(a) Explanation Given information: The elastic modulus ( E ) is 200 GPa . The section of the beam is W 250 × 22.3 . Calculation: Refer Appendix C, “Properties of Rolled steel shapes”. The moment of inertia ( I ) for the given section is 28.7 × 10 6 mm 4 or 28.6 × 10 − 6 m 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 C : M 1 = 5 × 3.5 = 17.5 kN ⋅ m Calculate the ratio of M 1 E I using the relation: Ratio = M 1 E I Substitute 17.5 kN ⋅ m for M 1 , 200 GPa for E , and 28.7 × 10 − 6 m 4 for I . M 1 E I = − 17 .5kN ⋅ m 200 × 10 6 × 28.7 × 10 − 6 m 4 = − 3.0488 × 10 − 3 m -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 3.5 m for b 1 and − 3.0488 × 10 − 3 m − 1 for h 1 . A 1 = 1 2 × 3.5 × ( − 3.0488 × 10 − 3 m -1 ) = − 5.3354 × 10 − 3 Show the free body diagram of beam by considering the uniformly distributed 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 C : M 2 = − 4 × 2.5 × 2.5 2 = − 12.5 kN ⋅ m Calculate the ratio of M 2 E I using the relation: Ratio = M 2 E I Substitute − 12.5 kN ⋅ m for M 1 , 200 GPa for E , and 28.7 × 10 − 6 m 4 for I (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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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 104P

(a)

To determine

Find the slope (θA) at point A.

(b)

To determine

Find the deflection (yA) at point A.

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Chapter 9.5, Problem 103P

Chapter 9.5, Problem 105P

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Find the slope ( θ A ) at point A .

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