(a) Explanation Given information: The elastic modulus ( E ) is 29 × 10 6 psi . The section of the beam is C6 × 8.2 . Two channel sections are provided. Calculation: Refer Table, “W shape properties”, the moment of inertia ( I ) for the given section C6 × 8.2 is 13.1 in . 4 Use moment area method: Show the free body diagram of beam by considering the point load as in Figure 1. Draw the moment diagram of the above beam as in Figure 2. Calculate the moment ( M 1 ) by taking moment about point A : M 1 = 1.1 × 6 = 6.6 kips ⋅ ft Calculate the ratio of M 1 E I using the relation: Ratio = − M 1 E I Substitute 6.6 kips ⋅ ft for M 1 , 29 × 10 6 psi for E , and 13.1 in . 4 for I . M 1 E I = − 6.6 kips ⋅ ft 29 × 10 3 × ( 2 × 13.1 ) 144 = 1.251 × 10 − 3 ft − 1 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 and h 1 is the height of the triangle. Substitute 6 ft for b 1 and 1.251 × 10 − 3 ft − 1 for h 1 . A 1 = 1 2 × 6 × ( − 1.251 × 10 − 3 ) = − 3.753 × 10 − 3 Show the free body diagram of beam by considering the second concentrated load as in Figure 3. Draw the moment diagram of the above beam as in Figure 4. Calculate the moment ( M 2 ) by taking moment about point A : M 2 = − 1.1 × 4 = − 4.4 kips ⋅ ft Calculate the ratio of M 2 E I using the relation: Ratio = − M 2 E I Substitute − 4.4 kips ⋅ ft for M 3 , 29 × 10 6 psi for E , and 13.1 in . 4 for I . M 2 E I = − 4 .4kips ⋅ ft 29 × 10 3 × ( 2 × 13.1 ) 144 = − 8.34 × 10 − 4 ft -1 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 and h 2 is the height of the triangle. Substitute 4 ft for b 2 and − 8.34 × 10 − 4 ft − 1 for h 2 . A 2 = 1 2 × 4 × ( − 8.34 × 10 − 4 ) = − 1.668 × 10 − 3 Show the free body diagram of beam by considering the third concentrated load as in Figure 5 (b) To determine Find the deflection ( y D ) at point D .

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

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Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

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Chapter 9.5, Problem 103P

(a)

To determine

Find the slope (θD) at point D.

(b)

To determine

Find the deflection (yD) at point D.

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Chapter 9.5, Problem 102P

Chapter 9.5, Problem 104P

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Find the slope ( θ D ) at point D .

Solution Summary: The author shows the free body diagram of beam by considering the point load as in Figure 1.