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

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Author: BEER

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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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A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Using the data given in the table, determine the largest permissible bending moment when the composite bar is bent about a vertical axis. Take x = 34 mm.

Problem 2.50

A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Using the data given below, determine the largest permissible bending moment when the composite bar is bent about a horizontal axis.Modulus of elasticity 70 GPa,105 GPa Allowable stress100 MPa,160 MPa

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

Solution Summary: The author calculates the largest permissible bending moment of the bar which bends about the vertical axis.

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