Twinning Engineering Programmes (TEP) & Thammasat English Programme of Engineering (TEPE) Faculty of Engineering, Thammasat University

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1 " Twinning Engineering Programmes (TEP) & Thammasat English Programme of Engineering (TEPE) Faculty of Engineering, Thammasat University Undergraduate Examination 2 nd Semester of 2019 (Mid-term) CE221: Mechanics of Solid Section Date 5 March, 2019 Time : Instructor: Dr Krisada Chaiyasarn Name : ID no. Seat no. Instructions : 1.! The test contains 4 problems, 9 pages (including the data sheets and this page). All necessary formula is given in exam questions. Answer the questions in the given answer sheets only. You can separate the answer sheets from the question sheets, both sides of answer sheets can be used. 2.! Print your name, identification number (ID), and seat number on all of your answer sheets. 3.! Scientific calculator is allowed, only the model allowed by the department can be used. The use of an inappropriate calculator will be considered as misconduct. 4.! No program in any form may be taken into the examination room. Also, calculators with facilities for storing and retrieving text, graphical calculators, personal organizers, dictionaries, thesauruses, computer are not allowed. 5.! Other communicating devices such as mobile phones, pagers, etc. are not permitted in the examination. 6.! Textbooks, short notes and relevant material are not permitted in the test room. 7.! There are marks allocated for working towards final answers, hence write and explain your answers clearly. Before entering the examination room, make sure that you do not to bring any disallowable materials into the examination room, intentionally or unintentionally. If proctors have found them in your occupation, you will be seriously punished by suspending your study for one year and receiving a Fail(F) grade in this subject. " 1"

1. As shown in Figure 1, the beam is pin connected to the rods AB and CD, in which both rod sare made of steel with a failure tensile stress of fail =510MPA.UsingafactorofsafetyF.S.=1.

2 1. As shown in Figure 1, the beam is pin connected to the rods AB and CD, in which both rod sare made of steel with a failure tensile stress of fail =510MPA.UsingafactorofsafetyF.S.=1.75fortension, answer the following questions. (a) Explain the following terms, normal stress, shear stress, average normal stress in axially loaded bar, and average shear stress. (2 marks) (b) Draw a free body diagram of the beam. (1 marks) (c) Determine the smallest diameter that can support the load system as shown in the figure. (4 marks) (d) With the diameter calculated in part C, determine the safety factor if Aluminium 2014-T6 is used instead (3 marks) B D 4 kn 6 kn 5 kn A 2 m 2 m 3 m 3 m Prob Figure 1: For question 1 C 1

3 D B 600 mm 2. From Figure 2, answer the following 45! A questions. 3m C 74normal strain C H Aand P T E Rshear 2 Sstrain TRA BI N using diagrams (2 marks) (a) Explain the terms, 1m (b) From Figure 2(a), force P is applied to the rigid arm ABC, point B displaces vertically downward 4m 2 21 PROBLEMS by 0.2 mm, determine the normal strainprob. developed in wire CD (5 marks) FUNDAMENTAL (c) From Figure 2(b), a square piece of material is deformed into the dashed position, determine the Prob When force P is applied to the rigid arm ABC, F2 4. The triangular plate is deformed shear strain at A F2 1. (3 marks) point B displaces vertically downward through a distance of mm.a Determine the normal strain developed in wire square piece of material is deformed intocd. the dashed position. Determine the shear strain gxy at A A square piece of materialdis deformed into the dashed parallelogram. Determine the average normal strain 200 mm 300 mm 400diagonals mm that occurs along the AC and BD. *2 24. A Asquare piece of material is deformed into the dashed position. Determine thebshear strain gxy at C. C shown by the dashed line. Determine th developed along edge BC and the averag AThe into the corner withmaterial respect todistorts the x and y axes. shown. Determine (a) the average norm sides AC and CD and the shear strain gxy average normal strain along line BE The material distorts into the y shown. Determine the average normal s along the diagonals AD and CF. A P B (a) F2 1 y y F2 2. If the applied force P causes the rigid arm ABC to rotate clockwise about pin A through an angle of 0.02, mm determine the normal strain developed in wires BD and CE. B mm 15 mm 300 mm 25 mm D C 10 mm B C E C E mm 15 mm 89.7! D 15 mm 400 mm mm A 7 90 mm F mm x D P A Probs. 2 26/27 Probs.(b) 2 22/23/24 A B Figure 2: For question mm F 80 mm C 600 mm F2 2 F2 5. The square plate is deformed into by the dashed line. Determine the avera along diagonal AC and the shear strain respect to the x and y axes. F2 3. The rectangular plate is deformed into the shape of a rhombus shown by the dashed line. Determine the average shear strain at corner A with respect to the x and y axes. y y 2 mm D 300 mm 400 mm A D C 300 mm F2 3 2 B x 4 mm C E A 300 mm 3 mm B 3 mm F2 5

4 3. The square hollow bar with the dimension shown in Figure 3 is subjected to the axial force P. The bar is made of a metal alloy with a stress-strain diagram as shown in the figure, answer the following questions (a) Explain, using the tension stress-strain diagram of a steel specimen, the meaning of plastic limits, yield stress, fracture stress, modulus of resilence and modulus of rupture. Also, explain the Poisson ratio and shear modulus, the relationship between the Young Modulus and shear modulus. (4 marks) (b) Find the elongation of the bar when P = 200 kn (2 marks) (c) Find the permanent elongation of the bar when the axial force P = 400 kn is applied and then released. (2 marks) (d) If the Poisson ratio of the bar is 0.3, find the contraction and the shear modulus of the bar. (2 marks) s (MPa) P 600 mm 50 mm mm P (mm/mm) P 50 mm 5 mm Figure 3: For question 3 3

(a) Explain statically indeterminate structures.

5 4. The rigid bar is supported by a pin at A and two steel wires, each with a diameter of 4 mm. If the yield stress for the wires is Y =530MPa,andE st =200GPa,assumingthatthesteeliselasticperfectly plastic, answer the following questions. (a) Explain statically indeterminate structures. (2 marks) (b) Draw an FBD of the rigid beam, write the equilibrium and compatibility equations in order to find the force developed in each wire. (3 marks) (c) Find the maximum w that can be placed on the beam that will just cause wire CD to yield and the displacement G for this case (5 marks) E D 800 mm A B C G 400 mm 250 mm 150 mm w Figure 4: For question 4 4

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[5] Stress and Strain

[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law