 29 × 10 6 psi for E and 238 in

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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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 9.6, Problem 154P

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The reaction at roller support (RB) and draw the bending moment diagram of the beam.

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Chapter 9.6, Problem 153P

Chapter 9.6, Problem 155P

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The reaction at roller support ( R B ) and draw the bending moment diagram of the beam.

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The reaction at roller support (RB) and draw the bending moment diagram of the beam.

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