Statics and Mechanics of Materials: Practice Problems Set 6

Page 1 of 7 McMaster University Department of Civil Engineering 2P04-Statics and Mechanics of Materials, Fall 2023 Practice Problems Set 6 (one problem will be in the weekly Quiz): Submit on A2L by Friday November 10 rd , 2023, at 11:59 PM ( See last page for grading rubrics ) These are only selected problems. You are invited to solve from your textbook as many problems as you can. Only the first three problems are mandatory. In all the following problems, replace the letters ABC by the last three digits of your student ID (replace any 0 with 1 ). For example, if your ID is XXXXXX 365 then A=3, B=6, and C=5. Therefore, the number ABC= 365 , while A+B+C= 3+6+5 = 14. However, if your ID is XXXXXX 946, then A= 1, B=4, and C=6. Therefore, the number ABC= 146 , while A+B+C=1+4+6=11. N.B: All figures are the credit of Pearson International Problem 1 (MANDATORY) If the average normal stress in each of the 20-mm- diameter bars is not allowed to exceed CBA MPa , determine the maximum force P that can be applied to joint C Problem 2 (MANDATORY) Determine the resultant internal loadings on the cross section through point D. Assume the reactions at the supports A and B are vertical. Problem 3 (MANDATORY)

Page 2 of 7 If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain in wires CE and BD (A and B in m) Problem 4 The wire AB is unstretched when u = 45°. If a load is applied to the bar AC, which causes u to become 47°, determine the normal strain in the wire Problem 5 The lever is attached to the shaft A using a key that has a width d and length of 25 mm. If the shaft is fixed and a vertical force of 200 N is applied perpendicular to the handle, determine the dimension d if the allowable shear stress for the key is tallow = 35 MPa. Problem 6

Page 3 of 7 The beam is supported by two rods AB and CD that have cross-sectional areas of 12 mm2 and 8 mm2, respectively. If d = 1 m, determine the average normal stress in each rod. Problem 7 The supporting wheel on a scaffold is held in place on the leg using a 4-mm-diameter pin. If the wheel is subjected to a normal force of 3 kN, determine the average shear stress in the pin. Assume the pin only supports the vertical 3-kN load Problem 8 The beam supports the distributed load shown. Determine the resultant internal loadings acting on the cross section at point C. Assume the reactions at the supports A and B are vertical Problem 9

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Page 4 of 7 The shaft is supported by a smooth thrust bearing at A and a smooth journal bearing at B. Determine the resultant internal loadings acting on the cross section at C. Problem 10 Determine the shear strain gxy at corners A and B if the plastic distorts as shown by the dashed lines

Page 5 of 7 Problem 11 Determine the average normal strain that occurs along the diagonals AC and DB Problem 12 The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8 kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of the plate defined by the section lines a–a, and the average shear stress in the bolt head along the cylindrical area defined by the section lines b–b Problem 13 Determine the maximum average shear stress in pin A of the truss. A horizontal force of P = 40 kN is applied to joint C. Each pin has a diameter of 25 mm and is subjected to double shear.

Page 6 of 7 Grading Criteria Overall Grade Breakdown To encourage students’ engagement in this course, a 12% bonus is assigned based on ( i ) submitting solved Practice Problems (7.5%) ; ( ii ) participating in In-class Participatory Activities (2.5%) and, ( iii ) submitting a quality Term Project (2.0%) . i. Practice Problems (PP) at 7.5% : There will be 12 PPs, each carrying 0.625% , totaling 7.5% . Because there are many questions in each PP, the Teaching Team will only be correcting a few of them, called Corrected Problem (s) . Nevertheless, students are expected to solve the entirety of each PP. The grade of each PP (0.625) is made-up of 60% for submitting all the questions and 40% for getting the Corrected Problem(s) right. The Teaching Team might discard any incomplete solution meant to just get the 60% for submission. For the Corrected Problem (s) , a meticulous correction and feedback is provided to the students, because this type of questions summarize the major objective of each chapter. See the two examples below: ▪ If a student submitted only 3 out 6 questions and obtained the Corrected Problem (s) right, this student gets (3/6) x 60% = 30% for submission and gets the full 40% for obtaining the Corrected Problem (s) right. Their total points will be 70% and their exact score in this Practice Problem will be 70% (0.625). ▪ If a student submitted all the problems, but only achieved 50% (correctness) in the Corrected Problem (s) , this student will receive the full 60% for submitting the Practice Problem in addition to 50% of the 40% (allocated for the Corrected Problem). The latter = 20% . Thus, their total points will be 60% and their exact score in this Practice Problem will be 60% (0.625). ii. Participatory Activities (PA) at 2.5%: PAs are directly run during the lecture classes. It is expected that we will have 15 or more PAs, out of which the best 10 attempts will be considered. Each of the 10 PAs has 0.25% , totaling to the 2.5% . In each participatory activity, your mark is made up of two components: (a) taking the quiz (1/3 of the PA mark), regardless of the answer, plus (b) the correctness of your answer (2/3 of the PA mark). iii. Quality Term Project (PA) 2.0%: The 2% bonus for the Term Project is assigned to the different Project Teams, also called Companies [the same bonus for all the members of a single Company] based on the outstanding final submission of the Term Project. Meaning : At the end of the session, the Teaching Team will evaluate how the different Companies did well in the Term Project [ based on the criteria well detailed at the last page of the Project Description ]. The Teaching Team will evaluate the performance of different Companies [and rank them from the highest to lowest] not encourage competition in the class at all , [because those marks are just bonus, not part of the core marks of 100%], but to mimic real life scenario where different companies submit Designs to clients to win the offer based on specific criteria. For example, if your Company presented the best performance (based on the overall mark) in the Term Project, then all the members will obtain 2% bonus on the top of the actual mark of their Term Project. Another Company that did bad in the Term Project

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Page 7 of 7 will lose this 2% bonus. Of course, their mark in the 25% contribution of the project is seen independently. N.B: Note that the weekly quizzes are not part of the bonus, but contribute to the core mark of 100% How is (are) the Corrected Problem (s) Graded? In each Practice Problem ( PP ) one or a few problems will be corrected and detailed feedback will be provided to learners via the A2L. The Grading of the Corrected Problems (s) is based on four Performance Bins explained below: Bin Description of Typical Cases Mark (%) (i) Unacceptable • No solution was provided ( 0% ) • A solution not following the submission requirements (Graphical Engineering Papers) ( 0% ) • The solution is totally irrelevant and does not rely on the relevant concepts addressed in class. 0-20% (ii) Marginal • A solution lacking the free-body diagram when the latter is intuitively needed. • A solution was provided but contains major errors such as: incorrect use of angles; incorrect use of trigonometry, use of mass for weight, etc. • The solution lacks clarity 20-60% (iii) Meets Expectations • A correct answer was provided using the Engineering Paper provided on A2L. • The final answer is clearly identified. • The sketch of the problem is either redrawn or reproduced on the answer sheet to clearly show the different dimensions and variables affecting the final answer. 60-80% (iv) Exceeds Expectations All the criteria of (iii) Meets Expectations plus: • All final answers use the proper SI units and prefixes. • All final answers are rounded up correctly to three decimal places. • The overall submission follows engineering requirements is terms of clarity and organization. 80-100%

Practice Problems Set 6

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