(a) Explanation Given information: The diameter d of a solid steel rod is 0.75 in . . The young’s modulus of steel is 29 × 10 6 psi . Calculation: Calculate the radius ( c ) of a solid steel rod using the relation: c = 1 2 d Substitute 0.75 in . for d . c = 1 2 ( 0.75 ) = 0.375 in . Calculate the moment of inertia ( I ) using the relation: I = π 4 c 4 Substitute 0.375 in . for c . I = π 4 ( 0.375 ) 4 = 0.015532 in . 4 Calculate the moment at point D due to the point load at A : M D = 150 × 4 = 600 lb ⋅ in . Calculate the moment at point E due to the point load at B : M E = − 300 × 6 = − 1 , 800 lb ⋅ in . Calculate the M D E I value for point D : Substitute 600 lb ⋅ in . for M D , 0.015532 in . 4 for I and 29 × 10 6 psi for E . M D E I = 600 29 × 10 6 × 0.015532 = 1.33215 × 10 − 3 in . -1 Show the M D E I diagram in below Figure 1. Calculate the M E E I value for point D ; Substitute 1 , 800 lb ⋅ in . for M E , 0.015532 in . 4 for I , and 29 × 10 6 psi for E . M E E I = − 1 , 800 29 × 10 6 × 0.015532 = − 3.99619 × 10 − 3 in . -1 Show the M E E I diagram in below Figure 2. Calculate the area ( A 1 ) using the relation: A 1 = 1 2 b 1 ( M D E I ) Here, b 1 is length between point D and E Substitute 24 in . for b 1 and 1.33215 × 10 − 3 in . − 1 for ( M D E I ) . A 1 = 1 2 ( 24 ) ( 1.33215 × 10 − 3 ) = 0.0159858 Calculate the area ( A 3 ) using the relation: A 3 = 1 2 b 2 ( M D E I ) Here, b 2 is length between point A and D (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 9.6, Problem 135P

(a)

To determine

Find the slope θD at point D.

(b)

To determine

Find the deflection yA at point A.

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Chapter 9.6, Problem 134P

Chapter 9.6, Problem 136P

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Find the slope θ D at point D .

Solution Summary: The author calculates the radius (c) of a solid steel rod using the relation: c=12d.