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Read and Analyze the sample problems given. Give a thorough analysis stating what type of situation the author dealt with, how the problem was solved, the assumptions that the author considered in solving the problem, and why where these assumptions were made.   5 sentences are more than enough in this for me to learn.

Read and Analyze the sample problems given. Give a thorough analysis stating what type of situation the author dealt with, how the problem was solved, the assumptions that the author considered in solving the problem, and why where these assumptions were made.   5 sentences are more than enough in this for me to learn.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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7.6

Read and Analyze the sample problems given. Give a thorough analysis stating what type of situation the author dealt with, how the problem was solved, the assumptions that the author considered in solving the problem, and why where these assumptions were made.

 

5 sentences are more than enough in this for me to learn. Thank you!

note: This is not a graded question, this is only to know the explanation; to know its concept. 

Sample Problem 7.6 The uniform 100-lb plank in Fig. (a) is resting on friction surfaccs at A and B. The coefficients of static friction are shown in the figure. If a 200-lb man starts walking from A toward B, determine the distance x when the plank will start to slide. -A=0.5 A- 0.2 A 10ft 40° (a) 353 Solution This is a Type II problem. When the plank is on the verge of moving, sliding must impend at both A and B. Impending sliding at A only, or at B only, would be physically impossible. Because the plank is a rigid body, any movement of end A must be accompanied by a movement of end B. The FBD of the plank is shown in Fig. (b). Observe that the friction forces are shown acting in their correct directions. When the plank is ready to move, the direction of impending sliding of end B is down the inclined plane. Con- sequently, end A would tend to slide to the left. The directions of FA and Fs must oppose these motions. Showing either of the friction forces in the opposite direction would lead to incorrect results. 200 lb B. 5 ft Inspection of the FBD in Fig. (b) reveals that there are five unknowns: NA. FA 50 N, FA, NB, FB, and x. There are also five equations: three equilibrium equations and N, 100 Ib two friction equations. Therefore, all the unknowns can be computed from the FBD as follows. (b) EMA =0 3 Ng sin 50° (10) + Fs sin 40°(10) -200x – 100(5) = 0 (a) EF, =0 + FA - Ng cos 50° + Fa cos 40° = 0 (b) EF, = 0 1 NA – 200 – 100 + Ng sin 50° + Fg sin 40° = 0 (c) Substituting the friction equations, FA = 0.2NA and Fg = 0.5Ng, and solving Eqs. (a)-(c) give NA = 163.3 lb, N- 125.7 lb, and x = 4.34 ft Answer Sample Problem 7.7 The spool in Fig. (a) weighs 25 N, and its center of gravity is located at the geo- metric center. The weight of block C is 50 N. The coefficients of static friction at the two points of contact are as shown. Determine the largest horizontal force P that can be applied without disturbing the equilibrium of the system. A Dimensions H.0.3- in mm H =0.4 B (a)
Transcribed Image Text:Sample Problem 7.6 The uniform 100-lb plank in Fig. (a) is resting on friction surfaccs at A and B. The coefficients of static friction are shown in the figure. If a 200-lb man starts walking from A toward B, determine the distance x when the plank will start to slide. -A=0.5 A- 0.2 A 10ft 40° (a) 353 Solution This is a Type II problem. When the plank is on the verge of moving, sliding must impend at both A and B. Impending sliding at A only, or at B only, would be physically impossible. Because the plank is a rigid body, any movement of end A must be accompanied by a movement of end B. The FBD of the plank is shown in Fig. (b). Observe that the friction forces are shown acting in their correct directions. When the plank is ready to move, the direction of impending sliding of end B is down the inclined plane. Con- sequently, end A would tend to slide to the left. The directions of FA and Fs must oppose these motions. Showing either of the friction forces in the opposite direction would lead to incorrect results. 200 lb B. 5 ft Inspection of the FBD in Fig. (b) reveals that there are five unknowns: NA. FA 50 N, FA, NB, FB, and x. There are also five equations: three equilibrium equations and N, 100 Ib two friction equations. Therefore, all the unknowns can be computed from the FBD as follows. (b) EMA =0 3 Ng sin 50° (10) + Fs sin 40°(10) -200x – 100(5) = 0 (a) EF, =0 + FA - Ng cos 50° + Fa cos 40° = 0 (b) EF, = 0 1 NA – 200 – 100 + Ng sin 50° + Fg sin 40° = 0 (c) Substituting the friction equations, FA = 0.2NA and Fg = 0.5Ng, and solving Eqs. (a)-(c) give NA = 163.3 lb, N- 125.7 lb, and x = 4.34 ft Answer Sample Problem 7.7 The spool in Fig. (a) weighs 25 N, and its center of gravity is located at the geo- metric center. The weight of block C is 50 N. The coefficients of static friction at the two points of contact are as shown. Determine the largest horizontal force P that can be applied without disturbing the equilibrium of the system. A Dimensions H.0.3- in mm H =0.4 B (a)
Solution The key to the analysis of this problem is understanding that there are two possi- bilities for impending motion (both could occur simultaneously): (1) impending sliding at A with impending rolling (without sliding) at B, and (2) impending sliding at B with impending rolling (without sliding) at A. Because it is initially not known which of these possibilities represents the actual mode of impending motion, this is a Type III problem. The free-body diagrams for the block and the spool are shown in Fig. (b). 50 N| Observe that both friction forces have been shown in their correct directions. The Ne force P tends to slide points A and B on the spool to the right. Therefore, both friction forces are shown acting to the left on the FBD of the spool. Inspecting the FBDS in Fig. (b), we conclude from EF, = 0 that NA = 50 N and Ng = 75 N. At this stage three unknowns remain in the FBD of the spool: FA, FB, and P. Because only two equilibrium equations are left (E F, = 0 has already been used), the remainder of the solution depends on the assumption regarding impending motion. NA Assume Impending Sliding at A FA A This assumption gives us the additional equation FA = 0.3NA = 0.3(50) = 15 N. The FBD of the spool then yields 80 EMB = 0 3 FA(240) – P(40) = 0 120 25 N which gives B P = 6FA = 6(15) = 90.0 N Fg Assume Impending Sliding at B This assumption gives Fg =0.4Ng =0.4(75) = 30 N. From the FBD of the spool, (b) we now obtain EMA = 0 3 - FB(240) + P(200) = 0 which gives P = 1.2FB = 1.2(30) = 36.0 N Choose the Correct Answer Up to this point, the analysis has determined that sliding impends at A if P=90.0 N and at B if P= 36.0 N. Consequently, the largest force P that can be applied without disturbing the static equilibrium of the spool is P = 36.0 N Answer with sliding impending at B. An alternate method for solving this problem is to assume impending sliding at one surface and then to compare the friction force at the other surface with its limiting static value. 355
Transcribed Image Text:Solution The key to the analysis of this problem is understanding that there are two possi- bilities for impending motion (both could occur simultaneously): (1) impending sliding at A with impending rolling (without sliding) at B, and (2) impending sliding at B with impending rolling (without sliding) at A. Because it is initially not known which of these possibilities represents the actual mode of impending motion, this is a Type III problem. The free-body diagrams for the block and the spool are shown in Fig. (b). 50 N| Observe that both friction forces have been shown in their correct directions. The Ne force P tends to slide points A and B on the spool to the right. Therefore, both friction forces are shown acting to the left on the FBD of the spool. Inspecting the FBDS in Fig. (b), we conclude from EF, = 0 that NA = 50 N and Ng = 75 N. At this stage three unknowns remain in the FBD of the spool: FA, FB, and P. Because only two equilibrium equations are left (E F, = 0 has already been used), the remainder of the solution depends on the assumption regarding impending motion. NA Assume Impending Sliding at A FA A This assumption gives us the additional equation FA = 0.3NA = 0.3(50) = 15 N. The FBD of the spool then yields 80 EMB = 0 3 FA(240) – P(40) = 0 120 25 N which gives B P = 6FA = 6(15) = 90.0 N Fg Assume Impending Sliding at B This assumption gives Fg =0.4Ng =0.4(75) = 30 N. From the FBD of the spool, (b) we now obtain EMA = 0 3 - FB(240) + P(200) = 0 which gives P = 1.2FB = 1.2(30) = 36.0 N Choose the Correct Answer Up to this point, the analysis has determined that sliding impends at A if P=90.0 N and at B if P= 36.0 N. Consequently, the largest force P that can be applied without disturbing the static equilibrium of the spool is P = 36.0 N Answer with sliding impending at B. An alternate method for solving this problem is to assume impending sliding at one surface and then to compare the friction force at the other surface with its limiting static value. 355
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