Explanation Given information: The mass of the crane is 500 kg. Calculation: Show the free body diagram of member as shown in Figure 1. Here, C x and C y denotes horizontal and vertical reaction, the point of force of action F D E is 0.4m above the horizontal axis member CD . Refer Figure 1, Write the equilibrium moment about C . ∑ M C = 0 F D E sin 30 ° ( 6 ) + F D E cos 30 ° ( 0.4 ) − 500 × 9.81 × 2 = 0 3 F D E + 0.346 F D E − 9 , 810 = 0 3.346 F D E − 9 , 810 = 0 F D E = 2 , 931.50 Show the equilibrium of free body diagram of the boom right cut segment as shown in Figure 2. The normal force reaction denoted N , the moment acting at M , and V is vertical shear force acting at downward direction. Refer Figure 2: The equilibrium force along x direction. ∑ F x = 0 N − 2931.50 cos 30 ° = 0 N − 2 , 538.75 = 0 N = 2 , 538.75 N The equilibrium force along y direction. ∑ F y = 0 2931.50 sin 30 ° − V = 0 1 , 465.75 − V = 0 V = 1 , 465.75 N ∑ M o = 0 2931.50 sin 30 ° ( 2 ) + 2 , 931.50 cos 30 ° ( 0.4 ) − M = 0 2931.50 + 1 , 015.50 − M = 0 M = 3 , 947 N ⋅ m Show the I section as in Figure 3. Refer Figure 3: Consider the size of big rectangle as 150 mm × 300 mm . and the size of two small rectangles as 130 mm × 260 mm . The moment of inertia of I - section is the subtraction of moment of inertia of big rectangle of 150 mm × 300 mm . and two small rectangles of 130 mm × 260 mm Determine the cross sectional area ( A ) as follows: A = b 1 d 1 − 2 ( b 2 d 2 ) (1) Here b 1 d 1 area of big rectangle and b 2 d 2 area of small rectangle. Substitute 150 mm for b 1 , 300 mm for d 1 , 65 mm for b 2 , and 260 mm for d 2 in Equation (1). A = 150 × 300 − 2 ( 65 × 260 ) = 45 , 000 − 33 , 800 = 11 , 200 mm 2 ( 1 m 2 10 6 mm 2 ) = 0.0112 m 2 Determine the moment of inertia ( I ) as shown in below: I = b 1 d 1 3 12 − 2 ( b 2 d 2 3 ) 12 (2) Substitute 150 mm for b 1 , 300 mm for d 1 , 65 mm for b 2 , and 260 mm for d 2 in Equation (2). I = 150 × 300 3 12 − 2 ( 65 × 260 ) 12 = 337 , 500 , 000 − 190 , 406 , 666

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 8.2, Problem 8.41P

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The state of stress (σB) at point B for boom.

The shear stress (τB) at point B for boom.

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Chapter 8.2, Problem 8.40P

Chapter 8.2, Problem 8.42P

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The state of stress ( σ B ) at point B for boom. The shear stress ( τ B ) at point B for boom.

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The state of stress (σB) at point B for boom.

The shear stress (τB) at point B for boom.