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

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

Combined Loading

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…

Videos

Question

Chapter 8.2, Problem 8.41P

To determine

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

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 8.40P

Chapter 8.2, Problem 8.42P

Students have asked these similar questions

Hints: Find the closed loop transfer function and then plot the step response for diFerentvalues of K in MATLAB. Show step response plot for different values of K. Auto Controls Show solutions and provide matlab code NO COPIED ANSWERS OR WILL REPORT!!!!

37. The vertical shaft shown in Figure P12-37 is driven at a speed of 600 rpm with 4.0 hp entering through the bevel gear. Each of the two chain sprockets delivers 2.0 hp to the side to drive mixer blades in a chemical reactor vessel. The bevel gear has a diametral pitch of 5, a pitch diameter of 9.000 in, a face width of 1.31 in, and a pressure angle of 20°. Use SAE 4140 OQT 1000 steel for the shaft. See Chapter 10 for the methods for computing the forces on the bevel gear. Figure P12-37: P37-Bevel gear drive with two chain sprockets Each problem includes the following details: ■Design the complete shaft, including the specification of the overall geometry and the consideration of stress con- centration factors. The analysis would show the minimum acceptable diameter at each point on the shaft to be safe from the standpoint of strength. Homework Problems 12-24, 12-35, and 12-37 from textbook, done in spreadsheet form. Place drawings of the load, shear, and bending moment body diagrams…

35. The double-reduction, helical gear reducer shown in Figure P12-35 transmits 5.0 hp. Shaft 1 is the input, rotating at 1800 rpm and receiving power directly from an electric motor through a flexible coupling. Shaft 2 rotates at 900 rpm. Shaft 3 is the output, rotating at 300 rpm. A chain sprocket is mounted on the output shaft as shown and delivers the power upward. The data for the gears are given in Table 12-5. Each gear has a 1412° normal pressure angle and a 45° helix angle. The combinations of left- and right-hand helixes are arranged so that the axial forces oppose each other on shaft 2 as shown. Use SAE 4140 OQT 1200 for the shafts. Figure P12-35: P35-Double-reduction helical drive Each problem includes the following details: ■Design the complete shaft, including the specification of the overall geometry and the consideration of stress con- centration factors. The analysis would show the minimum acceptable diameter at each point on the shaft to be safe from the standpoint of…

Chapter 8 Solutions

MECHANICS OF MATERIALS-TEXT

Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - The thin-walled cylinder can be supported in one...Ch. 8.1 - If the inner diameter of the tank is 22 in., and...Ch. 8.1 - Prob. 8.5P Ch. 8.1 - 8–6. If the flow of water within the pipe in Prob....Ch. 8.1 - A boiler is constructed of 8-mm-thick steel plates...Ch. 8.1 - 88. The steel water pipe has an inner diameter of...Ch. 8.1 - The steel water pipe has an inner diameter of 12...Ch. 8.1 - The A-36-steel band is 2 in. wide and is secured...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

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

Concept explainers

Videos

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

Want to see the full answer?

Chapter 8 Solutions

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

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