Explanation Given information: The modulus of elasticity ( E a ) of Aluminum is 70 GPa . The modulus of elasticity ( E b ) of Brass is 105 GPa . The allowable stress ( σ a ) of Aluminum is 100 MPa . The allowable stress ( σ b ) of Brass is 160 MPa . Calculation: Show the cross-section of the composite bar as shown in Figure 1. Refer Figure 1. Consider the brass and Aluminum is represented by rectangle 1 and 2. The width and depth of the rectangle 1 are b 1 = 30 mm and d 1 = 6 mm . The width and depth of the rectangle 2 are b 2 = 30 mm and d 1 = 30 mm . Consider Aluminum as the reference material, then the value of n 2 = 1 . Calculate the ratio n 1 for brass using the relation: n 1 = E b E a (1) Substitute 105 GPa for E b and 70 GPa for E a in Equation (1). n 1 = 105 70 = 1.5 Consider the entire cross-section of the composite bar is transformed into Aluminum. Calculate the moment of inertia ( I 1 ) of the rectangle 1 using the relation: I 1 = n 1 12 b 1 d 1 3 + ( b 1 d 1 ) y 1 2 (2) The distance ( y 1 ) between the neutral axis and the centroid of the rectangle 1 is 12 mm . Substitute 32 mm for b 1 , 8 mm for d 1 , 1.5 for n 1 and 12 mm for y 1 in Equation (2). I 1 = 1.5 12 × 32 × 8 3 + 1.5 × 8 × 32 × ( 20 ) 2 = 2 , 048 mm 4 + 153 , 600 mm 4 = 155 , 648 mm 4 Calculate the moment of inertia ( I 2 ) of the rectangle 2 using the relation: I 2 = n 2 12 b 2 d 2 3 (3) Substitute 8 mm for b 2 , 32 mm for d 2 , and 1 for n 2 in Equation (3). I 2 = 1 12 × 8 × 32 3 = 21 , 845

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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Bending Moment

In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

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Chapter 4.5, Problem 36P

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Find the largest permissible bending moment of the bar which bends about the vertical axis.

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Chapter 4.5, Problem 35P

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Mechanics of Materials, 7th Edition

Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - Using an allowable stress of 155 MPa, determine...Ch. 4.3 - Solve Prob. 4.3, assuming that the wide-flange...Ch. 4.3 - Using an allowable stress of 16 ksi, determine the...Ch. 4.3 - Knowing that the couple shown acts in a vertical...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...

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Find the largest permissible bending moment of the bar which bends about the vertical axis.

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