(a) Explanation Given information: The elastic modulus ( E ) is 29 × 10 6 psi . The section of the beam is S6 × 12.5 . Assume clockwise direction is positive and anticlockwise direction is negative. Calculation: Refer Appendix C, “Properties of Rolled steel shapes”. The moment of inertia ( I ) for the given section is 22 in . 4 . Use moment area method: Show the free body diagram of the beam as in Figure 1. Show the moment ( M E I ) diagram for the left side of the given loading beam as in Figure 2. Due to symmetric beam with symmetric loading, consider the left side of the beam. Calculate the moment ( M 1 ) by taking moment at C using the formula: M 1 = R B × 4.5 Calculate the ratio of M 1 E I : Ratio = M 1 E I Substitute 4.5 R B for M 1 . M 1 E I = 4.5 R B E I Calculate the area ( A 1 ) due to the moment ( M 1 ) using the formula: A 1 = 1 2 b 1 h 1 Here, b 1 is the width of the triangle in area ( A 1 ) and h 1 is the height of the triangle in area ( A 1 ) . Substitute 4.5 ft for b 1 and 4.5 R B E I for h 1 . A 1 = 1 2 × 4.5 × 4.5 R B E I = 10.125 R B E I kips ⋅ ft 2 Calculate the moment ( M 2 ) by taking moment at C using the formula: M 2 = − 1.5 × ( 2 + 4.5 ) = − 9.75 kips ⋅ ft Calculate the ratio of M 2 E I : Ratio = M 2 E I Substitute − 9.75 kips ⋅ ft for M 2 . M 2 E I = − 9 .75kips ⋅ ft E I Calculate the area ( A 2 ) due to the moment ( M 2 ) using the formula: A 2 = 1 2 b 2 h 2 Here, b 2 is the width of the triangle in area ( A 2 ) and h 2 is the height of the triangle in area ( A 2 ) . Substitute 4.5 ft for b 2 and − 9 .75 E I kips ⋅ ft for h 2 . A 2 = 1 2 × 4.5 × ( − 9.75 E I ) = − 21.938 E I kips ⋅ ft 2 Calculate the moment ( M 3 ) by taking moment at B using the formula: M 3 = − 1.5 × 2 = − 3 kips ⋅ ft Calculate the ratio of M 3 E I using the relation: Ratio = M 3 E I Substitute − 3 kips ⋅ ft for M 3 . M 3 E I = − 3 kips ⋅ ft E I Calculate the area ( A 3 ) due to the moment ( M 3 ) using the formula: A 3 = 1 2 b 3 h 3 Here, b 3 is the width of the triangle in area ( A 3 ) and h 3 is the height of the triangle in area ( A 3 ) (b) To determine Find the deflection ( y A ) at point A .

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 9.5, Problem 121P

(a)

To determine

Find the load (P) for which the deflection is zero at midpoint C of the beam.

(b)

To determine

Find the deflection (yA) at point A.

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Chapter 9.5, Problem 120P

Chapter 9.5, Problem 122P

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Find the load ( P ) for which the deflection is zero at midpoint C of the beam.

Solution Summary: The author shows the moment of inertia (I) for the given section of the beam as in Figure 1.